Saturday, October 02, 2021

Spherical Coordinates and Trinitarian Relations

To help people get a conceptual understanding of how Trinitarian relations work, I thought it might be helpful to borrow a concept from mathematics. In the Trinity, one can think of the Trinitarian relations or the relations of origin as three interrelated modes of existence working together to specify how the Trinity exists. There's an analogy to how three coordinates can work together to specify a location, and the most direct analogy is to how spherical coordinates work.

In the spherical coordinate system, there are three variables that define the location of a point P in space relative to an origin. Those variables are as follows:

  • rho, the radius, specifies the absolute distance of the point from the origin
  • theta, the polar rotation, specifies the direction of the radius within a two-dimensional plane
  • phi, the azimuth, specifies the angle of the radius above or below the plane
This is an illustration of the spherical coordinate system for a point P.


The radius is "special" in this system because it defines the absolute magnitude of the distance from the origin all on its own. It doesn't need the other two coordinates to specify that quantity in any way. We can think of that as the Father being unbegotten; the Father doesn't depend on either the Son or the Spirit to further define His mode of possession of the divine essence.

We can then think of the polar rotation as defining its own plane. It depends on the radius to define a circle, but given that circle, it further specifies the location on that circle. This is similar to the way that the Son further defines the Trinitarian existence, but that mode depends on the Father to do so.

We can then think of the azimuth as further specifying the location by elevation relative to the plane defined by the polar rotation. The reason that we might intuitively think of the azimuth as "further specifying" the location is that its range is only from 0 to 180 degrees, while the complete range of angles is from 0 to 360 degrees (as with the polar rotation). There is no reason in principle that the polar rotation could not be defined with respect to the azimuth, but the restricted range of the azimuth emerges naturally if we start with the polar rotation, as contrasted with just assuming it. For that reason, it is intuitive to say that, just as the polar rotation further specifies the position vis-a-vis the radius, the azimuth further specifies the position vis-a-vis the polar rotation. And we can analogize that to how the Holy Spirit further specifies the Trinitarian existence with respect to the Son.

In summary, spherical coordinates are like the Trinitarian relations as follows. First, the radius has a property of defining the absolute magnitude of the distance without reference to either of the other two coordinates, in the same way that the Father is the one source of the Trinity without respect to either of the other Persons. Second, the azimuth in some sense depends on the polar rotation, in that its range is limited based on the polar rotation. But the azimuth still depends directly on the radius to define the absolute magnitude of the distance in exactly the same way that the polar rotation does. This is similar to the way that the relation that defines the Holy Spirit in some way depends on the Son but not in a way that modifies the Holy Spirit's relation to the Father.

Wednesday, September 29, 2021

Historical Use of Reflexive Relations in the Trinity

The most clear Scriptural example of a reflexive relation is the image. I will now outline how that reflexive relation was used historically in Trinitarian theology and how reflexive relations were used more broadly in those discussions. 

St. John Damascene appears to have been the first commentator to explicitly note the reflexive relation between the Holy Spirit and the Son in calling the Son the Image of the Father and the Holy Spirit the Image of the Son. Since iconoclasm prompted the full-blown theological defense of images, it should not be surprising that this connection was only made in the context of making that defense. Based on that theology of the image, an image is first and foremost personal, which is why veneration and worship of the one transfers to its prototype. In the case of the Trinity, we find a natural image, a true image, that not only represents the person but is itself a person with an identical nature, as with a child being the spitting image of his father. We should not understimate the significance of the step that the Doctor of Icons has taken here: namely, that the Image is not restricted to begetting. Instead, it applies also to the other natural image of the Father and the Son, the proceeding Holy Spirit.

First, we will look at how the imaging relationship was used in the context of the Son in the Arian debates. Because Scripture only calls the Son the image of the Father, it is not surprising that it was first applied here.

Western Anti-Arian Commentary

In the West particularly, there was a tradition exemplified by Novatian's response to the modalists that focused on the Son's role in making God visible, as the visible image of the invisible Father. There is certainly an orthodox interpretation of that belief, since this is exactly what happen in the economy of salvation.  But at the level of the Trinity, this concept in tension with the idea of the Son being identical in nature with the Father. So it is necessary to distinguish the "image" in terms of making the Father visible in the economy, which is not necessarily a reflexive relation, from the true Image of the trinity, which is.

The Homoian Arians in the West appealed to this Latin tradition to argue that the Son must be of another nature from the Father, since He makes visible what is by nature invisible. Michel René Barnes outlines this theological "double-bind" in his article "The Visible Christ and the Invisible Trinity," describing how St. Augustine responded to this challenge. Based on what Barnes outlines here, Augustine does not seem to have used imaging as a reflexive relation in this specific context, so as to redefine the "image" relation in its immanent sense. But in passing (n. 70), Barnes comments on the reflexive relation that Augustine does use: the "psychological analogy." In describing Augustine's epistemology of faith, Barnes observes that Augustine explicitly disclaims that the psychological analogy gives us mental concepts for what the Trinity is and refuses even to call it an analogy. I agree with Barnes's assessment. As I have mentioned previously, the relevance of the "psychological analogy" is that it provides us a logical structure (specifically, reflexive relations) for thinking about the "who" of the Trinity and the relations of origin of the Persons, but that should not be confused with real insight into the "what" or "how," which remain impenetrably mysterious.

As Barnes documents in the article, St. Hilary of Poitiers also responded to this Homoian challenge, and his response is much more on point with regard to the imaging relation. Hilary's response is analyzed in greater detail by Mark Weedman in The Trinitarian Theology of Hilary of Poitiers. On p. 99, Weedman cites the image as a "key theme" in Hilary's response to the blasphemy of Sirmium (based on the list in De Synodis 27). Sirmium condemned those who said that "the image of God is God," a position they deem modalist. Hilary responds, in a way that is particularly important for our understanding of reflexive relations, with the statement that "no one can be his own image." Thus, saying that "the image of God is God" necessarily means that the Son and the Father are personally distinct from one another. But because the Son is a true image, He must also reproduce the "image, species and nature" of the prototype. Importantly, this is connected to the begetting of the Son, since a son is in the image of his father. Hilary explicitly makes the connection with, e.g., the begetting of Seth by Adam in Genesis 5:3 (pp. 111-12).

Interestingly, Weedman notes (at p. 100) that the argument might come from one deployed by the Homoiousian Basil of Ancyra against his and Hilary's common Homoian enemy, a conclusion that is suggested by Jeffrey Steenson in his 1983 dissertation "Basil of Ancyra and the Course of Nicene Orthodoxy." But according to Weedman, that link isn't clear, since the anti-Arian Marius Victorinus deployed the same argument with no clear connection to Basil's work, meaning that it could have come from a broader Latin tradition. Regardless of whether it came from Basil, Weedman notes a key distinction between the argument made by Basil and the one made by the anti-Arians. Basil cannot conceive of distinct spiritual substances having the same nature, so that the Father and the Son can only be "like" in nature. As Weedman observes at p. 64, Victorinus completely rejects that argument, maintaining that the simple nature of the divine essence precludes any likeness short of identity, a position that will also be taken by St. Gregory Nazianzen. Hilary (p. 104) neatly sidesteps the objection by distinguishing the essence possessed by the individuals from the substance in the individuals. In both instances, the image argument has been firmly claimed by the homoousian camp.

This establishes the use of "image" in Latin theology as (1) a distinction between Persons that (2) perfectly reproduces the essence between image and prototype. It is explicitly tied to the begetting of the Son from the Father, meaning that it is a "natural image" in the sense that we will also used in the East. And it is consciously used to deny that the Son has somehow made the divine visible by a different nature, as opposed to being in the image of the Father's invisible nature. In other words, it clearly distinguishes the natural image at the immanent level from the function the Son performs at the economic level.

Eastern Anti-Arian Commentary

In the article cited previously, Barnes notes that Origen first describes the Son as the "invisible" Image of the Father, employing the reflexive relation we have been discussing so far. In his book The Power of God, Barnes notes at p. 163, n. 113, that Origen cites John 5:19 to show that, because the Son does what the Father does, He is of the same substance and, therefore, a perfect Image of the Father. Weedman concurs with Barnes's overall conclusion at p. 147, noting that Origen distinguishes two kinds of image: (1) the kind painted or carved in stone, and (2) the child in the image of his parent. Origen puts the Son in the latter category, preserving the unity of nature. As Hilary does, Origen connects the concept of "image" to the begetting of the Son. Weedman observes at pp. 147-48 that St. Athanasius takes a "very similar" position when he says that a parent's offspring is "not as external or as foreign, but as from himself, and proper to his essence and his exact image" (Contra Arianos 1.26).

