Perhaps the sharpest way to phrase a major difference between Barth and Torrance on the Trinity is that Torrance had no place for the subordination that Barth built into his doctrine of the Trinity. This is, of course, not news to readers of Barth: his understanding of the eternal subordination of the Son is one of the key distinctions of his theology. Torrance resisted this subordinationism on the grounds that Barth had read elements of the economy into the immanent Trinity, and set out to correct Barth on this point. The plainest way to state the differences between the two here is this: Barth follows the Cappodicians in assigning (for lack of a better term) monarchy (or principle of Godhead) to the Father alone, while Torrance follows Athanasius in assigning monarchy to the Trinity as a whole. Indeed, for Torrance, this just is the definition of monarchy, ‘the one ultimate principle of Godhead, in which all three divine Persons share equally, for the whole indivisible Being of God belongs to each of them as it belongs to all of them’ (Torrance, Trinitarian Perpsectives, p. 112)
It is in the CD IV.1 that Barth discusses (implicitly, since he doesn’t use the term ‘monarchy’) what was so troubling to Torrance. Here Barth makes a claim that within the Godhead, within the life of the Trinity, there is ‘one who rules and commands in majesty and one who obeys in humility’ (p. 202). There is absolute authority and absolute obedience. Paul Molnar notes that what appears to happen here is that Barth assigns majesty to the Father, but not to the Son. This is roughly the same logic (though far from the same conclusion) as the Cappodicians doctrine that the Father alone was the principle of the unity of the Godhead, which Torrance notes carried notes of latent subordinationism:
Moreover, the Cappodician interpretation, under a lingering Origenist influence, concealed a serious ambiguity. From one point of view the so-called ‘Cappodician settlement’ meant the rejection of subordinationism, but from another it implied a hierarchial structure within the Godhead. This carried with it an ambiguous element of subordinationism that kept disconcerting thought within the Church and opening the way for division… (The Christian Doctrine of God, p. 182)
While Barth didn’t use the same language of causality as the Cappodicians (‘the uncaused Person of the Father is the cause of the personal nature of the son’ (p. 181) there is a similar kind of thinking here, in that in both the Cappodicians and in Barth there is hierarchy and structure within the Godhead that tilts towards dividing the Father and the Son within the Godhead. This is latent in the Cappodicians but much less so in Barth, who as we saw above explicitly says that within the Trinity there is one who has absolute authority and one who obeys absolutely. The implicit logic is then roughly equivalent to this: if the monarchy is restricted to the Father alone, then a division of the Father and Son appears to be entailed in that the deity of the Son is derived from the deity of the Father.
Torrance turned to Athanasius to combat this subordinationism as well as to resolve problems raised by the filioque (this will be revisited later). Athanasius, for Torrance, had a firmer grasp of the unity and identity of the persons within the Trinity:
He certainly thought of the Father as the Arche (but not Cause) of the Son in that he has eternally begotten the Son. He thus declared ‘We know only one Arche’, but he immediately associated the Son with that Arche, for, he added, ‘we profess to have no other form of Godhead than that of the only God.’ While the son is associated with the Arche of the Fathre in this way, he cannot be thought of as an Arche subsisting in himself, for by his very Nature he is inseperable from the Father of whom he is the Son. By the same token, however, the Father cannot bethought of as an Arche apart from the Son, for it is precisely as Father that he is Father of the Son. ‘The Father and the Son are two, but the Unity of the Godhead is one and indivisible.’ (p. 183)
Torrance here employed the concept of perichoresis. This concept plays an epistemic role for Torrance – the Trinity can only be known as a whole because it is only as a whole that God makes himself known – as well as a more ontological role. Perichoresis for Torrance defines and clarifies the concept of divine monarcy by asserting ‘the full equality of the divine persons’ (p. 175), while also affirming ‘the real distinctions between the divine Persons in their hypostatic relations with one another, as well as their real oneness, and does so by providing the frame within which we may think and speak of the three divine Persons in their proper differences without detracting from their complete equality, in line with the order given in Baptism into the Name of the Father, the Son and the Holy Spirit – the Father first, the Son second, and the Spirit third’ (p. 176). Torrance builds off this understanding of perichoresis to an understanding of divine monarchy where monarchy is understood in a holistic way, the same way we know the Trinity. So, just as we know the Trinity only as a whole, we understand divine monarchy as belonging to the Trinity as a whole. This has the end result of allowing for real distinctions within the Trinity without a hierarchial ordering within the being of the Godhead, thus avoiding a separation of the Father and the Son and a subordination of the latter as a result of that separation.
