I. Mindset considerations
Does Augustine Return to the Interpersonal Image of Love as Representing the Trinity, or Does He Abandon This in Favour of the Psychological Image? Behind this question may lurk another question that is both connected and distinct from it: 'Does Augustine have a relational understanding of the image, or is his understanding ultimately solipsistic?' I take Rowan Williams as an example of a scholar writing from a mindset which fails to adequately distinguish the two questions. He opens with quotes that read Augustine as almost Sabellian, and ends his opening paragraph with a spectacular strawman:
Augustine stands accused of collaborating in the construction of the modern consciousness that has wrought such havoc in the North Atlantic cultural world, and is busy exporting its sickness to the rest of the globe, while occluding the vision of the whole planet's future in its delusions of technocratic mastery — a hugely inflated self-regard, fed by the history of introspection.
Williams is building up to a rescue operation. He offers a careful study which either counterbalances Augustine's apparent meaning or replaces it. He brings up quotations like, 'In the West, especially since the time of Augustine, the unity of the divine being served as the starting point of Trinitarian theology', as examples of the reading he doesn't like. Williams's presentation of Augustine's text does not bring up Augustine's claim that all three persons of the Trinity speak in Old Testament theophanies. This claim is significant because Augustine rejects the Patristic claim that Old Testament theophanies are specially made through the immanent Son. Williams seems to be fighting an obvious reading so he can rescue relationality in Augustine. I would argue that the psychological image is relational from the beginning, and that Augustine's image is psychological.
We're looking for relationality in the wrong place if we look for it in where Augustine stood in the controversies of his day. The deepest relationality does not lie in i.e. his writing against Arianism, but something that was so deeply ingrained in the Church that he would never have thought it necessary to explain. The very individualism he is accused of helping construct had not come together. In the Reformation-era Anabaptist/Zwinglian controversy over infant baptism, the issue was not whether faith precedes baptism. Both sides believed that much. The issue was whether that faith was reckoned along proto-individualist lines, or whether the faith of a community could sanctify members too young to embrace faith on terms an individualist would recognise. Augustine lived over a thousand years before that controversy. His tacit theory of boundaries was that of a community's bishop, not a counselor imparting the 'value-free' boundaries that flow from atomist individualism. I mention these examples to underscore that Augustine's understanding of where one person ends and another begins is much less articulate, much less thorough, much less basic, much less sealed, and in the end much less focal than ours. The difference is like the qualitative difference between Father, Son, and Holy Spirit in the Bible, and what either Arian or a Trinitarian did with what is present in the Bible. One is tacitly present, something you can't explain ('That's just the way things are!'), and the other is articulate, the sort of thing you can at least begin to explain and give reason for. In the end Augustine's understanding of how one person can meet another arises from a very different mindset from a setting where scholars argue that communication is impossible. This means that combining passages with individualist assumptions gives a very different meaning from combining the same passages with Augustine's patristic assumptions. It is the latter which represents Augustine's thought. I believe that Augustine did plant proto-modernist seeds. These seeds became a vital ingredient of modernism with many thinkers' successive modifications. However, the fact that they have become modernism today with the influence of a millenium and a half of change does not make Augustine an early modernist. His beliefs were quite different from atomist individualist modernism.
What is most important in Augustine's thought, and what he believed most deeply, includes some of what would never occur to him to think needed saying. These things that leave less obvious traces than his explicit claims. With that in mind, I would like to look more closely at Augustine's interiority:
But it [the mind] is also in the things that it thinks about with love, and it has got used to loving sensible, that is bodily things; so it is unable to be in itself without their images. Hence arises its shameful mistake [errus dedecus ], that it cannot make itself out among the images of things it has perceived with the senses, and see itself alone...