We have seen the same line in the Cappadocians as traced by Barnes in The Power of God. Later Arian opponents of orthodoxy, such as Eusebius of Caesarea (pp. 132-34), Asterius the Sophist (pp. 138-39), and especially Eunomius (p. 201 nn. 124-25, pp. 205-6) characteristically reject this idea that the Son is the perfect Image of the Father, so as to have the same nature. Barnes notes again that St. Gregory the Theologian replies by using the Image to show identity of nature in the Fifth Theological Oration (pp. 217-18). As I have noted previously, this is based on the divine simplicity allowing only identity as opposed to any sort of likeness, which is the same argument offered independently by Marius Victorinus against the homoiousian interpretation of the Image.

So we have once again seen the same reflexive relation, the Image as the true image and the natural image of the Father, used in the identical context. The Arians argued that the image was "like" rather than "identical," and the pro-Nicene response was that the natural image has the same essence as the prototype. This was further reinforced against the homoiousian position by noting that simple essences did not admit of degrees of likeness but only identity, so that the image of God is Himself God. This should suffice to demonstrate that both East and West agreed on the immanent use of the imaging relationship.

Applications to the Holy Spirit

We still do not have a clear antecedent for John Damascene's "image of the Son" language, but we do have a clear view of the logical structure of images in the pro-Nicene interpretation of the Scripture. A true image replicates the prototype in nature, and in the case of the divine Persons, this means that the image is Himself God. The fact that it was not explicitly applied to the Holy Spirit does not mean that it could not, only that there would have been no reason to do so at the time. It was only when the theology of images was a critical theological matter that taking the additional step of showing its foundation in the Trinity was useful.

But do we really think that the Doctor of Icons was innovating here? Or that he did not know how "image" was used by the theologians of the East? It seems too much to believe that he would seize on this concept dating all the way back to Origen and deployed by two of the greatest theologians of the Trinity, St. Athanasius and St. Gregory Nazianzen, only to take it completely out of context for the benefit of a current dispute. Is it not rather more likely that John Damascene was reproducing the argument exactly as it was, merely completing its logical extension in summary fashion?

The fact that John Damascene appends "differing only in His procession" to the statement that "[t]he Holy Spirit is the perfect and unchangeable image of the Son" seems to preclude this possibility. One cannot avoid the conclusion that he has the immanent procession in view, which makes it difficult to believe that he was unaware of the fact that the natural image was used of "simple existences" by Gregory the Theologian. It is far more likely that he was using the argument exactly as originally intended and (correctly) applying it to the personal origin of the Spirit to show how fundamental the concept of "image" is to Christian theology.

Since the paradigmatic reflexive relation, the image, provides no precedent, the question is whether we can find other relations with the same logical structure. We have seen that Augustine's psychological analogy is one such model for ad intra reflection: God thinking on Himself, which begets the Word, then loving Himself as Father and Son, from which proceeds the Spirit. This is the basis of the identification of the Holy Spirit as Love/Bond (or Gift) in the writings of numerous theologians.

Is there such a model for the Holy Spirit in the East? Again, the answer is affirmative. The most ancient such reference was St. Dionysius of Rome, as cited by Athanasius in his work On the Decrees of the Council of Nicea. Dionysius says that "[i]t is necessary that the divine Word be united to the God of the universe; and it is necessary that the Holy Spirit live to have his dwelling in God and to reside in him. It is absolutely necessary that the Holy Trinity be recapitulated and guided back to unity, as to a summit, that is to the all powerful God of the universe." That likely continued to be reflected in the Latin tradition, and we can look to see whether these ideas also gained traction in the East. 

The most sophisticated work on the Holy Spirit from the Cappadocian Fathers was On Not Three Gods (Ad Ablabium) by St. Gregory of Nyssa. This work was analyzed in detail by Fr. Giulio Maspero in his book Trinity and Man, and there are two reasons presented in that work that commend this as an exemplary work. First (p. xxi), the tone and language of the work appears to be from a later period of Gregory's life that is no longer driven by clashes with the heresies that drove much of his earlier writing, which makes it much more didactic and expository. Given that the clash with Eunomius turned on demonstrating that the personal distinctions did not imply differences of nature, there was much more emphasis in showing the consubstantiality of nature by the principle of "what is not individual is common in God." Showing the relational unity of the Persons, as opposed to their consubstantiality, simply was not at the same level of priority, although there are some relevant passages even in the Contra Eunomium. Second (p. 178), Gregory has apparently developed beyond the relatively limited pneumatology of St. Basil the Great, which reflected an Origenist understanding of spirit that did not allow for full recognition of the Spirit's role in creation (effectively limiting it to the mental realm).

If we take this work as a refinement of Cappadocian pneumatology, then we can turn to the passage of AdAbl that might be the most important passage in the entire filioque controversy (quoted at p. 153):

If then one will falsely accuse the reasoning to present a certain mixture of the hypostases and a twisting by the fact of not accepting the difference according to nature, we will respond to this accusation that, affirming the absence of diversity of nature, we do not negate the difference according to causes and that which is caused. And we can conceive that the one is distinguished from the other uniquely since we believe that the one is that which causes and the other that which is derived from the cause. And in that which is originated from a cause we conceive yet another difference: one thing it is, in fact, to be immediately from the first, another to be through that which is immediately from the first. In this way the being Only-Begotten remains incontestably in the Son and there is no doubt that the Spirit is from the Father, since the mediation of the Son maintains in Him the being of Only-Begotten and does not exclude the Spirit from the natural relation with the Father.

As Maspero points out, "[t]his passage has an enormous importance in the history of theology and dogma; there are no publications on the question of the Filioque, or on the development of Trinitarian doctrine in patristic period, that do not cite it." I would also argue that Gregory's statement that "the mediation of the Son maintains in Him the being of Only-Begotten and does not exclude the Spirit from the natural relation with the Father" exactly describes a reflexive relation, which likewise does not separate the Image of the Image from the Prototype but fully reproduces the Prototype. It is therefore entirely compatible with St. John Damascene's statement that the Holy Spirit is "[t]he Holy Spirit is the perfect and unchangeable image of the Son" but "differing only in His procession." This passage is always one that must be "explained away" by the opponents of the filioque, but based on a survey of similar related passages, it can very easily be interpreted as a reflexive relation.

For example, even in the Contra Eunomium (p. 177), Gregory deploys a reflexive relation describing the Holy Spirit's personal mode of existence as the "mode of unity" [holos einai], thus reflecting back onto the Father and the Son:

And the Holy Spirit, who in the uncreated nature is in communion [koinonia] with the Father and the Son, is nevertheless distinguished in his turn by his proper characteristics. To not be that which is contemplated properly in the Father and the Son is his most proper characteristics and sign: his distinctive property in relation to the preceding does not consist in being in an [unbegotten] mode, nor in an only [begotten] mode, but to be in the mode of constituting a whole [einai de holos]. He is conjoined to the Father by the fact of being uncreated, but is distinguished in his turn by the fact of not being Father as he is. United to the Son by the uncreated nature and by the fact of receiving the cause of existence from the God of the universe, he is distinct from him in his turn by the peculiarity of not subsisting hypostatically as the Only Begotten of the Father and by the fact of being manifested by the Son himself. But further, since creation subsists by means of the Only Begotten, so that one does not think that the Spirit has something in common with it due to the fact that he is manifested by the Son, he is distinguished from creation since he is invariable, immutable and without need of any eternal good.

It is important to note this passage is speaking of the mode of hypostatic existence, meaning that it is unquestionably referring to the immanent Trinity even though it speaks about manifestation. There is a tendency to retroject the concept of eternal energetic procession into every mention of manifestation, but that is clearly not the case here.

In a passage that links the economy to the eternal unity of the Trinity, Gregory also uses the reflexive relation of "bond" in his homily on the Song of Songs (p. 181):

It is better to textually cite the divine words of the Gospel: "So that all be one. As You Father, are in Me and I in You, that they be also one in Us" [Jn. 17:21]. And the bond [syndetikon] of this unity is glory. But no prudent person could oppose the fact that the Spirit is called "glory", if the words of the Lord are considered. for he says: "The glory that You gave Me I gave to them" [Jn. 17:22]. He gave, in fact, that glory to the disciples saying to them "Receive the Holy Spirit" [Jn. 20:22].

Maspero outlines on p. 182 that this corresponds to the Latin understanding of the Spirit as Bond of Love (nexus amoris) of the Trinity, which we have already seen as a reflexive relation. Maspero refers to this concept, a reflexive relation, as "the summit of Gregory's pneumatology" (p. 184-85), noting the use of holos einai, syndetikon, and koinonia (itself a traditional greeting in the ancient Church) as specific characteristics of the Holy Spirit.

