Those interested in ‘subordination’ or its absence, and eternal begottenness Nicea -style, ought to take a look at what Warfield has to say about such questions. Below is a section toward the end of his paper ‘The Biblical Doctrine of the Trinity’ (Biblical Doctrines). The paper can be downloaded as a PDF by Googling it. In keeping with the theme, I've split up the section into three consecutive parts, as Warfield’s stately, compressed style needs to be read carefully.
‘Begottenness' in the NT
It may be very natural to see in the designation "Son" an intimation of subordination and derivation of Being, and it may not be difficult to ascribe a similar connotation to the term "Spirit." But it is quite certain that this was not the denotation of either term in the Semitic consciousness, which underlies the phraseology of Scripture; and it may even be thought doubtful whether it was included even in their remoter suggestions. What underlies the conception of sonship in Scriptural speech is just "likeness"; whatever the father is that the son is also. The emphatic application of the term "Son" to one of the Trinitarian Persons, accordingly, asserts rather His equality with the Father than His subordination to the Father; and if there is any implication of derivation in it, it would appear to be very distant. The adjunction of the adjective "only begotten" (Jn. i. 14; iii. 16-18; I Jn. iv. 9) need add only the idea of uniqueness, not of derivation (Ps. xxii. 20; xxv. 16; xxxv. 17; Wisd. vii. 22 m.); and even such a phrase as "God only begotten" (Jn. i. 18 m.) may contain no implication of derivation, but only of absolutely unique consubstantiality; as also such a phrase as "the first-begotten of all creation" (Col. i. 15) may convey no intimation of coming into being, but merely assert priority of existence. In like manner, the designation "Spirit of God" or "Spirit of Jehovah," which meets us frequently in the Old Testament, certainly does not convey the idea there either of derivation or of subordination, but is just the executive name of God --- the designation of God from the point of view of His activity - and imports accordingly identity with God; and there is no reason to suppose that, in passing from the Old Testament to the New Testament, the term has taken on an essentially different meaning. It happens, oddly enough, moreover, that we have in the New Testament itself what amounts almost to formal definitions of the two terms "Son" and "Spirit," and in both cases the stress is laid on the notion of equality or sameness. In Jn. v.18 we read: 'On this account, therefore, the Jews sought the more to kill him, because, not only did he break the Sabbath, but also called God his own Father, making himself equal to God.' The point lies, of course, in the adjective "own." Jesus was, rightly, understood to call God "his own Father," that is, to use the terms "Father" and "Son" not in a merely figurative sense, as when Israel was called God's son, but in the real sense. And this was understood to be claiming to be all that God is. To be the Son of God in any sense was to be like God in that sense; to be God's own Son was to be exactly like God, to be "equal with God." Similarly, we read in I Cor. ii. 10,11:' For the Spirit searcheth all things, yea, the deep things of God. For who of men knoweth the things of a man, save the spirit of man which is in him? Even so the things of God none knoweth, save the Spirit of God.' Here the Spirit appears as the substrate of the Divine self-consciousness, the principle of God's knowledge of Himself: He is, in a word, just God Himself in the innermost essence of His Being. As the spirit of man is the seat of human life, the very life of man itself, so the Spirit of God is His very life-element. How can He be supposed, then, to be subordinate to God, or to derive His Being from God? If, however, the subordination of the Son and Spirit to the Father in modes of subsistence and their derivation from the Father are not implicates of tbeir designation as Son and Spirit, it will be hard to find in the New Testament compelling evidence of their subordination and derivation. (163-4)
1. ‘Son’ and Spirit’ may seem to be obviously subordinate expressions. But this is not the semitic way of understanding these terms.
2. Sonship in 'only begotten Son' is simply ‘likeness’. Whatever the Father is the Son is also. It is thus an assertion of equality with the Father, and not of subordination.
3. So expressions of the ‘begottenness’ of the Son may convey no suggestion of coming into being, but of the Father's priority of existence. And similarly with ‘Spirit’.
4. There are in the NT almost full definitions of Sonship – in John.5.18 – and of Spirit – in I Cor. 2. 10 -11. – that are non-subordinationist.
