Quote set #1:
... my [Van Til's] disagreement with Kuyper does not pertain to the question whether formally believers and unbelievers think according to the same logical laws. I do not maintain that Christians operate according to new laws of thought any more than that they have new eyes or noses.
My only criticism of Kuyper was to the effect that this concept of metaphysical sameness must again by supplemented with the concept of ethical difference. The non-Christian uses the gifts of logical reasoning in order to keep down the truth in unrighteousness.
— Cornelius Van Til, The Defense of the Faith, 4th Ed. (Ed. by K. Scott Oliphant; Phillipsburg, NJ: P&R, 2008), 291
Quote set #2:
[Because of the Fall] The intellect of fallen man may, as such, be keen enough. It can therefore formally understand the Christian position. It may be compared to a buzz-saw that is sharp and shining, ready to cut the boards that come to it. Let us saw that a carpenter wishes to cut fifty boards for the purpose of laying the floor of a house. He has marked his boards. He has set his saw. He beings at one end of the mark on the board. But he does not know that his seven-year old son has tampered with the saw and changed its set. The result is that every board he saws is cut slantwise and thus unusable because [the board is] too short except at the point where the saw first made its contact with the wood. As long as the set of the saw is not changed, the result will always be the same.
When we say that sin is ethical, we do not mean, however, that sin involved only the will of man and not also his intellect. Sin involved every aspect of man's personality. All of man's reactions in every relation in which God had set him were ethical and not merely intellectual; the intellectual itself is ethical.
I have mentioned earlier that Cornelius Van Til is manifestly unsystematic. This can be seen while reading his books. The most charitable way of reading Van Til is to seek for understanding of the context in which the sentences are located, otherwise it can be clearly seen that Van Til contradicts himself countless times. Comparing the two sets of quotes above will expose a contradiction on the surface, of which Van Til did not help with his irrationalist appeal to "paradoxes" without explaining what "paradoxes" are and how exactly they work.
The most charitable reading of Van Til therefore attempts to understand why he says anything in Van Til's own context. For as Van Til wrote, the first quote shows that Van Til understands that logic and logical reasoning is not affected by either the Fall or regeneration. Both believers and unbelievers use the same logic laws, and Christians "do not .. operate according to new laws of thought any more than that they have new eyes or noses." Yet, Van Til seems to affirm the direct opposite in the second set of quotes on page 97 and page 70. In the first set Van Til seems to affirm the ontological immutability of reason; while in the second set Van Til seems to deny the ontological immutability of reason.
Reading the quotes in context will show that Van Til was trying to get at certain biblical truths in all three quotes. This surface contradiction therefore should not have existed. That they do exist therefore shows Van Til to be totally unsystematic, which is further complicated with his boasting in his aversion to be systematic, by masking such sinful actions (in expressing biblical truths in contradictory forms) as being pious and godly (under the guise of "paradox").
That the biblical truths behind the quotes are not actually contradictory can be seen by understanding them in context. The first quote is in reaction to the charge of irrationalism and of denying Kuyper's teachings by a critic Van Halsema. Van Til is here stating that he does not believe that reason is different between believers and unbelievers so that reasoning and communication is impossible between them. In the second quote, Van Til is trying to prove that the unbeliever's reason is defective (so that it cannot seek or understands God on its own) by an analogy. In the third quote, Van Til is trying to state the fact that the intellect itself cannot be trusted to be used as an instrument to lead us to truth as it is affected by sin.
When we read all of these quotes in context and understand them, we will realize that these three concepts that Van Til wanted to teach and defend are biblical and orthodox. The problem however comes when he adds his distinctive spin to teach and defend these truths, and then all of the logical problems rise up. Since the basic concepts are biblical, Van Til (and Vantillians too) treats any criticism of his teachings as an attack upon the biblical truths behind his teachings. The problem of course is not with the biblical concepts underlying Van Til's teachings, but Van Til's distinctive spin on the concepts which is careless, loose and not befitting of someone who is supposed to handle the truths of God's Holy Word.
The godly systematicians of God's Word use precise and measured language to ensure that no surface contradictions exist in their theologizing. In fact, that is what Reformed Scholasticism (and Medieval scholasticism in its method) is well known for. Certainly this is not to say that there are no mysteries left in the Bible. However, paradoxes are wrestled with and resolved in such a way that no contradictions are seen on the surface. For example, the early church came up with the "one essence, three persons" formula for speaking of the Trinity. Why did the early church not just leave it as "one person, three persons" and relegate the whole issue as a paradox reconcilable only by God? After all, if it was good enough for Van Til (who taught the "one person, three persons" heterodox theory), why was it not good enough for the early church fathers, who unlike Van Til were not blessed with the legacy of having available teachings of the giants of the faith?
By stating the teaching of the Trinity as "one essence and three persons," the early church resolved the paradox in favor of mystery. There is after all no formal contradictions between essences and persons! Now, what exactly are "essences" and "persons" can be discussed further, but as long as they are not ontologically equated, there is no contradiction in the formulation of the Trinity. Mystery yes, contradiction and paradox no.
The example of the church fathers is typical of godly systematicians through the ages. Van Til obviously is not one of them, being probably the most unsystematic systematician ever.
What shall we liken Van Til's thought? Van Til's teaching is just like taking the mirror of Reformed orthodoxy, smashing it to pieces, and then piecing them together with the addition of other fragments of glass that Van Til thinks should be part of the mirror. The result is a disparate amalgam consisting of sometimes large fragments of Reformed orthodoxy mixed with distinctive Van Tillian thought, and all this is meant to cohere together. Is it no wonder that with such confusion, Van Til has left behind a mixed legacy consisting of Vantillian Reformed orthodox, Frameans, Christian Reconstructionists, Theonomists, and Federal Visionists, all of whom claim Van Til as their spiritual godfather?
Whatever is orthodox in Vantillian thought can be found in better Reformed writers. Whatever good in Van Tillian thought in the realm of apologetics and philosophy has been said much better by others like Gordon Clark. If one really wants to learn the Reformed Christian faith, one would do well to avoid Van Til and read people like Calvin, Witsius, Turretin, Rutherford, Owen, and even [Richard] Muller. Ad fontes!