I agree with Maspero that this is the key interpretive concept for Gregory's notion of Trinitarian relations, especially his use of "through the Son." Viewed through that lens, the reflexive structure is visible in the concept of the relation of the Holy Spirit to the Father and the Son throughout his writings. Gregory's characteristic formulation of this structure is from-through-in [ek-dia-en], as concluded by Maspero at pp. 194-95. One can immediately see the reflexive nature of this structure with the Image-of-the-Image formulation: through (by mediation of) the Image, the Image-of-the-Image reflects back onto (resides in) the Image, in the same way that the Image resides in the Prototype. The en corresponds to the reflexivity of the relation in the manner in which an image points back to the prototype. (Because the Spirit is the terminus in this way, sometimes Gregory uses pros (to) instead of en, but the meaning is the same.)

In terms of that structure, Gregory provides a more detailed exposition of the from relationships with his concept of "relational succession." From his third homily on the Lord's Prayer (p. 158):

And since it is common to the Son and to the Spirit to not be without generation, so that a certain confusion not be maintained regarding the subject, it is necessary to find another distinction that does not generate confusion in their properties, so that that which is common be kept safe, and that which is proper not be confused. For the Sacred Scripture says that the Only Begotten Son [comes] from the Father and the affirmation defines the property. But it is also said that the Holy Spirit is from the Father, as it is also attested that he is from the Son [kai tou huiou einai prosmartureitai]. It says, in fact, "If anyone has not the Spirit of Christ, he does not belong to him." Therefore, the Spirit who is from God is also the Spirit of Christ. Instead the Son, who is from God, is not from the Spirit and is not said to be from the Spirit. And one cannot invert this relational succession [schetike akolouthia] so as to be able to indifferently invert with analysis the affirmation, and, as we say that the Spirit is of Christ, thus call Christ [as if he were] of the Spirit. Since, then, this property distinguishes clearly and without confusion the one from the other, while the identity in activity witnesses to the commonness of nature, the orthodox conception of the Divinity is reinforced from both affirmation, so that the Trinity is enumerated in the Persons and it is not disjointed into parts of different nature.

As Maspero points out on pp. 159-60, some manuscripts include ek in the passage translated as "also from the Son" here, so that it is explicitly a "double from" formulation in the manner of the filioque. For our purposes, though, it doesn't matter exactly what preposition Gregory uses here. The point is that the relations are successive from Father to Son to Holy Spirit, which defines an order that is never inverted. What ever the defining relation of the Spirit to the Father is, it is mediated by the Son, and in Gregory's view, this is indicated by the phrase "the Spirit of the Son." Whatever the phrase "of is not from" may come to mean in later theology, it is clear that Gregory does not take it to exclude the Son from the relational succession. 

I can now take a moment to point out how this idea of reflexive relations obviates some of the most fervent discussions on the meaning of the filioque. For example, Gregory makes an outright rejection of the spirituque approach to resolving the filioque (cf. Maspero at p. 159, n. 39), although that formulation is not technically or logically incorrect if it is articulated properly. But what I take from Gregory here is the same point I am trying to make in this series: if the Trinitarian relations are conceived as reflexive, there's no need for the spirituque to somehow "balance" the filioque. In addition, the focus on the relations as reflexive as contrasted with personalist clears away the idea of "social Trinitarianism." In that respect, I agree with Lucian Turcescu that this personalist idea never came from the Cappadocians in the first place (calling it a "modern misreading" in his article for Sarah Coakley's Re-Thinking Gregory of Nyssa). By contrast, Turcescu's conclusion in his book Gregory of Nyssa and the Concept of Divine Persons, which emphasizes both relationality and communion in the Trinity, is perfectly compatible with everything that I have said about reflexive relations. (I note that reflexive relations bypass Turcescu's criticism on p. 68 that the filioque requires that the Father and the Son combine into a single principle, since it provides an alternative explanation of how the Son as Image can simultaneously be one principle with the Father.)

That suffices, I think, to make the point that Gregory of Nyssa's view of the Trinitarian relations can be well explained in terms of reflexive relations and the Image-of-the-Image concept. The only supplement I would add to this lengthy discourse is that Gregory frequently uses the analogies that permit "looking back" to the origin through some intermediate stage (such as Speaker-Word-Breath or root-branch-fruit), which are particularly compatible with reflexive relations. Particularly, there is a traceable progression of one and the same nature from the origin through the mediator to the destination, where the destination in some sense completes the picture. This is further evidence that the reflexive structure of the relations is an integral part of Gregory's thinking.

Returning to John Damascene    

The excursus through Gregory of Nyssa's work cannot help but illuminate John Damascene's thought as well. If the reflexive relation is as predominant in Gregory's work as has been demonstrated before, then this would explain why John, who relied on Gregory as a source of Trinitarian dogma, would have picked up the theme. That would in turn explain why John could almost causally introduce the Image-of-the-Image formulation, bereft of any justification or citation from Scripture.

Remarkably, it appears that St. Thomas Aquinas actually recognized the similarity of this structure to the West's own reflexive relation: the psychological analogy. In ST I, q. 35, a. 2, he says the following:

I answer that, The Greek Doctors commonly say that the Holy Ghost is the Image of both the Father and of the Son; but the Latin Doctors attribute the name Image to the Son alone. For it is not found in the canonical Scripture except as applied to the Son; as in the words, "Who is the Image of the invisible God, the firstborn of creatures" (Colossians 1:15) and again: "Who being the brightness of His glory, and the figure of His substance." (Hebrews 1:3).

Some explain this by the fact that the Son agrees with the Father, not in nature only, but also in the notion of principle: whereas the Holy Ghost agrees neither with the Son, nor with the Father in any notion. This, however, does not seem to suffice. Because as it is not by reason of the relations that we consider either equality or inequality in God, as Augustine says (De Trin. v, 6), so neither (by reason thereof do we consider) that similitude which is essential to image. Hence others say that the Holy Ghost cannot be called the Image of the Son, because there cannot be an image of an image; nor of the Father, because again the image must be immediately related to that which it is the image; and the Holy Ghost is related to the Father through the Son; nor again is He the Image of the Father and the Son, because then there would be one image of two; which is impossible. Hence it follows that the Holy Ghost is in no way an Image. But this is no proof: for the Father and the Son are one principle of the Holy Ghost, as we shall explain further on (I:36:4). Hence there is nothing to prevent there being one Image of the Father and of the Son, inasmuch as they are one; since even man is one image of the whole Trinity.

Therefore we must explain the matter otherwise by saying that, as the Holy Ghost, although by His procession He receives the nature of the Father, as the Son also receives it, nevertheless is not said to be "born"; so, although He receives the likeness of the Father, He is not called the Image; because the Son proceeds as word, and it is essential to word to be like species with that whence it proceeds; whereas this does not essentially belong to love, although it may belong to that love which is the Holy Ghost, inasmuch as He is the divine love.

It is tragic that Thomas has uncovered the method to resolve the filioque by reflexive relations in a single passage, yet the full significance of the passage remained unrealized. In analyzing John's Image-of-the-Image, Thomas sees that it matches exactly what the West means by the Father and Son being "one principle" and that is harmonizes with the West's own paradigmatic reflexive relation that places the Holy Spirit as the love of the Father and the Son for one another. As per Thomas Ryba's observation that Augustine recognized the concept of reflexive relations without being able to articulate the term, Thomas has likewise outlined the logic of the reflexive relation perfectly, only without being able to name it or to put a single concept around it. 

Thomas also significantly misses on how John is using the term "image." Thomas says that John "and the other Greek Doctors commonly employ the term image as meaning a perfect similitude." In fact, they use it in the Trinitarian context to show identity of nature, not any degree of similitude, and Thomas has missed that even Hilary and Victorinus do the same. Had he made that connection, he could have connected what the Latin theologians said in the West with what the "Greek Doctors" were saying in the East. As it was, the opportunity was lost.

What makes this near miss even more agonizing is that, if the reflexive relation is recognized, it is ubiquitous in John Damascene, which is apparent from the Exact Exposition of the Orthodox Faith [OF]. (I have found relevant citations from an ecumenical online article by Michael Torres, although I differ from his conclusions.) John's replication of Gregory's ek-dia-en reflexive relation is impeccable. "And we speak also of the Spirit of the Son, not as through proceeding from Him, but as proceeding through Him from the Father. For the Father alone is cause." [OF I, 12] "God is also Holy Spirit, being sanctifying power, subsistential, proceeding from the Father without separation, and resting in the Son, identical in essence with Father and Son." [OF I, 13] "The Son is the Father's image, and the Spirit the Son's, through which Christ dwelling in man makes him after his own image. The Holy Spirit is God, being between [median of, meson] the unbegotten and the begotten, and united to the Father through the Son." [OF I, 13]

John's use of motion language for the Holy Spirit reinforces this reflexive, circular movement. As is appropriate for the one who proceeds, John calls the Spirit the "impulse" ("For there is no impulse without Spirit" [OF I, 12]). The impulse is critical in the Trinity, as "there is one and the same motion: for there is one impulse and one motion of the three subsistences, which is not to be observed in any created nature" [OF I, 14]. It is the relation of the Holy Spirit in the Trinity that drives the circular motion, that John calls perichoresis and that the Latins will call circumincessio (interpenetration) and circuminsessio (indwelling). That sense of motion resonates strongly with Latin Triadology, which starts literally "in the beginning" (in principium) when describing the origin of the Persons of the Trinity. This kinetic concept is, I suspect, why the West is using the term "from" in the sense of "[moving] out of," more like the way the East uses "through" (dia) than "[produced] out of" (ek). 

