In Barth’s section on “God the Father” in volume one of his Church Dogmatics, he makes some interesting statements about the relationship between the Father and the Son.
He opens his discussion with this affirmation of the deity of the Son:
Who is the Lord and therefore the God to whom the Bible is referring? As we have seen already, it is typical of the Bible in both the Old Testament and the New that its answer to this question does not point us primarily to a sphere beyond human history but rather to the very centre of this history.
The answer is that at the climax of the biblical witness Jesus of Nazareth is the Kyrios. He is the One who approaches man in absolute superiority. He is the self-revealing God. (I, 1, 384)
Just a little further he says,
In the first instance the New Testament ascribes the true and real deity expressed by the predicate Kyrios to One who is quite other than Jesus.
In the name Christ, which it gives to Jesus, it reminds us of the prophets, priests and kings of the Old Testament as authorised and sanctified men of Yahweh behind whom and above whom there stands the One who is primarily and properly authoritative and holy. It calls Jesus the Word or Son of God, the One who was sent into the world by God as the light and life of men. It understands the dignity of Jesus, the lordship of Jesus and the superiority of Jesus as basically different and subordinate compared to that of the Other who is properly called θεός. In the so-called Synoptic Gospels this approach is especially prominent. It almost sounds like a false note, and is certainly an enigma, when even and precisely in these Gospels Jesus is called Kyrios. . . . The One who is properly called God in the Synoptics seems unquestionably to be the “Father in heaven” who constitutes the background of the event recorded and therefore, with incomparable significance, the basis of its meaning. Even in John there not only stands the much-noted “The Father is greater than I” (Jn. 14:28) but once again Jesus consistently portrays Himself as the emissary of the Father (the μόνος ἀληθινὸς θεός, Jn. 17:3) whose life is to do His will and speak His words and finish His work, whose triumph is simply to go to the Father, and through whom men come to the Father (Jn. 14:6). (I, 1, 385)
Then he turns to Paul, who
never tired of pointing to the Father, the “Father of Jesus Christ,” who is side by side with Jesus and in some sense beyond Him and above Him. The greeting in nearly all his letters runs: Χάρις ὑμῖν καὶ εἰρήνη ἀπὸ θεοῦ πατρὸς ἡμῶν καὶ κυρίου Ἰησοῦ Χριστοῦ. Does this imply that he is expressly calling “God our Father” the Father of our Lord Jesus Christ too? According to Eph. 1:17, where He is called ὁ θεὸς τοῦ κυρίου ἡμῶν Ἰησοῦ Χριστοῦ, ὁ πατὴρ πῆς δόζης this might undoubtedly be the case. Or is it that the two, θεὸς πατήρ and κύριος Ἰησοῦς Χριστός, as is assumed in the Vulgate and Luther’s translation, are set alongside one another as the common source of grace and peace? What is beyond question is that the κύριος Ἰησοῦς Χριστός is separate from and subordinate to θεὸς πατήρ· Ἠμῖν εἷς θεὸς ὁ πατὴρ . . . καὶ εἷς κύριος Ἰησοῦς Χριστός (1 Cor. 8:6); ὑμεῖς δὲ Χριστοῦ, Χριστὸς δὲ θεοῦ (1 Cor. 3:23); Ἀνδρὸς ἡ κεφαλὴ ὁ Χριστός ἐστιν . . . κεφαλὴ δὲ τοῦ Χριστοῦ ὁ θεός (1 Cor. 11:3). Jesus Christ is κύριος εἰς δόξαν θεοῦ πατρός (Phil. 2:11), He is the προσαγωγὴ πρὸς τὸν θεόν (Eph. 2:18). He will finally hand over the kingdom τῷ θεῷ καὶ πατρί (1 Cor. 15:24). He is the εἰκὼν τοῦ θεοῦ (2 Cor. 4:4; Col. 1:15). And so Hebrews calls Him the ἀπαύγασμα τῆς δόξης (Heb. 1:3), the πιστὸν ὅντα τῷ ποιήσαντι αὐτόν (Heb. 3:2), who offered Himself without spot to God (Heb. 9:14) . . . . Looked at along these lines the lordship of Jesus as the Son of God is obviously only a manifestation, exercise and application of the lordship of God the Father. The essence of the deity ascribed to Jesus is to make clear and impart and give effect to who God the Father is, who God is in the true sense, and what He wills and does with man. It is to represent this God the Father. (I, 1, 385–86)
I readily admit that I’m not a Barth scholar, but I have a hard time meshing the above with the completely egalitarian picture of the Trinity that Kevin Giles tries to paint of Barth in The Trinity and Subordinationism, 87–91. It’s not at all clear that what Barth says can be explained merely in terms of the temporal incarnate ministry of Christ.
While Giles acknowledges that Barth made some statements that don’t fit well with a completely egalitarian trinitarianism (88), he suggests that Barth’s theology changed and that these earlier statements are not representative of the mature thought of Barth. Again, I haven’t read enough of Barth to be able to challenge that assertion, but I will note that the texts that led me to this passage (1 Cor 3:23; 8:6; 11:3; 15:28) don’t get later explications that contradict what Barth says here. Rather, Barth’s discussions of them elsewhere in his CD seem to concur with his earlier remarks (e.g., III, 3, 440).