So what of the subordinationist language in the NT?
There is, of course, no question that in "modes of operation," as it is technically called - that is to say, in the functions ascribed to the several Persons of the Trinity in the redemptive process, and, more broadly, in the entire dealing of God with the world - the principle of subordination is clearly expressed. The Father is first, the Son is second, and the Spirit is third, in the operations of God as revealed to us in general, and very especially in those operations by which redemption is accomplished. Whatever the Father does, He does through the Son (Rom. ii. 16; iii. 22;v. 1,11, 17, 21; Eph. i.5; I Thess. v.9; Tit. iii. v) by the Spirit. The Son is sent by the Father and does His Father's will (Jn. vi. 38); the Spirit is sent by the Son and does not speak from Himself, but only takes of Christ's and shows it unto His people (Jn. xvii. 7 ff.); and we have Our Lord's own word for it that 'one that is sent is not greater than he that sent him' (Jn. xiii. 16). In crisp decisiveness, Our Lord even declares, indeed: 'My Father is greater than I' (Jn. xiv. 28); and Paul tells us that Christ is God's, even as we are Christ's (I Cor. iii. 23), and that as Christ is "the head of every man," so God is "the head of Christ" (I Cor. xi. 3). But it is not so clear that the principle of subordination rules also in "modes of subsistence," as it is technically phrased; that is to say, in the necessary relation of the Persons of the Trinity to one another. The very richness and variety of the expression of their subordination, the one to the other, in modes of operation, create a difficulty in attaining certainty whether they are represented as also subordinate the one to the other in modes of subsistence. Question is raised in each case of apparent intimation of subordination in modes of subsistence, whether it may not, after all, be explicable as only another expression of subordination in modes of operation. It may be natural to assume that a subordination in modes of operation rests on a subordination in modes of subsistence; that the reason why it is the Father that sends the Son and the Son that sends the Spirit is that the Son is subordinate to the Father, and the Spirit to the Son. But we are bound to bear in mind that these relations of subordination in modes of operation may just as well be due to a convention, an agreement, between the Persons of the Trinity - a "Covenant" as it is technically called - by virtue of which a distinct function in the work of redemption is voluntarily assumed by each. It is eminently desirable, therefore, at the least, that some definite evidence of subordination in modes of subsistence should be discoverable before it is assumed. In the case of the relation of the Son to the Father, there is the added difficulty of the incarnation, in which the Son, by the assumption of a creaturely nature into union with Himself, enters into new relations with the Father of a definitely subordinate character. Question has even been raised whether the very designations of Father and Son may not be expressive of these new relations, and therefore without significance with respect to the eternal relations of the Persons so designated. This question must certainly be answered in the negative. Although, no doubt, in many of the instances in which the terms "Father" and "Son" occur, it would be possible to take them of merely economical relations, there ever remain some which are intractable to this treatment, and we may be sure that "Father" and "Son" are applied to their eternal and necessary relations. But these terms, as we have seen, do not appear to imply relations of first and second, superiority and subordination, in modes of subsistence; and the fact of the humiliation of the Son of God for His earthly work does introduce a factor into the interpretation of the passages which import His subordination to the Father, which throws doubt upon the inference from them of an eternal relation of subordination in the Trinity itself. It must at least be said that in the presence of the great New Testament doctrines of the Covenant of Redemption on the one hand, and of the Humiliation of the Son of God for His work's sake and of the Two Natures in the constitution of His Person as incarnated, on the other, the difficulty of interpreting subordinationist passages of eternal relations between the Father and Son becomes extreme. The question continually obtrudes itself, whether they do not rather find their full explanation in the facts embodied in the doctrines of the Covenant, the Humiliation of Christ, and the Two Natures of His incarnated Person. Certainly in such circumstances it were thoroughly illegitimate to press such passages to suggest any subordination for the Son or the Spirit which would in any manner impair that complete identity with the Father in Being and that complete equality with the Father in powers which are constantly presupposed, and frequently emphatically, though only incidentally, asserted for them throughout the whole fabric of the New Testament. (165-7)
1. In the NT there is subordination in the ‘modes of operation’ of the persons in respect of redemption, but it is ‘not so clear’ that there is subordination in each person’s ‘mode of subsistence’, the way in which the person’s are related to each other.
