My [Van Til's] notion of the incomprehensibility of God is, therefore, as the poles apart from what is today called modern irrationalism. And from your point of view [referring to GWF Hegel], my doctrine of the incomprehensibility of God must be hopelessly determinist and rationalist.
— Cornelius Van Til, An Introduction to Systematic Theology, 2nd Ed. (ed. by William Edgar; Phillipsburg, NJ: P&R, 2007), p. 294
The later part of Van Til's work sees Van Til imagining an encounter of Calvin (made in Van Til's image of course) with the idealist philosopher Georg Wilhelm Friedrich Hegel and the Danish existentialist philosopher Søren Kierkegaard. Hegel and Kierkegaard represents in their philosophy the extremes of rationalism and irrationalism respectively. Hegel dislikes [Immanuel] Kant's noumenal/ phenomenal distinction, and rejects it for total comprehension of everything in the world through the dialectical process. Kierkegaard in horror at the rationalism of Hegel agreed that the thesis/ antithesis pair exists, but that no synthesis is ever possible and therefore resolution has always to be via an existential [and irrational] leap of faith.
As an application of Van Til's philosophy, it is indeed intriguing how Van Til attempts to navigate the troubled waters between rationalism and irrationalism. The approach however was a mess. It is interesting that Van Til near the end starts psycho-analyzing his opponents as to how they would respond to his particular formulation of the doctrine of the incomprehensibility of God.
The problem comes when Van Til seems to think that Hegel will think that his doctrine of the incomprehensibility of God (as Van Til defines it) is deterministic and rationalistic. In fact, this is how Van Til navigates the "central path" between the two extremes. According to Van Til, rationalists will think that his theory is "hopelessly determinist and rationalist" as Hegel denies the knowability of God (p. 293), while irrationalists will of course think the same. As Van Til said,
We may therefore imagine Hegel and Kierkegarrd as standing together as irrationalists and indeterminists against Calvin [as remade in Van Til's image] the rationalist and determinist. They will say to Calvin that since it is impossible for him to know the mind of his god exhaustively by his own admission and assertion, therefore he ought with them to become an irrationalist. (p. 291)
As someone who has more than a mere interest in philosophy, this entire imaginary apologetic encounter shows the defect of Van Tillian philosophy and apologetics. It is extremely amazing that Van Til thinks that Hegel will say that Van Til's incomprehensibility of God is deterministic and rationalistic. In fact, Hegel as the ultimate rationalist will see Van Til's incomprehensibility of God thesis as just as irrational as Kant's noumenal/ phenomenal distinction. Van Til posits a dual reality (which all Christians hold to), and this dual reality will sound to Hegel like Kant's ontological dualism.
The idea of being above the fray when it comes to the rationalist/ irrationalist duality is very tempting. While it is true that biblical Christianity rises above the fray, it is not true that the world thinks that what any theologian teach is above the fray. Yes, both Hegel and Kierkegaard will team up against Van Til, but not for the reasons Van Til posited. Hegel will accuse Van Til of bringing back the ontological dualism of Kant and thus he is an irrationalist, while Kierkegarrd will regard Van Til as being a rationalist because he believes that Man can know the things of God not by a leap of faith. They will team up only because Van Til is an unwelcome guest in the conversation. Both sides see Van Til's incomprehensibility of God thesis as an a priori addition which has no basis of proof whatsoever — Hegel as a irrationalist addition, and Kierkegaard as a rationalist addition.
Hegel therefore will never think that Van Til's incomprehensibility of God teaching is deterministic and rationalist. In fact, the converse will very much be the case. And this is the problem with Van Tillian philosophy and apologetics. Firstly, by exactly correlating his philosophy to biblical truth, it makes any criticism of his philosophy analogous to the criticism of God and the Bible. Secondly, the fact that he misrepresents Hegel just to pigeonhole him into his neat system of categories reveals that Van Til''s philosophy and apologetics is not even representative of the actual condition of the world and her philosophies. It furthermore reveals Van Til's arrogance in not listening to what others have to say but instead just hear enough to pigeonhole them into the categories that he has already formed in his philosophy.
If Van Til can do this to Hegel, what makes us so sure that any of Van Til's critiques are similarly invalid? Why must we accept Van Til''s horrendous caricature of Gordon Clark's position? Why should we accept Van Til's criticism of Bavinck on the primacy of the intellect?
Van Til may be a brilliant mind, but one that is in a world of it's own refusing to properly interact with what others actually say. By conflating his philosophy with the teachings of Scripture, he has all but made his philosophy resistant to any sort of criticism, and those who embrace his philosophy likewise.