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.
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:
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.