Both Van Til and Barth rejected all forms of bare theism. That is, they denied a generic view of God. Both believed this “god” was an idol. This is the god of human autonomy and philosophy. It comes from an apologetic approach which seeks to first prove or show that there is “a god” before it seeks to prove that this god is in fact the Triune God of Christianity. The blame for this approach may, arguably, be placed at the feet of Thomas Aquinas who first seeks to prove “an unmoved mover” on the ground of reason before he moves to talk about the Trinity from divine revelation. The impression left is that there is validity to speaking about God in any other way than the Triune God of Scripture.
Van Til says this about that idea:
It is accordingly no easier for sinners to accept God’s revelation in nature than to accept God’s revelation in Scripture. They are no more ready of themselves to do the one than to do the other. From the point of view of the sinner, theism is as objectionable as is Christianity. Theism that is worthy of the name is Christian theism. Christ said that no man can come to the Father but by him. No one can become a theist unless he becomes a Christian. Any god that is not the Father of our Lord Jesus Christ is not God but an idol. (Christian Apologetics, 79)
For Van Til the God of creation is the Triune God. The God of the Old Testament is also the Triune God. That unbelievers or the saints of the Old Testament do not articulate a Nicean doctrine of the Trinity does not mean that God is anything else or anything other than Father, Son, and Holy Spirit; the one God who is at the same time three persons. The God who reveals himself in both nature and Scripture is the one Triune God.
Van Til and Barth share a common anti-Scholasticism at this point.
But, unfortunately, here the commonality ends. As we mentioned in an earlier post, Barth’s ontological starting part is actualism. That is, things are understand properly only by way of their acts and relations. So, for instance, there is no eternal Logos (i.e., the Word of John 1:1) who stands behind or apart from Jesus Christ as the Logos come in human flesh. So when he says the only God who is is the Christian God he is not affirming what Van Til is affirming. For Van Til the Triune God has always existed, even quite prior to and independent of the incarnation. What is more, the Triune God—Father, Son, and Holy Spirit—existed eternally and happily even prior to and independent of his decision to create and redeem by becoming the God-man in Jesus Christ. But for Barth the Triune God is who he is precisely because and only insomuch as he is the God who from all eternity has acted by way of a sovereign and free decision to become Father, Son, and Holy Spirit in and by Jesus Christ.
To put it in very simple terms, for Barth God is dependent on creation (even the humanity of the incarnate Logos) to be (more accurately: to eternally become) a Trinity. However, for Van Til the God of the Scriptures is “the self-contained ontological Trinity.” (see, for example, Christian Apologetics, p. 97). In other words, for Barth God’s act of grace toward his creatures in Christ becomes the constituting event which renders God as Trinity. For Van Til God does not need to be constituted as Trinity, for he is always and everywhere Trinity, and as Trinity the sovereign Lord over creation.
Unfortunately, the logical conclusion to Barth’s approach is that creation is sovereign over his god.
And that god is no Christian God. But for Van Til the Triune God is the Christian God—and the only God—precisely because he is not dependent on creation for his being or identity. If there never was a fall, there would be no incarnation. And still God would be Trinity. Perhaps the irony is that, according to Van Til, the Triune God does not need the incarnate Christ in order to be the Christian God. To say otherwise is to make God dependent on the creature. And a dependent God can in no way be the God and Father of our Lord Jesus Christ.
 I understand that whether or not, or to what extent, God’s act of electing grace in Christ constitutes his being as Triune is hotly debated among Barth scholars. I do not intend to engage that discussion here. I make this statement without prejudice to the current debate. I am simply speaking from within the context of how Van Til himself reads Barth.