That is why I think that there is far too much being read into John's statement from OF I, 8: "And we do not speak of the Spirit as from the Son : but yet we call Him the Spirit of the Son. For if any one has not the Spirit of Christ, he is none of His [Romans 8:9], says the divine apostle. And we confess that He is manifested and imparted to us through the Son." John is meticulously reproducing Gregory's distinction between ek and dia, which we should expect. And in Greek, given how ek is interpreted, it is perfectly reasonable to follow that rule. Although Gregory himself might have broken it in his homily on the Lord's Prayer, it is clear that the use ek only for ekporeusis is the overwhelming choice. But in Latin, where procedere is used more generally to convey motion from the beginning (principium) with adverbs used to qualify it, the "from" has a completely different implication. While various commentators, including no less than St. Maximus the Confessor, have focused in the difference in the terms ekporeusis and processio, it is probably worth mentioning that the prepositions ek and ex do not use "from" in the same way either.

We can also ask whether distinguishing the eternal procession of the Holy Spirit as being "through the Son" violates John's prohibition, taken from Gregory the Theologian, that we cannot inquire into the difference between begetting and proceeding on pain of madness. I think this is plainly not the case. I would point to Gregory's statement in Ad Ablabium that this distinction "does not exclude the Spirit from the natural relation with the Father," and John's own statement that the fact that the Spirit is Image of the Image still means that the Spirit differs from the Son "only by procession." In other words, the fact that the Spirit proceeds through the Son or is the image of the Son in no way speaks to the nature of the procession but only to how it happened. One can again appeal to Gregory's analogy of the transplanted plant versus the seedling. Saying that the Spirit is "through the Son" pertains to the manner of origin, but it does not say anything about its nature.

To complete the picture, John Damascene's characteristic analogies for the Trinity are the same sort of "looking back" analogies that Gregory uses. Now that we have a good understanding of how this relates to the "flow" of the Holy Spirit, the distinctive feature that makes these suitable as images of the reflexive relation. They originate in the Father, move through the Son, and rest in the Spirit. John's favorite triad is Speaker-Word-Breath, which is also the most Scriptural and which was used by Gregory as well, but others used by both John and Gregory include spring-river-sea, root-branch-fruit, and sun-radiance-ray.

When we view John Damascene with the background of Gregory and also with the lens of the reflexive relation, the continuity is unmistakeable. As with Augustine, the Greek Fathers never articulate the concept of "reflexive relation," but they clearly use it. John is even more explicit than Gregory in using the Image-of-the-Image description, but that use was clearly anticipated by the use of the reflexive structure more broadly. Just as Thomas Ryba found the unarticulated concept of reflexive relation in Augustine, we have found the same in Gregory of Nyssa and John Damascene. And we even have a Western theologian, Thomas Aquinas, recognizing the similarity, although he is likewise unable to put his finger on the broader concept.

Eternal Manifestation and Other Theological Considerations

The reason that I consider the concept of reflexive relations to be so powerful in this context of Trinitarian relations is that it makes explicit a logic that is already implicit. It is not a new concept; it is a concept that these theologians have used without putting a label on it. The concept was first extracted from a theologian by Thomas Ryba in "Augustine's Trinitology and the Theory of Groups." I have only taken that application further by recognizing the concept in Trinitarian relations as they are articulated by Augustine (in the psychological analogy) and various other authors. The clearest case is imaging, which is inherently reflexive in the Trinitarian context, but we have seen that Ryba's formulation is inherent in the logic of many other structures of Trinitarian relations.

The question that must be raised is the same one that must be asked in any situation where there is a new interpretation of past thought: how was this missed? In the case of the authors themselves, it is completely understandable; they were deploying the tools that were available to them in completely novel and unexpected ways. What is amazing in retrospect is that these theologians, starting solely from the teaching of Scripture and the idea that Persons are defined by relations, came to this incredible diversity of ways to express the same fundamental concept: that the Persons are modes of reflection upon the Father. Perhaps most impressive is Gregory's deployment of causality in this context, using the scientific method of tracing back the causes of phenomena as a reflective tool for how the Persons came to exist. So I do not say that these authors missed anything. On the contrary, they were extraordinarily effective in utilizing an implicit concept without any of the tools to make it explicit.

But then the question is why we have missed it. I think there are two reasons. The first is that this work is all relatively recent. There has been an extraordinary amount of progress in this area in the last three decades, and Ryba's own publication was only made in 1993. I rely primarily on four works concerning Gregory of Nyssa all published within the last twenty years: The Power of God: Dynamis in Gregory of Nyssa's Trinitarian Theology (2001), Re-Thinking Gregory of Nyssa (2003), Gregory of Nyssa and the Concept of Divine Persons (2005), and Trinity and Man: Gregory of Nyssa's Ad Ablabium (2007). The Trinitarian Theology of Hilary of Poitiers was also published in 2007. These works are effective at debunking the idea of a fundamental gap between one-to-three (Latin) and three-to-one (Greek). As I hope to have demonstrated, both sides used both paths extensively: the one-to-three path via reflexive relations and the three-to-one path via common operation. I have not found anyone who has similarly deployed these works to find a common conceptual underpinning for Western and Eastern Triadology, although that may be more due to my own ignorance than to the lack of effort. Regardless, it is unlikely that the full impact of any of these works has been assimilated by the scholarly community.

The second is that, if my theory is sound, there was a massive red herring hurled into the discussion by the doctrine of the eternal manifestation. If West and East were both articulating reflexive relations in their own respective idioms, then what St. Photius criticized was truly based on a difference of the sense of ek (produced from) and ex (flowing from) in the two languages. That explains why Photius quite reasonably inferred that the Latin description of the procession of the Spirit from the Father must have been defective, for if they used the preposition ex they must surely have meant the same thing that the Greeks meant by ek. His picture was one of the Spirit being produced out of two Persons in the manner of a birth, and one can see even today how horrific and aberrant that must have seemed. We might be more charitable to our opponents with hindsight, of course, but it must have seemed to Photius like the Arian madness of the worst sort. This is why he emphasized John Damascene's observation that "'of' is not 'from'" and rebuked them sharply for trying to assemble some Frankenstein-style abomination in the Trinity. And well he should have!

But in the effort to be charitable and to correct the Latin error (which they did not truly understand), the East later proposed a solution that actually brought the two sides farther away from the common understanding of reflexive relations and farther apart from one another. This solution was to say that all of the characteristic passages that would have pointed to a reflexive relation were at the level of manifestation rather than hypostatic origin. This was in no way at all intended to be divisive; far from it! They shared Photius's genuine concern to return the West to the true faith. But it was nothing short of devastating in terms of burning down every bridge that might have led the two sides to the common understanding of reflexive relations.

That wedge continues to separate to this day. David Bradshaw, an author with an incredibly astute intellectual grasp on the philosophical divide between Latin and Greek, evidences how the eternal manifestation derails this train of thought from the beginning. In Aristotle East and West, he writes on p. 217 about John Damascene's notion of the Spirit coming to rest on the Son, which he considers to be a clear example of the eternal manifestation as opposed to temporal (economic) procession. He makes the following remark during that explanation: "Obviously such a reading is far from the filioque (which had at this time not yet become an issue), for if the Spirit proceeds eternally to the Son He cannot also proceed from the Son." Yet that is precisely what happens in a reflexive relation! If John Damascene describes the Spirit as the image of the Son, as the Son is the image of the Father, there is no reason to think that he does not understand the reflexive structure or that it is not applicable to the other examples he gives. In a summary, one-sentence dismissal that is presented as obvious, Bradshaw has completely removed what may be the key interpretive concept from the picture.

We see the same with Gregory's Ad Ablabium. In interpreting the key passage (p. 215), Bradshaw says the following:

In at least one passage Gregory of Nyssa seems to come close to the filioque. He states that the Son is "immediately" from the Father whereas the Spirit is "by" (dia) the Son; in this way, he says "the attribute of being only-begotten remains unequivocally with the Son, and it is also not in doubt that the Spirit is from the Father, since the mediation of the Son both preserves for the Son the attribute of being only-begotten and does not deprive the Spirit of His natural relation to the Father." This passage is, on the face of it, rather puzzling, for one would think that mediation by the Son would deprive the Spirit of an immediate (or "natural") relation to the Father. For the answer, we must look elsewhere in Gregory's works.