What is interesting is what Augustine doesn't say here. A materialist would see bodily things as including other people, but Augustine did not think from that starting point. Would he have included people? That's a little less clear-cut. People are equal to oneself, and purely sensible objects are inferior. One is trying to go upwards, and Augustine does not seem to include equal people with inferior objects. Perhaps he does not raise this question. Augustine does go on to give a primacy to 'Know thyself,' but this is a matter of means,not of final end. Augustine is telling us to start with what is near at hand. The distinction between what Augustine called 'interior' and what we would call 'private' is significant. It contains not only phantasms (sense impressions) but the res ipsa (the realities themselves) of intelligible things, and is where the soul meets intelligible truth. God is in the interior, and is shared between people. Furthermore, when we unite with God, we are united with others united with God. Where there is privacy, this is darkness caused by the Fall.
II. Is the psychological image relational?
I would suggest that the psychological image is relational. Furthermore, I would suggest that the deepest relationality comes before making God the object of the vestigia (divine shadows or traces in Creation) of memory, understanding, and will. Augustine comments:
Even in this case [I Cor. 8:2], you notice, he [Paul] did not say "knows him", which would be a dangerous piece of presumption, but "is known by him." It is like another place where as soon as he said, But now knowing God, he corrected himself and said,Or rather being known by God...
Before we worry if God is the object of our love, he must be the Subject behind it. And that does not mean we need to worry about orienting the vestigia (traces of God imprinted in Creation) so we add relationality as something external; relationality is there in the beginning, as God knowing us.
Is remembering, understanding, and willing oneself a relational activity? If it's sought on the right terms, it is. That means that it is not the pre-eminent goal , but a means, the bridge that must be crossed to gain access to other places. That means that remembering, understanding, and willing have God as their goal even before he is their object. Augustine comments in another draft of the psychological image:
This word is conceived in love of either the creature or the creator, that is of changeable nature or unchangeable truth; which means either in covetousness or in charity. Not that the creature is not to be loved, but if that love is related to the creator it will no longer be covetousness but charity. It is only covetousness when the creature is loved on its own account.
Augustine's discussion of use and enjoyment forbids the psyche to enjoy itself: regardless of immediate object, God is the goal or goal of 'Know thyself.'
In regard to the rest of Creation, it is much easier to read a psychological image as non-relational. His enjoyment/use distinction is not utilitarian but helped make utilitarianism. Whilst he chose Christianity over Manicheanism and Platonism, these other beliefs left a lasting imprint; Augustine rejected their claims that matter was evil, but his conversion to believing in the goodness of created matter was less thorough than one could desire. At one point Augustine considered sex a major to reject marriage; later he acknowledged sex an instrumental good when it propagates the people of God. Augustine's much-criticised views on sex were in continuity with his understanding of creation, especially material creation. The created order that is neither called evil nor fully embraced as good, even fallen good: 'Cleansed from all infection of corruption, they are established in tranquil abodes until they get their bodies back—but incorruptible bodies now, which will be their guerdon [beneficial help], not their burden.' This negative view of our (current) bodies is not a view of something one would want to be in relation with, and that is part of who we are created to be. From these, one could argue a continuity, if perhaps not parity, with a mindset that would support an individualistic psychological image. The argument has some plausibility, but I believe it is not ultimately true.
The biggest difference between a person and mere matter is that a person has spirit. Augustine can say, 'Now let us remove from our consideration of this matter all the many other things of which man consists, and to find what we are looking for with as much clarity as possible in these matters, let us only discuss the mind,' and abstract away a person's body to see the mind. I did not find a parallel passage abstracting away a person's mind to see body alone. Even if we assume he remained fully Manichean or fully Platonist, both Manicheanism and Platonism find some people to be above the level of matter. Augustine was free enough of Platonism to forcefully defend the resurrection of the body in De Civitate Dei (The City of God). His belief in community is strong enough to make the interpersonal image important in his discussion. As argued in 'Mindset Considerations', he was quite far from individualism to begin with.
If community is important, why have a psychological image? Let me give one line of speculation. Augustine may be trying to put community on a proper ground. The Trinity turns outwards, not in an attempt to remedy any kind of defect, to try to get the creation to fill some need that it can't fill itself. The Trinity turns outwards out of abundance and fulness. Augustine may not want half persons seeking other half persons to try and create fulness. I believe he wants whole persons turning outwards out of the fulness within. In other words, a psychological image lays the ground for robust interpersonal relationship. Leaving this speculation aside, community was deeply ingrained in the patristic mindset, so that it didn't need saying. A psychological image could be explored without Augustine needing to add constant footnotes saying, 'But I still believe in community.'
