I wish to comment on Mulvihill’s lecture. First, Mulvihill, by his articulation of the Transcendental Argument for God’s existence (TAG), seems to mistake Cornelius Van Til for Gordan Clark and/or Edward John Carnell. Since he wrongly claims TAG is properly understood as a reductio or abductive argument. Despite what Mulvihill may think, Van Til in fact taught that TAG is an argument for the impossible of the contrary. It is an indirect argument that demonstrates Christianity is true by presupposing its contradiction, (tokens of the same type) Non-Christianity. Non-Christianity is shown to be impossible, and therefore, it proves the contrary, namely, Christianity is true. “In other words, the structure of the argument is a disjunctive syllogism. Either A or ~A,~~A, therefore, A.”
Mulvihill as a side comment says Van Til might not even be rightly considered a philosopher. Mulvihill seems to follow the footsteps of his colleague William Lane Craig to take such a stance about Van Til. The trouble is both man show their ignorance of Van til; if only they would have bothered to look at Van Til’s dissertation on Hegel’s Absolute, they would not make such inaccurate claims.
Mulvihill’s criticisms of TAG can be summarized as follows:
- It is an indirect argument.
- It is complex.
- It is not unique.
Certainly TAG is indirect but it does not exclude giving positive answers directly. The main concern with TAG is to uphold biblical authority. Man cannot have a positive argument if man thinks it gives him the right to judge God.
TAG can be formulated in different ways both for the academic and student. So it can be simple or complex. To illustrate watch this simple use of TAG by Sye Ten Bruggencate.
TAG is unique; the problem lies with a misunderstanding of the structure of TAG. Michael Butler's comments would be helpful here. Butler explains,
"But Bahnsen makes the further point is that this criticism misses the thrust of TAG altogether. TAG argues for the impossibility of the contrary (the non-Christian worldview) and not the impossibility of an infinite number of possible worldviews. TAG does not establish the necessity of Christianity by inductively refuting each and every possible non-Christian worldview (as finite proponents of TAG, this is an impossible task), but rather contends that the contrary of Christianity (any view that denies the Christian view of God) is shown to be impossible. And if the negation of Christianity is false, Christianity is proved true. In other words, the structure of the argument is a disjunctive syllogism. Either A or -A, -- A, therefore, A.
At this point the clever opponent will simply deny the first premise. He will contend that it should not be construed as a disjunction of a contradiction, but a simple disjunction. The argument should thus be restated along the following lines: A or B, -B, therefore, A. And once this move is made he will then contend that while the argument is valid, the first premise involves a false dilemma. That is, he will grant that given A or B and the negation of B, A does indeed follow, but nevertheless maintain that the argument is unsound because the first premise (A or B) is not true. The reason being that there are more possibilities than just A and B. Given a true first premise, A or B or C or D ... n, the negation of B merely entails that A along with the disjunction of other propositions besides B (C, D,...n) follows.
In order for this to be successful, it is incumbent upon the opponent of TAG to defend two claims. First, he must defend the contention that the original first premise is not the disjunction of a contradiction and, second, he must show that there are other possible disjuncts besides B (what we can call the view that is opposed to the Christian worldview)."
I strongly suggest Mulvihill and anyone interested in learning a correct presentation of the Transcendental Argument for God's Existence (TAG) to listen to Dr. Greg Bahnsen's lectures Here and Michael Butler (Bahnsen's former student) Here
 Butler, Michael. The Standard Bearer: A Festschrift for Greg L. Bahnsen (Covenant Media Press: Nacogdoches, 2002) p.85. www.butler-harris.org/tag/
 Butler, Michael. ;www.butler-harris.org/tag/;