On the contrary, I maintain that if we look at the rest of Gregory's works, as Maspero has done in exacting detail, this passage is not "puzzling" at all. And if we look at that collection through the lens of reflexive relations, it not only fails to be puzzling but also emerges absolutely naturally from Gregory's thinking. Moreover, it explains why John Damascene, who faithfully follows Gregory, has no qualms at all about calling the Spirit "the Image of the Son," knowing full well that "image" in this context refers to the hypostatic origin of a natural image. That use of image applies only to "simple existences" according to Gregory Nazianzen, which rules out eternal manifestation as a context. So when we "look elsewhere," as Bradshaw asks us to do, we find that the passage is ruled out as an instance of eternal manifestation and that it is genuinely a filioque-like passage. I would go so far as to say that, properly interpreted, it is exactly what the West means by the filioque.

Bradshaw points to a letter attributed to Basil but probably written by Gregory that mentions the Spirit being "known after" the Son even though "He has his subsistence from the Father." Bradshaw makes much of the fact that this "making known" is an instance of manifestation. It is not clear what textual or logical connection there would be between this passage and Ad Ablabium, leaving aside the fact that the Spirit having subsistence from the Father in no way contradicts Gregory's description of the relations. As compared with the exhaustive survey that Maspero made of related passages, this simply cannot compare. Moreover, even Bradshaw admits that this "making known" concept does not have a specific order or path of origin. Based on the passages Bradshaw cites, I would point out that the "making known" concept seems to be used to show consubstantiality more than origin. With respect to hypostatic origin specifically, the collection of passages that Maspero offers is far more convincing as an effort to "look elsewhere."

I do not say any of this to diminish Bradshaw's analytical acumen. On the contrary, when one sees brilliant thinkers struggling mightily with the reasoning of a passage while dismissing alternative explanations as obvious, one must suspect that something is being missed. St. Thomas Aquinas, who is unquestionably one of the most brilliant men ever to live, missed this in his analysis of John Damascene's Image-of-the-Image passage, despite coming incredibly close to seeing it. But I do believe that, until Ryba pointed out reflexive relations as a truly viable solution, we all missed it. And that meant that it was impossible to see the truly common logical structure that would have reconciled East and West on this point.

Suggestions for Moving Forward

Suppose that I am right for a moment. How might we use the realization to bring the sides closer together?

In the West, we need to stop anthropomorphizing the concept of love in the context of the Trinity, which I honestly think would have appalled both St. Augustine and St. Gregory of Nyssa. If I am correct, the psychological analogy was intended solely to show a form of reflection between two as opposed to the intellectual reflection of the Word. I firmly believe that St. Augustine intended no more than that, and he even says that we should not take this analogy so literally (or even as an analogy at all, as per Barnes). The East doesn't even use this title; Gregory calls the Holy Spirit the bond of unity, which expresses the same thing in a way much less susceptible to overstatement. ("Bond" is also a perfectly acceptable concept in the West.)

Despite Augustine's warning, since Richard of St. Victor, the West has piled more and more significance on the fact that the Holy Spirit is "subsistent Love." At this point, even the ecumenical proposals (like the one I linked above from Michael Torres) are calling for us to talk even more about how the Holy Spirit is Love. While it might seem odd for a Christian to argue against love, I must say it: for the love of God, stop! It is strictly counterproductive for the understanding of Trinitarian relations at this point. Logically, it is absolutely equivalent to speaking of the Holy Spirit as the bond of unity. Anything else is theologoumenon, and much of that seems ill-advised. Even when St. Thomas missed the use of reflexive relations by St. John Damascene, it was because he couldn't reduce the concept of "love" to its pure reflective aspects. We are going to have to dig through so much of this accumulated detritus to get to the fundamental concept that it would be better to stop thinking about it entirely.

That brings us to the big issue separating East and West once the filioque is set aside: what is the experience of God? Precisely because of this emphasis on love, Western mysticism has tended to emphasize this affective notion of mystical experience to a level that I think is all out of proportion. The gap between Western and Eastern mysticism is probably the clearest example of a massive separation between the two sides on what it means to experience God. What is theosis? What is the beatific vision? That is, in my mind, the real and substantive issue that has been irreconcilable. Unfortunately, it was tied to the filioque by the doctrine of eternal manifestation, where I don't think it actually belongs at all. But filioque aside, the issue is very real, and it will require much more intensive metaphysical scrutiny. That is where I believe the future lies.

[Update: After I wrote this, Deacon Anton Usher helpfully located other "image of the image" references before St. John Damascene. One was from St. Athanasius in Serapion 1:24: "The Spirit is said to be, and is, the image of the Son. For 'Whom he foreknew, he also foreordained to be confirmed to the image of His Son.' If then they admit that the Son is not a creature, then neither may his image be a creature." This is noted by the translator C.R.B. Shapland as an unusual bit of exegesis of Romans 8:29 that is echoed by Pseudo-Basil in Adv. Eun. V.724C and St. Cyril of Alexandria in de Trin. VII.1089B, which I have not read. The others were in the creeds attributed to St. Gregory Thaumaturgus; the Son is called "the prototype of the Spirit" in the longer creed and the Spirit, "the image of the Son, Perfect of the Perfect" in the longer creed. The Athanasius reference is similar to what he had said in the economic context, so it is somewhat less surprising and, in any case, completely consistent with what I wrote. The creedal references were a complete surprise; I was not aware of anything like them.]

Thursday, September 23, 2021

Reflexive Relations in the Trinity

I want to focus now on a specific aspect of the tri-unity matrix: reflexive relations.

[Update: I've added an illustration of what reflexive relations look like below.]



Much as with the numerous relative identify formulations introduced in analytic philosophy, there may be a sense that this is too sophisticated a concept for the various historical figures to have held. This modern sophistication conveys the impression that these early forays into Triadology were a bit embarrassing and that contemporary Christian philosophers are covering their fathers' nakedness, at least in the sense of correcting some logical mistakes that they made. I myself accept that possibility on certain matters such as  the creation of the universe, the evolution of man, and even theological matters such as the the spiritual status of Judaism after the first century. What is in common in these matters is that they are factual judgments based on principles in revelation. But when it comes to fundamental matters about theology and Christology, we are dealing with principles of revelation. For those matters, "the faith that was once for all delivered to the saints" (Jude 1:3) is all we have; this is the substance of the apostolic deposit. We can only learn it from the Fathers; we cannot correct them.

This might seem a little rich from someone offering group theory and matrix representation as an explanation for what the Fathers were saying. But what Thomas Ryba offered in his article "Trinitology and the Theory of Groups" and what I offered in the tri-unity matrix are merely logical representations of reflexive relations. Given that is the case, the question is whether reflexive relations themselves are the right description of the concept they had in mind. I believe that we have good reason to think so.

A reflexive relation is, as one might expect, it is a relation that looks back on itself (Lat. "re-flectere" meaning "to bend back"). Formally, it is a relation that maps a set back to itself. The most basic such relation is equality of a real number with itself, the reflexive property, i.e., for any real number a, a = a. In most cases, reflexive relations are trivial in their application simply because they are taken for granted as axioms of any system. But in the case of the Trinity, we are already dealing with relative identify, where Leibniz's Law cannot apply, so it is not surprising that reflexive relations would end up being more a useful tool.

The function that reflexive relations serve is to make copies of sets. The name is not coincidental; mirrors bend back (reflect) images of their prototypes. That is certainly not a concept that ancient people would have had difficulty understanding. Nor is this idea of copying foreign to Scripture. Hebrews 1:3a calls Jesus "the radiance of the glory of God and the exact imprint of his nature." Colossians 1:15 describes Jesus as "the image of the invisible God."

And did the Fathers use this concept for the Persons of the Trinity? Unquestionably! 

St. Gregory Nazianzen does so explicitly in the Fourth Theological Oration: 

And Truth, as being in nature One and not many (for truth is one and falsehood is manifold), and as the pure Seal of the Father and His most unerring Impress. And the Image as of one substance with Him, and because He is of the Father, and not the Father of Him. For this is of the Nature of an Image, to be the reproduction of its Archetype, and of that whose name it bears; only that there is more here. For in ordinary language an image is a motionless representation of that which has motion; but in this case it is the living reproduction of the Living One, and is more exactly like than was Seth to Adam, or any son to his father. For such is the nature of simple Existences, that it is not correct to say of them that they are Like in one particular and Unlike in another; but they are a complete resemblance, and should rather be called Identical than Like.

