I'm always amazed, although I shouldn't be at this point, your thorough quoting of material, thanks. For what it's worth let's assume Van Til was actually stating a method of argumentation rather than a particular argument, with premises and conclusions, so no exact premises existed at the time but only applications of said method?
Do you think, although if I'm right he probably should have been clearer about it, that's why he may not have provided the syllogism for consideration? If I'm right then it does seem he's off the hook for a lack of syllogism, even though he should have made it clearer?
A rather speculative question, do you think that Clark was wanting a deductive argument but a transcendental argument is logically different and he may have been ignorant of that? I'm not sure on timing but I believe philosophers were developing the logical form of this type of argument (and arguing over whether it's legitimate or not) by this time?
I'm not knocking Clark but perhaps a misunderstanding is responsible for this disagreement by both parties.
I for one wish Van Til would have have stayed away from the argument language and stuck with the method language but here we are. For record no presupp's worth their salt use a single argument but applications of a method.
I address this in the post to which I linked, although I do so by reference to Bahnsen rather than Van Til:
Bahnsen does not think his transcendental argument proceeds from premises to conclusions. In that case, though, in what sense can Bahnsen's transcendental argument even be considered an argument? Don't arguments have premises? Is Bahnsen just offering a transcendental assertion? Rather, isn't it the case that if Bahnsen compares worldviews via preconditions for knowledge, the conclusion of his comparison will have been premised on whatever Bahnsen takes to be preconditions for knowledge?
...Elaborating on the transcendental argument, Bahnsen says:
The argument has been stated, but it's not a deductive argument. Please notice that that is what Dr Clark is looking for, and that's why he says, "tell me the premises." Because the transcendental argumentation doesn't proceed in terms of premises, it proceeds by a comparison of world views and asking after the preconditions of knowledge.
Rather than supposing that Clark was still bitter about the outcome of the 1940s debate, I think it makes more sense to consider that he was predisposed to think of arguments as syllogisms. Van Til's transcendental "argument" apparently did not meet this condition, so Clark failed to consider it to be an argument at all.
It is interesting that Bahnsen does not think transcendental argumentation proceeds in term of premises (minute 27). Digiacomo's transcendental argument proceeded in terms of premises, and I find Digiacomo's presentation more thorough persuasive. As noted earlier, Bahnsen can sometimes come off as if he is begging the question or merely making an assertion. All this is simply to say that Bahnsen's rhetoric can be improved, which shouldn't be controversial.
A method of "argument" that contains neither premises nor conclusions is opaque to me.
Now, I do not allege Van Til never makes a transcendental argument (one which includes premises and conclusions). I am not well read enough on Van Til to know that.
What I contend against is Bahnsen's apparent view of transcendental argumentation (at least as he presents it in the quote above). I do
not agree that transcendental argumentation "proceeds by a comparison of worldviews and asking after the preconditions of knowledge." Any talk of "preconditions of knowledge" ironically presuppose a worldview in the first place (as one's "premise," foundation, axiom, first principle, etc.), and such is logically prior to any "comparison" of worldviews.
The "impossibility of the contrary" is either a mere assertion or premised on something. In his conversation with Sproul (who gets the better of Bahnsen), Bahnsen appears to suggest that the impossibility of the contrary is based on inductive reasoning:
Sproul: All right, how is the contrary impossible?
Bahnsen: Well, you want me to go through a few of the schools of philosophy and show you? I mean, how is it utterly impossible and unthinkable that there be no God?
Bahnsen's response already walks back his own statement that "transcendental argumentation does not proceed in terms of premises," for when Sproul asks for one, Bahnsen implicitly accepts the question as legitimate. It's just that Bahnsen's apparent premise(s) for the impossibility of the contrary come from the internal contradictions within "a few of the schools of philosophy," a procedure Bahnsen himself elsewhere points out is flawed:
Bahnsen said:
Presuppositionalism is not a case by case by case inductive survey. It's not like we're going out there and saying, "Okay, here's a version of the enemy. It didn't work, now let's find another one. Oh, now this second one didn't work, now let's find another one. This third one didn't work..." And then eventually we stand back, either because we've gotten tired or we think we've done enough work and we say, "Well, then all of them won't work." That is not the argument. If it were, it would be weak, because any inductive survey that's incomplete. You don't know how much more of this is out there. But that isn't the argument. We don't consider this. I believe Christianity is the only option. On a case-by-case basis, I begin by saying Christianity is the only option. Now, who wants to fight?
Bahnsen may have been better in other writings. I have notes, but have not had the time to revisit them in the past 5 months or so. As for whether Bahnsen accurately represents Van Til's thought, you would probably know better than I.