III. What understanding does Augustine hold in the end?
Augustine explores a number of possible images of the Trinity before settling on one. He starts with an interpersonal image of lover, beloved, and love representing Father, Son, and Spirit respectively. Then he explores a 'psychological' image of mind, mental word, and will, which he revises into memory, understanding, and will.  Besides these images there are others not explored in this essay, such as thing seen, sense impression formed, and will. I would like to show which image Augustine chooses.
I would also like to make a distinction which makes sense of his choosing one image from several candidates. The distinction is the distinction between images that are 'built in' and 'after the fact'. The difference between an image that is 'after the fact' and one that is 'built in' is the difference between a portrait which resembles a person, and a cloud in which a resemblance is found. Is the image something prior to anything observable, something around which other things are shaped, or is the image what we can find when we find things that look like a trinity?
This is arguably latent in Augustine's discussion of enigmas, and in remarks like 'It is true of all of his creatures, both spiritual and corporeal, that he does not know them because they are, but that they are because he knows them.' The discussion of enigmas discusses things mysteriously hidden and then brought forth: Augustine mentions the story of Hagar and Sarah and then Paul drawing out their hidden symbolism. He wrote, 'As far as I can see then, by the word "mirror" he wanted us to understand an image, and by the word "enigma" he was indicating that although it is a likeness, it is an obscure one and difficult to penetrate.' Augustine has looked through any number of images 'after the fact.' Now Augustine is trying to find out which of these plausible 'after the fact' candidates holds its plausibility precisely because it is the image 'built in'. He wants to know which of the resemblances to the Trinity is there precisely because the Trinity created it to be 'after our likeness'.
What, at heart, is the distance between an image 'built in' and 'after the fact'? An 'after the fact' image is an 'after the fact image' because the behaviour and properties it shows, whilst a 'built in' image is such by its internal logic. An early draft of the psychological image compares the mind to the Father, its word to the Son, and the will joining them together to the Holy Spirit. Augustine, conscious of Arianism, says that a human mental word is equal to the mind that begot it. Even if he did not say this, and the word was described as inferior to the mind, there would be reason to see the mind/word/will psychological image as a 'built in' image. A person looking for an 'after the fact' image would look for the property that word and mind are equal because Father and Son are equal; if we look at 'built in' logic it is possible that uncreated God can beget a Word equal to himself, but a creaturely mind lacks the stature to beget a word that is its equal. Then the image would lack the property of equality, but it would have the internal logic of begetting what word one can beget, and reflect the Trinity at a deeper level.  This is like the difference between a literal translation and a dynamic equivalent. A literal translation tries to faithfully represent the text word for word; a dynamic equivalent tries to faithfully represent the text's impact, and it may give the text much more breathing room than a literal translator feels is respectful. A literal translation preserves details, but only a dynamic equivalent can render a poem into something that breathes as poetry. This may be part of why Williams writes, 'Growing into the image of God, then, is not a matter of perfecting our possession of certain qualities held in common with God... It is for us to be at home with our created selves...' Growing into the image of God is not to look as if we had not been created, a literal rendering of God's attributes, but a creaturely dynamic equivalent in which a glimpse of the Trinity is rendered in creaturely idiom. This is inadequate; the creaturely idiom isn't powerful enough to capture the divine original, regardless of how it is rendered. Yet Augustine does settle on one image, one translation, not just as bearing 'after the fact' resemblance, but as having been constructed to have a 'built in' resemblance.
At the end of XV.3, Augustine quotes Wisdom 13:1-5 on recognising creation as the work of the Creator, and comments:
I quote this passage from the book of Wisdom in case any of the faithful should reckon I have been wasting time for nothing in first searching creation for signs of that supreme trinity we are looking for when we are looking for God, going step by step through various trinities of different sorts until we arrive at the mind of man.