Regarding the Holy Spirit, there is a similar passage from St. John Damascene that I saw referenced in an article by Vladimir Lossky. This quotation is found in Part III of the APOLOGIA OF ST JOHN DAMASCENE AGAINST THOSE WHO DECRY HOLY IMAGES:

The Son is the first natural and unchangeable image of the invisible God, the Father, showing the Father in Himself. ‘For no man has seen God.’ Again, ‘Not that any one has seen the Father.’ The apostle says that the Son is the image of the Father, ‘Who is the image of the invisible God,’ and to the Hebrews, ‘Who being the brightness of His glory, and the figure of His substance.’ In the Gospel of St John we find that He does show the Father in Himself. When Philip said to Him, ‘Show us the Father and it is enough for us,’ our Lord replied, ‘Have I been so long with you and have you not known Me, Philip? He who sees Me, sees the Father.’ For the Son is the natural image of the Father, unchangeable, in everything like to the Father, except that He is begotten, and that He is not the Father. The Father begets, being unbegotten. The Son is begotten, and is not the Father, and the Holy Spirit is the image of the Son. For no one can say the Lord Jesus, except in the Holy Spirit. Through the Holy Spirit we know Christ, the Son of God and God, and in the Son we look upon the Father. For in things that are conceived by nature, language is the interpreter, and spirit is the interpreter of language. The Holy Spirit is the perfect and unchangeable image of the Son, differing only in His procession. The Son is begotten, but does not proceed. And the son of any father is his natural image. Thus, the natural is the first kind of image.

What is critical to perceive about these passages is that they refer to the image of the Person producing a copy according to nature, a natural image, as a child reproduces the nature of his father. The Theologian's reference here to "simple existences" can be nothing other than the hypostatic existence of the Persons with the divine essence. In the context of what Gregory says about the names of the Persons being relations, the imaging establishes a reflexive relation, in the way a son reflects a father or an impress reflects a seal. And because the divine essence is simple, the image is not merely like but absolutely identical. 

This kind of process is already implicit in Latin theology, which is why it seemingly appears to "start with the essence." That is simply another way of saying that the Latin approach focuses on the divine essence being copied from the Father in the Persons. Rather than collecting examples, I will point to a characteristic Trinitarian picture of the West: Augustine's so-called "psychological analogy." In that model, the Father thinks upon Himself, which though is the Word (by mode of intellection) and the mutual love of the Father and that Word is the Holy Spirit (by mode of willing). The number of scholarly interpretations of this concept is so voluminous that the pages are uncountable. For our purposes, it doesn't matter. The point is that the self-reflective nature of the model definitely places it in the category of reflexive relations. It is, moreover, exactly the same set of reflexive relations that Ryba outlines for Augustine's Trinitarian formalism, even though he did not specifically mention the psychological analogy.

St. Thomas Aquinas made the same assessment in the Disputed Questions on the Power of God, Part 9:

On the other hand God does not acquire knowledge from things, but by his knowledge is the cause of things: nor by his will does he tend to anything external as his end, but he directs all external things to himself as their end. Accordingly both in us and in God there is a certain rotation in the acts of the intellect and will: for the will returns to that whence came the beginning of understanding: but whereas in us the circle ends in that which is external, the external good moving the intellect and the intellect moving the will, and the will by appetite and love tending to the external good; in God, on the other hand, the circle ends in him. For God, by understanding himself, conceives his word which is the type of all things understood by him, inasmuch as he understands all things by understanding himself, and from this word he proceeds to love of all things and of himself. Thus someone has said that a “monad engendered an atom and reflected its own beat upon itself.” And the circle being closed nothing more can be added, so that a third procession within the divine nature is impossible, although there follows a procession towards external nature. Hence in God there must be but one person that does not proceed, and only two persons that proceed, one of whom proceeds as love, the other as word: and thus the persons in God are three in number.

Aquinas neatly summarizes how the psychological analogy is reflexive. God knows Himself as Father, begetting the Son, then loves Himself as Father and Son, from which the Spirit proceeds.

It is important to distinguish reflexive relations from the Neoplatonic exitus-reditus, with which it could easily be confused. Neoplatonism starts from how the One can communicate itself, which has nothing to do with the One having any manner of relationship with itself. Rather, it describes how the One relates outside of itself through Nous and Soul. There is a certain harmony between this idea and the economy, the activity of the Trinity in the world, which is why there can be Christian Neoplatonism in St. Dionysius the Areopagite and similar influences in many others. But the relations defining the Trinity is always ad intra; the relations are reflexive within God and not in any way directed out of God.

To understand the difference, one can look at the difference between the Son as the true image of God when compared to man's creation in the image of God. The concept "image" appears in both places, but the true image of the divine nature itself is only within the Trinity. The "image" found in creation is different in kind, although it is still in some sense an image. While the Christian view is compatible with Neoplatonic emanations at the level of creation, it is thoroughly incompatible with the ad extra steps through Nous and Soul from the One. The Father, the Logos, and the Holy Spirit are instead the One God.

Much as there was a legitimate fear of the Neoplatonic Dyad reflected in Eastern resistance to the Latin formulation, there is a legitimate fear of the Neoplatonic Triad in the psychological analogy. Hearing this language of intellect and will immediately connotes the production of the Nous and the Soul to someone steeped in Neoplatonism, even though that concern simply wouldn't apply to reflexive relations at all for the reasons Aquinas gives above (the relations are directed solely ad intra).

It is entirely legitimate to view these reflexive relations as imaging the divine essence. At its root, the filioque says nothing that St. John Damascene has not already said: the Son is the Image of the Father, and the Holy Spirit is the Image of the Son, the Image of the Image of the Father. And based on what St. Gregory Nazianzen says, this true (which is to say, identical) imaging cannot be any kind of energetic procession, because the identity pertains to the "nature of simple Existences" rather than the plurality of the energies. As this pertains to the "invisible God," being the Image is likewise not a showing forth or manifestation of the Trinity in the economy, although like any aspect of the Trinity, it certainly has implications for economic activity. And while it is a natural imaging, it is both personal and relational; therefore, it pertains to the mode of existence of the Persons. In short, this double imaging is a matter of hypostatic origin, not eternal energetic procession.

The double imaging is also compatible with all of the typical Trinitarian formulae. Prototype, Image, and Image of the Image is no different than Father, Word, and Love/Bond; Uncaused, Immediately Caused, and Mediately Caused (the formula St. Gregory of Nyssa uses); or Principle Without Principle, Principle From Principle, and Proceeding. The copying aspect of being Image of the Image accounts for all of the references to what the Son has or receives and gives to the Spirit. As long as the Trinitarian relations are understood as reflexive, these are all the same.

More broadly, it accounts for a number of the "authorized" analogies for the Trinity that all have in common this feature of looking back to how we arrived at a certain point. St. Gregory of Nyssa provides a helpful analogy to a plant that could have grown as a seedling or could have been planted (from the Ad Ablabium, quoted in Giulio Maspero's Trinity and Man at p. 155-56). When we talk about how the plant got there, we aren't talking about the nature of the plant, which is common, but we can still talk meaningfully about its origin or cause. In the Trinity, these analogies involve the same process of looking back: pond to stream to source, third torch lit by second torch lit by first torch, warmth to ray to sun, leaf to branch to root ... all successful analogies that involve a reflexive view of something being passed in the manner of Image of the Image.

In short, by correctly conceiving the Trinitarian relations as reflexive, every objection to the filioque is disarmed. There is no eternal energetic procession needed to explain away relationships between the Persons, no fear of the Neoplatonic Dyad or Triad introducing itself into the idea of God, and no introduction of a tertium quid into between the Persons and the divine essence. That is not to say that an eternal energetic procession is wrong; on the contrary, it is hard to see how it could not be true. But it isn't needed in order to explain away a belief no one actually held. This seems to be a successful resolution of the discrepancy of the filioque with the virtue that it actually corresponds with the thought of the Fathers, as opposed to anachronistically transporting what seems to be a working solution today back into the past.

Now, as I mentioned previously, there are alternative formulations that could work. One is Basil Lourié's quasi-ordinal set that defines relations in a Triad. A similar one is Fr. Thomas Weinandy's spirituque proposal: "We believe in the Holy Spirit, the Lord the Giver of Life, who comes forth (ejkporeuvetai) from the Father as the one in whom the Son is begotten and who proceeds (proei'si) from and through the Son in communion with the Father, and together with the Father and the Son is worship and glorified." As with the eternal energetic processions, I do not believe that either is necessarily wrong. My friend Michael Liccione gives a good explanation as to why it is implicit in what we all believe and why there is even historical precedent for this give-and-take of the Son and Spirit (citing a passage from St. Symeon the New Theologian on the Spirit as Icon of the Icon, which fits in well here). Lourié has pointed to the same Ethiopian tradition that reversed the Son-Spirit causality.

My concern is that the resolution is anachronistic, and the historical precedent to which it cites is obscure and difficult to harmonize with the main communities in which this dialogue is taking place. Therefore, I do not believe that these approaches speak to the concerns and needs that each side is trying to express. They try to come up with a new language rather than allowing the traditions to speak. I would prefer to say "we have heard, and we proclaim the same." There may be skepticism about that claim, but it seems that reflexive relations have a long and successful pedigree on both sides, and that what I have proposed is only to make explicit what has been said implicitly for a very long time.

Thursday, September 16, 2021

The Tri-Unity Matrix?

Copyright 2021 Jonathan E. Prejean; all rights reserved.