It was this same understanding of the divine monarchy that formed the backbone of The Agreed Statement on the Trinity, an agreement between the World Alliance of Reformed Churches and the Eastern Orthodox Church which Torrance brokered. Torrance’s own understanding of the Trinity fit neither classical Western nor Eastern patterns:
In in essay detailing the main features of the Agreed Statement Torrance identifies four significant points: First, the Statement affirms the personal status of the Father, the Son and the Holy Spirit but also affirms as orthodox the person status of the one Being of God. Thus in the doctrine of the Holy Trinity the Being of God does not refer to static essence or abstract ousia but to the intrinsically personal “I Am” of God. Second, the statement lays stress on the monarchy of God, “or the one ultimate principle of Godhead, in which all three divine Persons share equally, for the whole indivisible Being of God belongs to each of the as it belongs to all of them.” The monarchy is thus the triune Godhead and the person of the Father, but, strictly speaking, it is the being of the Father, the one triune Godhead, that monarchy actually refers to. Third, and consequently, the Spirit proceeds from the Father, but given the previous definition of monarchy, “the Holy Spirit proceeds ultimately from the Triune Being of the Godhead.” Thus the Spirit proceeds out of the mutual relations within the one being of the Holy Trinity “in which the Father indwells the Spirit and is Himself indwelt by the Spirit.” And finally, the Agreed Statement recommends an approach to the Trinity that is neither from the three persons to the one God (Eastern), but rather, starts with the “dynamic Triunity of God as Trinity in Unity and Unity in Trinity.” (Myk Habtes, Filioque? Nein, in Trinitarian Theology After Barth, eds. Habets and Tolliday, pp. 180-181, bold mine)
Perichoresis plays a key role in ensuring what Torrance saw as lost in Barth’s doctrine of the Trinity: absolute equality of persons. Barth’s assigning of monarchy to the Father over against the Son built in a kind of subordinationism that Torrance saw latent within the Western theological tradition. Torrance saw in Athanasius and others (Cyril and Epiphanius are two other important figures in Torrance’s thinking, though they will be passed over here) a way through the East/West stalemate:
It has been important to say something in detail of the teaching of Athanasius and Epiphanius, for in pressing further the biblical stress of Athanasius on the ‘I am’ of the one ever-living ever acting Being of God understood in his internal relations, Epiphanius did more than any other to clear away problems that had arisen in the doctrine of the Holy Trinity and to prepare the ground for the ecumenical consenssus that was registered in the Nicene-Constantinopalitan Creed. It is important to throw the spotlight on this development today for it is actually somewhat different from what is found in the usual textbook tradition: it was upon the Athanasian-Epiphanian basis that classical Christian theology developed into its flowering in the great work of Cyril of Alexandria. In our day it has been upon the Athanasian-Epiphanian-Cyriline basis, together with the trinitarian teaching of Gregory Nazianzen who insisted that the Monarchia may not be limited to one Person, that doctrinal agreement on the doctrine of the Holy Trinity has been reached between Orthodox and Reformed Churches. It is of particular significance for our discussion here that the conception of perichoresis played a crucial role in clarifying and deepening the conception of the Monarchia for the understanding of the interlocking of Unity and Trinity, Trinity and Unity, in the doctrine of God. (Torrance, The Christian Doctrine of God, pp. 184-185)
In conclusion, I’ll end with a passage of commentary on the Agreed Statement that Torrance quotes directly after the above passage:
Of far-reaching importance is the stress laid upon the Monarchy of the Godhead in which all three divine Persons share, for the whole indivisible Being of God belongs to each of them as it belongs to all of them together. This is reinforced by the unique conception of coinherent or perichoretic relations between the different Persons in which they completely contain and interpenetrate one another while remaining what they distinctly are in their otherness as Father, Son and Holy Spirit. God is intrinsically Triune, Trinity in Unity and Unity in Trinity. There are no degrees of deity in the Holy Trinity, as is implied in a distinction between the underived Deity of the Father and the derived Deity of the Son and the Spirit. Any notion of subordination is completely ruled out. The perfect simplicity and indivisibility of God in his Triune being mean that the Arche or Monarchia cannot be limited to one person, as Gregory the Theologian pointed out. While there are inviolable distinctions within the Holy Trinity, this does not detract from the truth that the whole Being of God belongs to all of them as it belongs to each of the, and thus does not detract from the truth that the Monarchy is One and indivisible, the Trinity in Unity and the Unity in Trinity. (p. 185)
Theologians, Inc. 
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