The Eunomians, following the Arians (and Arius) maintained that there was a time when the Son was not. In other words, they maintained that the Logos of God was a creature; an exalted creature, but a creature nonetheless. So, when we see Jesus, we don’t actually see the Father in the face of the Son, we only see an exalted emissary of the singular 
(monadic) God of pure being. In a similar line of heresy, known as adoptionism, the Ebionites maintained that Jesus was just a man, already existent, that God adopted for His purposes to be His prophet. TF Torrance provides definition: “Ebionism — the view that Jesus was not God but an ordinary man, adopted to become Son of God.”[1] Ultimately, adoptionism applies to most Christological heresies wherein, as the central feature, Jesus isn’t God, but simply adopted into God’s purposes as a Prophet (akin to an exalted version of an Old Testament prophet, or the final prophet in the line of the Prophetic school—ironically this is exactly the way Muslims see Jesus, as a mere man and prophet of God—also ironically Mohammed spent significant time with his uncle, an Ebionite “Christian”).
In contrast to this heresy of adoptionism, the orthodox Church fathers introduced an important dogmatic teaching with reference to the personhood of Jesus Christ. They argued, from the inner-logic of Scripture and its reality in the analogy of the incarnation, that Jesus had no personal independence from the second person of the Godhead in the eternal Son. So, they contended, the ground of the singular person of Jesus Christ, the personalizing, personating reality, was the person of the Son who has always already eternally been the Son of the Father, as the Father has been the Father of the Son in the eternal bond of koinonia and self-given love provided for by the unioning work of the Holy Spirit. Torrance explains the significance of this at length:
(i) The humanity of Jesus has no independent reality
The first thing we have to note here, is that, taken together with anhypostasia, for the two are not to be separated, the enhypostasia asserts that the incarnation is an act of pure grace alone, and repudiates any form of adoptionism, that is the adoption of a preexisting man to become Son of God. It asserts then that true man is a predicate of God’s gracious action. When the Word was made flesh, God and man were so related that Jesus came to exist as man only so far as he now exists as God. In other words, there is only one Christ, one mediator, one Lord, only one person in Jesus Christ the incarnate Son of God. This one person means that his human nature had no independent subsistence or hypostasis, no independent centre of personal being. If there had been a human person to whom a divine person was added, there would have been an independent centre of personal being in Jesus over against the person of the Son of God; but the human nature of Jesus never existed apart from the incarnation of God the Son. At the first moment of the existence of his human nature, it was in hypostatic union with his Godhead. That is, the human nature from the first moment of its existence had its hypostasis or personal subsistence in the personal subsistence of God the Son. That is the meaning of en-hypostasis.
(ii) The humanity of Jesus has full reality in the person of the Son
But when we have said that, we have to add that although there was no independent personal being called Jesus apart from the incarnation, that does not mean that in the incarnation there was no particular individual called Jesus existing as a particular human being, with a rational human mind and will and soul; and therefore it does not mean that he did not completely possess human nature. Jesus had a fully human mind and human soul and human will; he lived a fully human life in hypostatic union with his divine life, and in that union with his divine life, his human life had manifested the most singular and unique personality as man. That is the emphasis of enhypostasia. It preserves the acknowledgement of the full humanity of Jesus, and indeed of his historical person as a man among others, and as one of mankind, a true man. The anhypostasia stresses the general humanity of Jesus, the human nature assumed by the Son with its hypostasis in the Son, but enhypostasia stresses the particular humanity of the one man Jesus, whose person is not other than the person of the divine Son.
Therefore from the enhypostasis we have to go back again to the anhypostasis and say this: while the Son of God assumed our human nature, and became fully and really like us, nevertheless his full and complete human nature was united to God in a unique way (hypostatically in one person) as our human nature is not, and never will be. Therefore he is unlike us, not unlike us as to the humanity of his human nature, but in the unique union of his human nature to the divine nature in the one person of God the Son. (This is the baffling element in the virgin birth, which tells us that while it is our very human nature he assumed, he did not assume it in the way we share in it, because he took it in a unique relation with his deity). But it is upon the unique, hypostatic relation of his human nature to his divine nature, that the truth of our human nature depends, for it is as we share in his human nature, which is hypostatically united to God, that we are in union and communion with God.[2]
The next time you come across someone who denies the deity of Jesus just say: anhypostasia/ en-hypostasia! Then explain to them that Jesus has no independent existence as a human being apart from the personalizing personhood of the eternal Son of God. That Jesus’ singular person as both fully human and fully God is funded by, grounded in the eternal Logos’ person as the second person of the divine Monarxia (Godhead). Tell them further that to genuinely think biblically materially about these matters follows the lead of the patristics who posited this aesthetically pleasing doctrine of an/ -enhypostasis. That is to say, to attempt to think biblically about who Jesus was/is requires the conclusion that the Son enfleshed in the man from Nazareth, Jesus Christ; and that without this free and gracious action of the Son in concord with the indivisibility of the triune life, that there never would have been a man from the Galilee whose name was Jesus Christ. Tell them this is the unique sui generis reality of Jesus Christ: that is, that He is Theanthropos the Godman, or He isn’t at all. Tell them that the adoptionist notion, with reference to the man, Jesus, is driven by an over-reliance on a rationalistic philosophical maneuver wherein the miracle of the ineffable God become human is so domesticated, so gated-in by the dusty mind of little men and women, that it ends up being a fantasy of the human imagination; that it becomes a way to cope with the unfathomable, and make it fathomable—make it small enough to be generated by thinking from a sense of human pure nature (that is an independent human nature that is not contingent upon God’s Word, but theirs).
There are other significant implications of this doctrine, particularly when we get to a doctrine of pre-destination and election/reprobation. We won’t pursue those here. Further, and recently in his book The Humility of the Eternal Son: Reformed Kenoticism and the Repair of Chalcedon Bruce McCormack critiques the patristic, and Barth’s reception of the doctrine of an/ -enhypostasis as not adequate to the task of thinking the personhood of Jesus Christ. In its place McCormack constructively offers his alternative which he identifies as ontological receptivity. We will have to pursue that further at a later time as well (although I have broached BLM’s book here).
[1] T. F. Torrance, ed. Robert T. Walker, Incarnation: The Person and Life of Christ (Downers Grove, IL: IVP Academic, 2008).
[2] Ibid., 229-30.