A bit over five years ago, I had the idea of writing an alternative account of the disconnect on the filioque between East and West. There were a couple of significant hurdles to overcome at the time that made the idea of that work a daunting prospect. 

First, the state of historical research on the subject was quite contentious. Although it remains so to some extent, it does seem that moderate positions are becoming more accepted. I should say that nothing that I will present actually depends on the historical conflict over the filioque. My thesis is that there is an analytical framework that is consistent with both that obviates the basis of the dispute. But in the general realm of the discussion, a raging historical debate is a distraction, so that quieting the polemics is more conducive to dialogue.

Second, at the time, there were a number of analytical proposals on how to handle the paraconsistent logic of the Trinity, and I wanted to give some interaction to these. One article that was particularly interesting to me was Basil Lourié's "Nicephorus Blemmydes on the Holy Trinity and the Paraconsistent Notion of Numbers: A Logical Analysis of a Byzantine Approach to the Filioque," a draft at the time that was later published in Studia Humana 5:1 (2016), pp. 40—54.  In addition, there were some historical views of the Trinity that I wanted to compare and contrast with the formalism. For the most part, I've accepted that this is too much to take on in any comprehensive way, and I hope that presenting the proposal will trigger a fruitful dialogue that will provide such engagement on its own. Happily, I did come across another of Lourié's articles that is directly on point for this discussion, which I will cover later.

But mostly, I feel like we need something now. Where Christians, East and West, could be coming together, we are becoming as atomized as the society. In reflecting on how bad it was right now on social media, I thought that it wasn't so long ago when I participated in reasonable discussions about the filioque on the Internet. I went back and looked at one of those blog discussions initiated by my friend Scott Carson; it was nearly fifteen years ago. One good thing is that I am still friends with people in those discussions to this day, but I wish that the same feeling were spreading everywhere. So I write this in the hope that it might bring people together.

I've put a copyright notice at the top for that purpose. I would like to kick off a wider discussion, and I hope to be part of it. I don't even know how to count links or hits or whatever, but I figured it might help to have the discussions point back to the same place.

With that explanation setting the stage, I start with the fundamental problem of Leibnizian identity in the Trinity. The logical problem of any Triadology is first and foremost why, if the Father is identical to the One God, the Son is identical to the One God, and the Holy Spirit is identical to the One God, yet the Father, the Son, and the Holy Spirit are all not identical to one another. Of course, the Trinity is a mystery beyond comprehension; it is entirely inscrutable how the three divine Persons can be the One God. But it is worth asking if the statement that the three divine Persons can be the One God is nothing more than a contradiction in terms. In both East and West, this was the challenge presented by Arianism, and the two regions of the Christian world answered this challenge in different ways. 

St. Augustine's response is paradigmatic for the Western approach. In Augustine's formulation, each divine Person possesses and is identical with the divine essence as a result of divine simplicity. In order to explain this, St. Augustine posits that the Persons are distinguished (and named) by relations, a metaphysical concept which he has taken from Aristotle's Categories and modified for his own use. Augustine was criticized by some later commentators for failing at his task of defending the Trinity, since the category of relation must either be not real, in which case Augustine is a modalist, or real. If the relations defining the Persons are real, then Leibniz's Law means that either the Persons must be identical to one another or that they are not, which would entail tritheism.  

Thomas Ryba responds to that argument (as made by A.C. Lloyd) in his article "Augustine's Trinitology and the Theory of Groups"(from J. Lienhard, S.J., et al., eds., Augustine: Presbyter Factus Sum, Collectanea Augustiniana, Peter Lang (NY 1993), pp. 151-168), which is the foundation of my own thesis. In the article, Ryba uses group theory to show that reflexive relations on the same set need not be identical with one another, even while the set itself remains identical. This is not to suggest that Augustine had this argument in mind; as Ryba explains, "Augustine does not make use of a Latin synonym of the English word 'reflexive,' but the notion of reflexivity of the trinitarian relations is implicit in his notion that all of the persons are of the substance and yet related to one another." Although Augustine himself could never have had such a proof in mind, the formal structure he employs matches the group theory proof. In Ryba's formulation, the Father is the set defined as the divine essence. The Son is a set defined by a first reflexive relation (generation) that maps the Father set back onto itself and therefore is also the divine essence. The Holy Spirit is set defined by a second reflexive relation (spiration) that maps both the Father and Son sets, which are each the set of the divine essence, back onto itself and is therefore also the divine essence.

This is all well and good, in that the argument shows that Augustine's notion of relations (explicitly including the filioque) does not run into either tritheism or modalism. One could extend this further to Boethius's concept of the Persons as "subsistent relations" and even further to St. Thomas Aquinas's "relations of opposition," and the explanation works equally well. We might even go so far as to say that it vindicates the view of St. Gregory Nazianzus in several of his Orations, such as when he says the following in his Third Theological Oration: "Father is not a name either of an essence or of an action, most clever sirs. But it is the name of the Relation in which the Father stands to the Son, and the Son to the Father." Likewise, he says in his Fifth Theological Oration: "But the difference of manifestation, if I may so express myself, or rather of their mutual relations one to another, has caused the difference of their Names. For indeed it is not some deficiency in the Son which prevents His being Father (for Sonship is not a deficiency), and yet He is not Father." (More on Gregory the Theologian later.)

I believe that Ryba's concept can be taken a step further by transforming it into a matrix. The matrix formalism has been enormously helpful in the counterintuitive discipline of quantum mechanics by providing a framework for mathematical operations, even when the real-world analogue is difficult to perceive. For example, spinors and Pauli matrices are used to describe the properties of particle spin for fermions, which are subject to exclusion rules that are in some ways like the exclusive distinctions between the Persons of the Trinity. The example of particle spin also illustrates that even simple two-by-one and two-by-two matrices can describe phenomena that in some ways defy comprehension.

For this application, I would propose the following tri-unity matrix:

The tri-unity matrix T illustrates the formal structure of relations in the Trinity, the union of the three Persons. The sets (Persons) of the divine essence (Godhead G) are denoted by the indices alpha (A) and omega (Ω). Respectively, these indices indicate whether the Person is in the domain (0) or range (1) of the reflexive relation and whether it is the first reflexive relation (0) or the second reflexive relation (1).  The matrix is therefore the smallest possible matrix including the relevant degrees of freedom that uniquely specify each Person in Ryba's formalism. The Father is uniquely in the domain of the first reflexive relation (00), the Son is uniquely in the range of the first reflexive relation (10), and the Holy Spirit is uniquely in the range of the second reflexive relation (11).

As is often the case in a matrix formalism, there is a built-in excess of information, which we call degeneracy. In this case, given the information required to specify each of the other three Persons in the formalism, there must necessarily be a fourth element (01) that does not uniquely specify any Person. In fact, this position would correspond to each of the Father and the Son in the domain of the second reflexive relation. It is impossible to uniquely specify each of the three Persons without implicitly including this additional information; the fourth element provides redundant information about other Persons without actually defining them in any way. The tri-unity matrix is therefore the minimal formal structure needed to count the Persons of the Trinity based on reflexive relations, and this irreducible excess of information is needed to do so. That excess element in the two-by-two matrix is the filioque.

That last point about the filioque may seem like an abrupt conclusion, but let's retrace the path that took us here. All we have done is to specify the minimum formal content for a way to think coherently about the Trinity without modalism or tritheism. The only assumptions we made are that the Persons are defined by reflexive relations, that these relations map a domain to a range, and that the relations are discernible from one another. We don't even have to take a position on the metaphysics of relations or of the divine essence. As with spinors, we can meaningfully talk about their formal properties without necessarily having any clear idea about what the underlying reality is.

That this approach is purely logical and formal is why I have taken it. Augustine, Boethius, Aquinas, and Scotus all had different metaphysical principles in play. That's to say nothing of many Eastern saints: the Cappadocian Fathers, Dionysius the Areopagite, Maximus the Confessor, John Damascene, Photius, Gregory Palamas, Mark of Ephesus, Gregory of Cyprus ... one could go on for days just explaining how different they are. But none of those differences matter. We do not need to know what a relation is, what counts as a cause, or what the exact formulation of divine simplicity we should adopt; we need only know what logical content is required to coherently deny modalism and tritheism.

The formalism clearly fits with the Triadology of the West. To take the most developed example, which is Aquinas's account, there are four relations of opposition: generation, filiation, active spiration, and passive spiration, but active spiration does not in any sense define the Father and the Spirit. This simply restates the (01) element of T. In other words, it is a necessary logical consequence of distinguishing the relation of passive spiration (procession) from generation-filiation without saying anything more about the properties of the Father or the Son. Far from adding something, the filioque does nothing but to reproduce Ryba's relational structure in its simplest form. Aquinas recognizes both the formal content and the fact that it does not define a person, exactly as the (01) element in T shows. To put it another way, reciting the filioque is an affirmation that the relations of all three persons are inextricably linked in this four-element structure, not an attempt to somehow distinguish the Holy Spirit from the shared properties of the Father and the Son.