2 It may be that the subordination in respect of redemption rests on subordination in modes of existence, but it might equally well be based not on nature but on convention, a one-willed convention of a covenantal character. And it looks that way because of the pervasiveness of the NT teaching on the Covenant of Redemption, on the humiliation of Christ, and on the two-natured character of Christ.
3. But this must be understood as being not at the expense of the NT’s teaching on the ‘complete identity’ of the three persons in their being and powers. The three are one God.
The three - fold causality of the saving process
The Trinity of the Persons of the Godhead, shown in the incarnation and the redemptive work of God the Son, and the descent and saving work of God the Spirit, is thus everywhere assumed in the New Testament, and comes to repeated fragmentary but none the less emphatic and illuminating expression in its pages. As the roots of its relation are set in the threefold Divine causality of the saving process, it naturally finds an echo also in the consciousness of everyone who has experienced this salvation. Every redeemed soul, knowing himself reconciled with God through His Son, and quickened into newness of life by His Spirit, turns alike to Father, Son and Spirit with the exclamation of reverent gratitude upon his lips, "My Lord and my God!" If he could not construct the doctrine of the Trinity out of his consciousness of salvation, yet the elements of his consciousness of salvation are interpreted to him and reduced to order only by the doctrine of the Trinity which he finds underlying and giving their significance and consistency to the teaching of the Scriptures as to the processes of salvation. By means of this doctrine he is able to think clearly and consequently of his threefold relation to the saving God, experienced by Him as Fatherly love sending a Redeemer, as redeeming love executing redemption, as saving love applying redemption: all manifestations in distinct methods and by distinct agencies of the one seeking and saving love of God. Without the doctrine of the Trinity, his conscious Christian life would be thrown into confusion and left in disorganization if not, indeed, given an air of unreality; with the doctrine of the Trinity, order, significance and reality are brought to every element of it. Accordingly, the doctrine of the Trinity and the doctrine of redemption, historically, stand or fall together. A Unitarian theology is commonly associated with a Pelagian anthropology and a Socinian soteriology. It is a striking testimony which is borne by F. E. Koenig ("Offenbarungsbegriff des AT," 1882, 1,125): ‘I have learned that many cast off the whole history of redemption for no other reason than because they have not attained to a conception of the Triune God." It is in this intimacy of relation between the doctrines of the Trinity and redemption that the ultimate reason lies why the Christian church could not rest until it had attained a definite and well-compacted doctrine of the Trinity. Nothing else could be accepted as an adequate foundation for the experience of the Christian salvation. Neither the Sabellian nor the Arian construction could meet and satisfy the data of the consciousness of salvation, any more than either could meet and satisfy the data of the Scriptural revelation. The data of the Scriptural revelation might, to be sure, have been left unsatisfied: men might have found a modus vivendi with neglected, or even with perverted Scriptural teaching. But perverted or neglected elements of Christian experience are more clamant in their demands for attention and correction. The dissatisfied Christian consciousness necessarily searched the Scriptures, on the emergence of every new attempt to state the doctrine of the nature and relations of God, to see whether these things were true, and never reached contentment until the Scriptural data were given their consistent formulation in a valid doctrine of the Trinity. Here too the heart of man was restless until it found its rest in the Triune God, the author, procurer and applier of salvation. (167-9)
1. The threefold work of God in redemption is echoed and thus borne out in Christian experience.
2. The Christian finds the doctrine of the Trinity underlying and giving their significance and consistency to the teaching of the Scriptures as to the processes of salvation.
3. So the doctrine of the Trinity and the doctrine of redemption stand or fall together.
So if Warfield is correct, what he says affects the theory that the Son is subordinate, being begotten, but subordinate only by a convention, the Persons' co-willingness, the willingness of one eternal will, to take different roles in redemption.