“The” doctrine of the Trinity was established neither at Nicea (325 AD) nor at Constantinople (381 AD). In catholic lore, it is all supposed to hang on the then novel term homoousios – but it does not – that is, not only on that. This one catholic Trinity doctrine is in fact not a fully determinate doctrine at all, but only a template, a set of boundaries within which to build a doctrine. (Not unlike the statement from Chalcedon in 451 AD.) Hence, the plethora of mutually incompatible theories since, all aiming to be catholic.
By itself this template gives one only a vague, fuzzy mental image of what “the Trinity” or “the triune God” amounts to. Admittedly, many individual Christians and denominations are perfectly happy with that, as evidenced by the proliferation of formulaes which can only be hopelessly vague to one seeking evidence for or against them. (e.g. “one God, existing in three Persons”)
Back to the fourth century, though. I found this passage from patristic scholar Mark Edwards’s Catholicity and Heresy in the Early Church helpful. I think he sketches the template somewhat too specifically, but he makes a number of excellent points. (I’ve silently corrected a few obvious typos and added some bold highlights and links.)
For over 1,500 years the presuposition of systematic theology has been a doctrine of the Trinity which states that there are three divine persons, Father, Son, and Holy Spirit, each of whom is properly and fully identical both with the being called God and with that substance or nature which we call the Godhead. It is both a logical and ecclesiastic deduction from these tenets that the Godhead is identical with God – to speak philosophically, that the essence of God is identical to his existence – but the church does not accept that the identity of each person with the Godhead entails that the persons are identical with one another. Nor is it acceptable to argue that each is God individually while all three are generically identical with the Godhead, for that would be, not only to divorce God from his essence, but to treat this essence as though it were a category or species exemplified by three particulars, as the human species is exemplified by particular humans. That would be to postulate three gods, whereas the axiom of good Churchmanship is that, while the Father is God and the Son is God and the Holy Spirit is God, there are none the less not three gods but one.
It is also held as an indefeasible premise that no one of the three is greater or less than either of the other two, though it is admitted that the Son and the Spirit depend upon the Father for their existence and that in the divine economy it is they who are sent by the Father and the Son who saves the world by his obedience. To infer that this obedience bespeaks inferiority to the Father is the heresy of ‘subordinationism’; to suggest that because the Son and Spirity depend upon the Father they are posterior to him in time is Arianism; to circumvent the difficulties of the orthodox doctrine by treating the persons merely as designation of the same divine subject in distinct epiphanies is ‘modalism’, ‘monarchianism’, or ‘Sabellianism’. The names are a coaltion of ancient and modern; the teaching is supposed to be that of the creeds established in the patristic era, though in fact it is clearly adumbrated only in [the so-called "Athanasian" creed]… A modern theologian who is challenged to state its provenance is likely to answer either that it can be derived from scriptural testimonies – a claim that now appears fanciful to most professional students of the New Testament – or that the nucleus of it is found in the creed that was promulgated in 325 at the Council of Nicea and refined by the Second Oecumenical Council of 381. The majority of scholars now engaged in writing the history of doctrine in the first five centuries of the Christian era would agree that this is too sanguine a reading even of the text that is somewhat questionably traced to Constantinople in 381, let alone of the [325 creed]. (pp. 105-6)
I would put the point more bluntly. Look at the 325 and 381 creeds. They start off, like many earlier, non-trinitarian creeds with confession of belief in the one God, the Father. They go one to insist that this one true God shares his ousia with one or two others. But no triune God, no tripersonal God of equally divine persons, is stated in those creeds. There’s nothing close to that in the 325 creed. The 381 creed – or rather a letter attached to it – does get close, in its assertion that “the Father, the Son and the holy Spirit have a single Godhead and power and substance” and its talk of “the uncreated and consubstantial and co-eternal Trinity.” But one has to keep in mind that in early Trinity talk the one God isn’t thought of as the whole Trinity, but rather as one member of it. But still, even that creed appears to identify the one God with the Father at the outset (like the New Testament, and most pre-Nicene catholic “fathers.”)
In the rest of the chapter Edwards parses through many definitions of “Arian” and relates this to what we think various parties in the mid 300s actually thought. It is a refreshing alternative to many textbook and history book retellings which essentially parrot Athenasius’s side of the dispute, on which the Arians are theological retards and worthless human beings. Here’s one more helpful passage from that chapter:
‘Subordinationism’ is almost a synonym for ‘Arianism’ in modern historiography, but in the Church of the first five centuries it was not a recognized category of error. Before the Nicene council the affirmation of equality between persons of the Godhead could be regarded as a dangerous compromise with the polytheism of the ambient culture; more pernicious still… were the Gnostic myths in which the Creator is overthrown by an heir whom he sires in ignorance, or the exegesis of Genesis 1:3 according to which the Father prays to the Son for light. If one holds not only that the other two persons depend for their existence on the Father, but that the unity of the Godhead resides in his primacy as cause, one is almost bound to conclude that in some sense he is greater than the Son. Even to Athanasius this is the natural exegesis of Christ’s own confession at John 14:28. (pp. 113-4)
Right. The Father, but not the other two, will, given the generation and procession speculations, exist a se, or idendependently of any other. And there’s no reason to limit the term “subordinationist” to the so-called “Arians” of the 4th century, for the term “subordinationist” well describes some early theologians like Origen, who when challenged on their monotheism emphasize how much greater the Father (Yahweh) is than the Son, though both are, singly, called “God.” But more on that another time.