Looking East

It is no surprise that what Ryba says for Augustine goes for the West generally. What of the East? Here we turn to a perspicacious account by Basil Lourié titled "What Means ‘Tri-’ in ‘Trinity’? An Eastern Patristic Approach to the ‘Quasi-Ordinals’" in Journal of Applied Logics — IfCoLog Journal of Logics and their Applications 6:6 (2019), pp. 1093-1107. This follows the same approach to paraconsistent logic found in the article on Nicephorus Blemmydes. But while Blemmydes's formulation was not widely or explicitly adopted by the Eastern commentators on the filioque, the approach described in this later paper likely was. 

Specifically, Joseph Bryennios, whose approach Lourié analyzes, was a direct influence of Mark of Ephesus, the most prominent filioque opponent at the Council of Florence. In another article ("A Logical Scheme and Paraconsistent Topological Separation in Byzantium: Inter-Trinitarian Relations according to Hieromonk Hierotheos and Joseph Bryennios"), Lourié notes that "Mark of Ephesus in his epitaphion to Bryennios called him Ὁ τοῦ Λόγου πρόμαχος ἐνθέοις λόγοις ‘The front-fighter of the Logos with divine logoi.’" I say this to indicate that we are not talking about some fringe theologian, obscure scribe, or minor player in the filioque debate. Bryennios was directly motivating the theological doctrines that were being debated. Lourié further argues that Bryennios was an authentic inheritor of a much longer tradition through Hierotheos all the way back to Gregory of Nazianzus and Evagrius Ponticus, making Bryennios's arguments not only relevant for the filioque debate but also representative of a much broader Eastern perspective.

As Lourié outlines the situation, the concern in Eastern Christian thought was to avoid the idea that the Trinity was, in Evagrius's terms, "a Trinity of numbers." By this Evagrius means that we do not count the Persons of the Trinity as a first Person, a second Person, and a third Person but only as a mutually interrelated Trinity of Persons. Lourié also cites a passage from Gregory Nazianzen's Oration 23 about how the Dyad is "overstepped" in moving from the Monad to the Triad. Lourié convincingly argues that the Dyad is not referring here to the Son (which some Byzantine writers later misunderstood) but rather to the Dyad of the dialectic of opposition, which produces composition and division. In other words, if there were an ordinal counting for the Trinity, in the form of first Person, second Person, and third Person, it would necessarily involve some form of Arianism, subordinationism, or tritheism. Lourié notes that "[t]his idea of skipping the Dyad is an innovation peculiar to the Greek patristics," no doubt because Neoplatonism and the One-Nous-Soul triad was the philosophical opponent of Christianity. I'll mention here a very similar quote from Gregory of Nyssa in Ad Graecos: "No other Person is ever generated or proceeds from the Father or from one of the Persons, in such a way that the Trinity could ever be a group of four; nor does one of these Persons ever finish, as if in the blink of an eye, so that the Trinity would ever become a dyad, not even in thought" (reproduced in Giulio Maspero, Trinity and Man: Gregory of Nyssa's Ad Ablabium, p. 161).

Much like Augustine, Bryennios establishes a formalism to account for the distinction of the Persons based on relations, which can likewise be understood in terms of group theory. In this case, his method for avoiding counting in the manner of ordinal numbers, characterized by binary adding operations (1+1=2, 2+1=3, etc.), is to define relations that are only and always distinguished from one another in relation to two other second elements. This is the ternary exclusive OR operator, which defines each element relative to the other two second elements. The operation defines a sextet, so it includes symmetric degeneracy as well, such that each Person is defined in two different relation sets. For example, the Holy Spirit appears as the Spirit of the Son and the Person proceeding from the Father.

Most remarkably, the article includes a graphical illustration of the concept, based on a version first drawn by Hierotheos in in the 1270s and upon which Bryennios had further elaborated in the 1420s. To see the very logical structure that Lourié described being illustrated is nearly as surprising as it would have been to see a drawing of Ryba's reflexive relations in one of Augustine's letters. I am hard pressed to imagine what could be a more convincing piece of evidence that Lourié's formalism is what Bryennios, and likely Mark of Ephesus, had in mind. (The illustrator also used A and Ω to index two of the sets, which gave me the feeling that all readers of history will recognize: any idea you might consider clever has very likely already been taken.)

Reconciling the Two Views

I hope that it won't be be difficult to accept at this point that Ryba has the Western view described correctly and that Lourié has the Eastern view described correctly. Both are purely logical formalisms that defy modalism and tritheism while also avoiding the objection from Leibnizian identity. Using "reflexive" to refer to this type of identity, Lourié maintains that Bryennios has presented a "super-reflexive" logic that overcomes the limitations of reflexive identity, as contrasted with a merely "non-reflexive" logic that might bypass the limitations of reflexive identity. Ryba's logic of reflexive relations without reflexive identity is likewise "super-reflexive" in this sense. And in like manner to my observation about the tri-unity matrix earlier, Lourié found similar logical structures put to use in the counter-intuitive realm of quantum mechanics.

We have now reached the point where I hope my small expansion of Ryba's idea will come into service. Because Ryba's relations define two degrees of freedom, they can suitably be represented by a two-by-two matrix. The critically important observation is this: a two-by-two matrix is not a dyad! One does not count from a monad (one-by-one matrix) to a two-by-two matrix in the manner of ordered pairs; the relations in T are all simultaneous and inseparable. So if Ryba's relations accurately capture the Western view of the Trinity, which I have every reason to believe they do, then they do not run afoul of the legitimate Eastern concern about attempting to reach the Trinity through a dyad. They are not counted in sequence; rather, they all appear at once by mutual definition.

In case Ryba's account is unconvincing on its own, I can avail myself of Chekov's gun placed in the first act, to wit, Scott Carson's article on St. Anselm. In that article, Scott quotes from Anselm in Section 15 of On the Procession of the Holy Spirit, a treatise written on this very topic. Anselm says the following:

If we should consider the Father and the Son and the Holy Spirit in pairs, it is clear from what I have said that it is necessary either that one of the pair is from the other, since the other is not from that one, or that that one is not from the other, since the other is from that one. For example, if we should pair the Father and the Son, we perceive that the Son is from the Father, since the Father is not from him, and that the Father is not from the Son, since the Son is from the Father. And similarly, if we should consider the Father and the Holy Spirit, we find that the Holy Spirit is from the Father, since the Father is not from him, and that the Father is not from the Holy Spirit, since the Holy Spirit is from him. So also, if we should explore how the Son and the Holy Spirit are related to one another, we shall understand that the Holy Spirit is from the Son, since the Son is not from him, and that the Son is not from the holy Spirit, since the Holy Spirit is from the Son. Therefore, what I said before [in section 1] is evident, that the aforementioned relations, although they are in one thing, cannot let their plurality be absorbed in the unity nor can the unity let its uniqueness be absorbed in the relations.

I'll commend the article to you for the excellent explanation and borrow the conclusion: this is part of a purely logical structure to accomplish exactly what Ryba's and Lourié's "super-reflexive" logical structures accomplish. The only reason that Anselm's language seems suspicious to Eastern readers is that this idea of pairing sounds like a dyad. That is not the case; the pairings Anselm is describing here are the same relations that result from comparing elements in the matrix T. It is not an attempt to use pairings to produce the Trinity; rather, it is taking the structure of two relations and two positions in each relation (the two-by-two matrix) and looking at the elements in pairs.  
There is much more that could be written about the metaphysical and theological implications, but again, this explanation is purely logical. Based on the logic of the two formalisms, both consistently avoid modalism and tritheism, and neither reaches the Trinity by way of counting through a dyad, which is clearly proscribed among the Eastern Fathers. We have two valid "super-reflexive" formalisms that explain the Trinity as a set of relations inseparable and inextricable from one another. Strip away all of the confusion of language, all of the various metaphysical systems, and all of the cultural baggage, and you find two different approaches to reach the same end.

Conclusion

We have left only to apply the reality check; is it really possible that this whole thing came down to the inability of the two sides to express their implicit logical assumptions? I would say almost certainly. Matrices used to describe spatial degrees of freedom only date to the 19th century; how would we expect the Western theologians to have articulated the difference between "by twos" and "two-by-two" explicitly? Likewise, how could the East explain their objection to the dyad to people who had been speaking in this way without incident for centuries? Ryba didn't write his own paper until 1990, and he didn't explicitly use a matrix based on the degrees of freedom so that it could be contrasted with a dyad. Lourié's paper providing the background for Mark of Ephesus is only two years old, so much of the logical underpinning of the Eastern view remained unstated and potentially obscured by philosophical concepts. But there is very little excuse to remain at the impasse if we can abstract these explanations from the writings of these various authors. I hope that we will not.