This sets the programme for much of book XV. This program has subtleties of various sorts, and Augustine says far more than merely settling on the psychological image. The mind is the genuine image of the Trinity in that God has projected his own likeness downwards, but if we try to project anything in creation upwards—even the image God himself has fashioned—it must fall immeasurably short. The most faithful photograph captures at best a glimpse of the living person it portrays. So while Augustine settles with the psychological image, he is careful to portray its fundamental incompleteness. The psychological image may hold a unique privelege. Of all the 'after the fact' images surveyed, it alone bears apparent 'after the fact' resemblance because it was built to be image. In the end, this privelege of place underscores the book's apophasis all the more powerfully. Not only do the various apparent 'after the fact' images which we see fail to accurately convey the Trinity, but theimage which the Trinity itself has built into us, itself falls fundamentally short of God's transcendence. This is a far greater testimony to the divine transcendence: if an 'after the fact' image breaks down on closer observation, that only says that one specific 'after the fact' image breaks down on closer inspection. When the one 'built in' image, created by the Trinity itself, also breaks down, this says that the Trinity utterly transcends anything the creation can contain. The bigger it is, the immeasurably harder it falls, and the more we can learn from its failure.
But is this a failure of the created image?
Let's look more specifically at Augustine settling on the psychological image. In book X, Augustine writes:
These three, then, memory, understanding, and will, are not three lives but one life, not three minds but one mind.... Are we already then in a position to rise with all our powers of concentration to that supreme and most high being of which the human mind is the unequal image, but image nonetheless? [emphasis added]
This is an important distinction. Augustine is not looking for a perfect and uncreated image of the Trinity, as the Son is the perfect and uncreated image of the Father. This is stated here, but I am not sure that this is a basic insight which informed his thought. He writes,
Again, there is this enormous difference, that whether we talk about mind in man and its knowledge and love, or whether about memory, understanding, and will, we remember nothing of the mind except through memory, and understand nothing except through understanding, and love nothing except through will. But who would presume to say that the Father does not understand either himself or the Son or the Holy Spirit except through the Son...
This is an observation that the 'built in' image he has chosen does not have what one would seek in a 'after the fact' image. In the surrounding text, Augustine doesn't explicitly state that the differences are failings. However the long discussion of how much of the Trinity is not captured in this image does not seem a verbose way of saying that this image functions along 'built in' rather than 'after the fact' lines. It seems to be criticising the 'built in' image for failing to demonstrate 'after the fact' properties. If so, Augustine made something like a category error. This would suggest that the meticulous Augustine, so careful in accounting for the details of Bible verses, didn't conceive this as something to be meticulous about. The impression I receive from reading Augustine is that Augustine probably had thoughts like the 'built in'/'after the fact' distinction I drew, but they were probably tacit, much less developed and much less prominent, and in particular not an organising principle or winnowing tool Augustine used in deciding which of many trinities he would rest with.
And there are other texts which show a psychological image:
So the trinity as a thing in itself is quite different from the image of the trinity in another thing. It is on account of this image that the thing in which these three [memory, understanding, and love] are found is simultaneously called image...
IV. Directions for further enquiry
The distinction between 'built in' and 'after the fact' appears to be significant. It would be interesting to study more specifically what is the relation between Augustine and this concept. There are quotations one could piece together to argue that Augustine thought in these terms, but other passages make this somewhat less clear. I have raised a question, but I believe more work needs to be done. My comments about that distinction in regard to Augustine's choice of image may be treated more as a question than an answer.
People who read Augustine as overly unitarian seem to find a psychological image, and people who read him as a balanced Trinitarian seem to find an interpersonal image. Reading the psychological image as relational may suggest an alternative placement with regard to these basic positions.
The earliest Church Fathers, writing more or less systematic theological treatises, generally didn't write about the Church. Was this because it was not important or not believed? To the contrary, it was air they breathed so deeply that they would never have thought of that as needing saying. Augustine was a Church Father and had the mindset of a Church Father. He chose a psychological image and did not try too hard to make it relational because he never thought it was the sort of thing that needed to have relationship added.
