We turn from our consideration of the incommunicable attributes of God to that of his triunity. The fact that God exists as concrete self-sufficient being appears clearly in the doctrine of the Trinity. Here the God who is numerically and not merely specifically one when compared with an other form of being, now appears to have within himself a distinction of specific and numerical existence. We speak of the essence of God in contrast to the three persons of the Godhead. As we say that each of the attributes of God is to be identified with the being of God, while yet we are justified in making a distinction between them, so we say that each of the persons of the Trinity is exhaustive of divinity itself, while yet there is a genuine distinction between the persons. Unity and plurality are equally ultimate in the Godhead. The persons of the Godhead are mutually exhaustive of one another, and therefore of the essence of the Godhead. God is a one-conscious being, and yet he is also a tri-conscious being. (p. 220)
It is sometimes asserted that we can prove to men that we are not asserting anything that they ought to consider irrational, inasmuch as we say that God is one in essence and three in person. We therefore claim that we have not asserted unity and trinity of exactly the same thing.
Yet this is not the whole truth of the matter. We do assert that God, that is, the whole Godhead, is one person. We have noted how each attribute is co-extensive with the being of God. We are compelled to maintain this in order to avoid the notion of an uninterpreted being of some sort. In other words, we are bound to maintain the identity of the attributes of God with the being of God in order to avoid the specter of brute fact. In a similar manner we have noted how theologians insist that each of the persons of the Godhead is co-terminus with the being of the Godhead. But all this is not to say that the distinctions of the attributes are merely nominal. Nor is it to say that the distinctions of the persons are merely nominal. We need both the absolute cotermineity of each attribute and each person with the whole being of God, and the genuine significance of the distinctions of the attributes and the persons. "Each person," says Bavinck, "is equal to the whole essence of God and coterminous with both other persons and with all three" (Vol. I, p. 311)... Over against all other beings, that is, over against created beings, we must therefore hold that God's being presents an absolute numerical identity. And even within the ontological Trinity we must maintain that God is numerically one. He is one person. When we say that we believe in a personal God, we do not merely mean that we believe in a God to whom the adjective "personality" may be attached. God is not an essence that has personality; He is absolute personality. Yet, within the being of the one person we are permitted and compelled by Scripture to make the distinction between a specific or generic type of being, and three personal subsistences. (p. 229-230)
— Cornelius Van Til, An Introduction to Systematic Theology (Phillipsburg New Jersey: Presbyterian and Reformed, 1978)
In reply to Van Til's error, it has been suggested that we should read Van Til in context. With this in mind, the entire relevant section from Chapter 17 in Van Til's book has been reproduced above so we can see Van Til's words in context.
As mentioned, nobody has said that Van Til does not believe in the orthodox formula of one essence and three persons. What Van Til did was not to deny the one essence three persons orthodox formula but to add to that his idiosyncratic theory that God is both three persons and one person. Attempt to say that Van Til was orthodox merely because he repeated orthodoxy and affirms it is irrelevant, because Van Til did not merely say that God is one essence in three person, but that God is also one person. To say that merely because Van Til in most of the chapter stated orthodox beliefs is to misrepresent Van Til, who insists on believing in BOTH the orthodox formula plus his "one person" formula. It clearly is not a dichotomy of which one Van Til holds to, because he holds to both.
If Gordon Clark is to be viewed as being a rationalist for attempting to solve the problem of evil, why isn't Van Til charged with the same offence for his similar speculations into the nature of the Trinity? The orthodox formula does say that "each of the persons of the Trinity is exhaustive of divinity itself" but to extrapolate from that that therefore God is a one-conscious being while simultaneously a tri-conscious being is invalid. Using the theory of archetypal and ectypal language which Van Til recovered (from Franciscus Junius), what Van Til is doing is to illegitimately peer into the mysteries of God. Van Til himself ignores his own teaching about analogy and insists on doing archetypal theology to reconcile how the fact that "each of the persons of the Trinity is exhaustive of divinity itself" translates to the fact that God is one person.
Now, I am not accusing Van Til of being a rationalist. What I am saying is that his topic is just as philosophical as trying to solve the problem of evil and theodicy. One cannot call Clark a rationalist while exonerating Van Til of the same charge. Either both aren't, or both are rationalists.
If one insists that it is irrational to hold that Van Til holds to both a one person and three person view of the Trinity, such a person should come to know quickly Van Til's idea of "paradox". The whole teaching is a paradox when Van Til says it is a paradox of which both theories are both true yet they contradict each other on the surface. Now, there are true paradoxes in Scripture to be sure, but calling anything that one thinks is a paradox a paradox does not make it a true paradox, nevermind a biblical paradox. It is an abuse of the word "paradox" to make it consists of any two or more propositions who have real or perceived contradiction. After all, the words "contradiction" and "antinomy" exist for a reason! Sadly, Van Til prefers to appear pious than clear.
As stated in Chapter 17, a reason why Van Til came up with his one person view is that "We need both the absolute cotermineity of each attribute and each person with the whole being of God, and the genuine significance of the distinctions of the attributes and the persons." However, the reasoning does not follow. What exactly in the fact that each person qua individual person of the Godhead is fully God and co-terminus with the other two person necessitates that there is one person in the Godhead?
In the spirit of "Doctor, heal thyself", Van Til should have consistently followed the Reformed distinction between the archetypal/ectypal distinction. The one person formula is not even necessitated by the orthodox doctrine of each person being individually fully God anyway. Van Til should have just embraced perichoresis instead of coming up with new formula that make no sense whatsoever. Perichoresis solves the problem of how there is one God and yet each person of the Godhead is fully God and co-terminus with the other two persons of the Trinity too, for the interpenetration of the persons in the Godhead means that every person is fully God.