For Van Til no form of unbelief escapes the charge of rationalism. Irrationalism is only a disguised form of rationalism. But before getting to that, it might help to explain what he means by irrationalism.
Irrationalism is modern critical thinking in the tradition of Kant. Irrationalism rejects any form of ultimate authority and therefore must have chance as its ultimate basis. If there is no God back of time and history whose plan is absolutely necessary then chance must rule. This is the logical descendant of the pre-Kantian (rationalistic) philosophy. Van Til explains:
It is this conception of the ultimacy of time and of pure factuality on which modern philosophy, particularly since the days of Kant, has laid such great stress. And it is because of the general recognition of the ultimacy of chance that rationalism of the sort that Descartes, Spinoza and Leibniz represented, is out of date. It has become customary to speak of post-Kantian philosophy as irrationalistic. It has been said that Kant limited reason so as to make room for faith. … In the first place the irrationalism of our day is the direct lineal descendent of the rationalism of previous days. The idea of pure chance has been inherent in every form of non-Christian thought in the past. It is the only logical alternative to the position of Christianity according to which the plan of God is back of all. (Christian Apologetics, 163-64).
It is often assumed that Kant provides a kind of Copernican revolution in the history of philosophy, overturning every Scholastic table that came before him. But Van Til does not see it that way. Kantian irrationalism is just another form of rationalism. Kant and Descartes are not enemies, but rather twins struggling in the womb of mother rationalism.
So, how then is irrationalism actually rationalism? Before we answer that, we first need to say more about what Van Til means by irrationalism understood in the tradition of Kant. Another phrase we can use for this tradition is “critical thought” (hereafter CT). CT begins with a basic dualism between the noumenal and phenomenal realms. The phenomenal realm is everything we can perceive with the senses. We can only know this realm through the categories of the mind. Therefore, there is a “contribution” that man makes to knowing objective reality. What he can know is only that which is phenomenal. The noumenal realm is, however, directly unknowable by man. It contains things which cannot be perceived – the things of faith (God, being, etc.). In his critique of pure reason Kant, as Van Til says above, limited reason to make room for faith. Man can reason only according to what he can know in the phenomenal realm. Faith then is for those things in the noumenal realm which cannot be known.
It is with regard to the noumenal realm that Van Til speaks about irrationalism. Irrationalism does not mean that man does not use reason. Rather, irrationalism is the idea that there is a place (the noumenal realm) that reason cannot go. It is the realm of ineffable mystery. It is the realm of the unknown. The noumenal realm cannot be known, at least not directly. This means that no source of ultimate authority can be accessed by us living in the here and now. The final arbiter of all truth is inaccessible to us.
Now we can begin to see how irrationalism is really just rationalism. If there is no access to the transcendent realm, then there is no direct knowledge of God or his revelation. That means that man along with his reason is completely on his own. He can speak about facts without any reference to an ultimate and final authority. In this way man is autonomous and is able to interpret reality quite apart from or without reference to God. Irrationalism “boxes out” the noumenal realm where transcendent truth is found. This allows fallen man to interpret reality according to his own sinful reason. Van Til gives a great illustration of this situation which is worth quoting at length here:
In the second place modern irrationalism has not in the least encroached upon the domain of the intellect as the natural man thinks of it. Irrationalism has merely taken possession of that which the intellect, by its own admission, cannot in any case control. Irrationalism has a secret treaty with rationalism by which the former cedes to the latter so much of its territory as the latter can at any given time find the forces to control. Kant’s realm of the noumenal has, as it were, agreed to yield so much of its area to the phenomenal, as the intellect by its newest weapons can manage to keep in control. Moreover, by the same treaty irrationalism has promised to keep out of its own territory any form of authority that might be objectionable to the autonomous intellect. The very idea of pure factuality or chance is the best guarantee that no true authority, such as that of God as the Creator and Judge of men, will ever confront man. If we compare the realm of the phenomenal as it has been ordered by the autonomous intellect to a clearing in a large forest we may compare the realm of the noumenal to that part of the same forest which has not yet been laid under contribution by the intellect. The realm of mystery is on this basis simply the realm of that which is not yet known. And the service of irrationalism to rationalism may be compared to that of some bold huntsman in the woods who keeps all lions and tigers away from the clearing. This bold huntsman covers the whole of the infinitely extended forest ever keeping away all danger from the clearing. This irrationalistic Robin Hood is so much of a rationalist that he virtually makes a universal negative statement about what can happen in all future time. In the secret treaty spoken of he has assured the intellect of the autonomous man that the God of Christianity cannot possibly exist and that no man therefore need to fear the coming of a judgment. If the whole course of history is, at least in part, controlled by chance, then there is no danger that the autonomous man will ever meet with the claims of authority as the Protestant believes in it. For the notion of authority is but the expression of the idea that God by his counsel controls all things that happen in the course of history. (Christian Apologetics, 164-65).
In short, irrationalism (or pushing all forms of ultimately authority, i.e., God, into an unknowable realm) serves rationalism by pleading ignorance (“makes a universal negative statement “) about time. It knows nothing about the meaning of history (because it does not know God whose plan stands back of history) nor does it know what the future holds (because it knows no God and his plan back of the future). The true meaning and significance of time (whether past or future) is inaccessible to man. Therefore time (whether past or future) only has the meaning that autonomous man would assign to it. That is to give to man’s mind a quasi-divine status, thus breaking down the distinction between the Creator and creature. And that is the heart and soul of rationalism.
 Before we get to that, it is necessary to briefly acknowledge that the interpretation of Kant is quite variegated. I am no Kant scholar, and neither was Van Til. So, here I recognize that what I am about to say can legitimately be quibbled with by Kant scholars who would argue on the lines of a different school of interpretation. Our purpose here, however, is not to enter those debates but simply to explain what Van Til understood by modern thought after Kant.
 The noumenal realm if it is to be known can be known only indirectly. That is, by way of deduction from what can be known.