I have chosen an obvious reading which people may give people pause because it appears individualistic and not relational; this reading is that Augustine chose memory, understanding, and will as the 'built in' image of the Trinity. Of things raised in this essay that could merit further study, the most interesting is probably the concept of 'built in' images as contrasted with 'after the fact' images.
Ayres, Lewis, 'The Discipline of Self-Knowledge in Augustine's De Trinitate Book X', in ed. Ayres, Lewis, The Passionate Intellect, Rutgers University Studies in the Classical Humanities, vol. 7, Brunswick: Transaction, 1995, pp. 261-96
Bourassa, F., 'Théologie trinitaire chez s. Augustin', Gregorianum 58, 1997
Brown, Peter, Augustine of Hippo (revised edition), London: Faber and Faber Ltd., 1967, 2000
Cavadini, John, 'The Structure and Intention of Augustine's De Trinitate,' Augustinian Studies 23, 1992
Fitzgerald, Allan D. (ed.), Augustine through the Ages: An Encyclopedia, Eerdmans: Grand Rapids, 1999
Hill, Edmund (tr.), The Trinity, New City Press: Hyde Park, 1991.
MAXIMOS O PLANOUDHS, AUGUSTONOU PERI TRIADOS BIBLIA PENTEKAILEKA APER EK TES LATINON DIALEKTOU EIS THN ELLADA METENEGKE, AQENAI: KENTRON EKDOSEWS ERGWN ELLHNON SUGGRAFEWN, 1995 (Maximus the Traveler, Augustine's On the Trinity, Fifteen Books From the Latin Translated to [medieval] Greek Brought Together [in parallel translation], Athens: Center For Giving Greek Work and Collaborative Writing, 1995)
Meyendorff, John, Byzantine Theology. Historical Trends and Doctrinal Themes, London, 1975
Williams, Rowan, 'Sapientia and the Trinity: Reflections on the De Trinitate', Augustiniana, 1990.
Yates, Frances, The Art of Memory, London: Routledge and Kegan Paul Ltd., 1966, pp. 1-49
 Williams 1990, 317-332
 Williams 1990, 317
 Meyendorff 1974 (page number not specified), as quoted in Williams 1990, 317
 II.19-22; Williams 1990, 317-332. Unless otherwise noted, all references to Augustine are from De Trinitate, and all English quotations from De Trinitate are from Hill's translation.
 'The mind you see is not told Know thyself in the same way as it might be told "Know the cherubim and seraphim"; of them, as absent beings, we believe what they are declared to be, that they are certain heavenly powers.' (X.12)
 These latter observations in the same paragraph are taken from Fitzgerald 1999, 454-5.
 X.12 presents 'thyself' as more immediately knowable than (higher) 'cherubim and seraphim'.
 Hill 1991, 283-4.
 Fitzgerald 1999, 341, 591.
 Ibid., 535-6.
 Fitzgerald 1999, 653.
'Memory', 'understanding', 'will', and (mental) 'word' are all understood very differently in Augustine from their meanings today. I can give a bare hint at the nature of difference by saying will is not a Neitzchian Übermensch's power to domineer, crush, and persevere in lonely selfishness, but something whose nature is to incline towards the other in love, and something that holds things together even inside a person. Beyond that, it would be at least another essay to try to explain these different concepts. I'm going to have to content myself with saying there are significant cultural differences that I can't fairly explain. A good understanding of Augustine's memory, for instance, is suggested by reading Confessions X, complemented by Yates' (1966, 1-49) treatment of memory in relation to ancient rhetoric.
 I have thought of this distinction out of discussion of universalia ante rem and universalia post rem that I had read, and I had originally used the more precise, if less vivid, terminology of 'ante rem' and 'post rem' for 'built-in' and 'after the fact' respectively. So far as I know, this usage is original to me.
 Gen 1:26, RSV
 This distinction applies to other images Augustine looks at; I chose and modified this example to highlight something also present in other parts of the text.
 Williams 1990, 321