Bahnsen's first answer
In one of his last courses before he died (Transcendental Arguments), after Butler had finished giving a historical account of TAs and their original function, Bahnsen illustrated that there are two ways of picturing us as knowers that we must take into account when using TAs:
1. [The first way of picturing us says that God created us and our minds, and God also created the world that we know with our minds.] This is the Christian view of things. God made the mind and the objects that the mind knows. Therefore, our conceptual scheme is automatically in touch/automatically corresponds with the objects of experience on this presupposition.
2. The second way of picturing us says that we can’t know anything about God at the outset. All we can know is that we have a human mind, we assume its sufficiency, and we are pretty sure that there are objects out there that the mind can know. Everything here is loose and disjointed; the objects of knowledge are not connected to one another by God’s sovereign work, nor are the objects automatically connected to the mind of man in his conceptual scheme. In fact, all minds are loose and disjointed as well. God is not brought into the picture here because we don’t want to do theology in the place of philosophy after all, right? We begin with man and then work out from man.
The whole context leading up to this moment in the course was illustrating the fact that historical transcendental arguments always assumed the second picture of knowing us - from Aristotle to Kant to Strawson - not starting with God, but with man. Stroud eventually comes along and says that TAs don’t necessarily prove ontological sufficiency, but at best conceptual coherence. And if this is the case, then TAG doesn’t really prove Christianity is true after all.
So Bahnsen, after making this distinction of two pictures of man, then answers the objection of the ontological sufficiency of TAG directly:
If somebody says, ‘Well how do you know that the mind is in contact with objects, that the conceptual scheme corresponds to objects?’ you say, ‘Well that by definition is my worldview. That’s what I start with.’ Now I realize that people will say, ‘Oh, you’re begging the question.’ But I’m not begging the question; that’s my worldview … Not only can we show that rationality is justified in terms of God’s existence and man being made in His image, but if you take that picture (picture 1 above), you’ve already overcome the egocentric predicament (of picture 2), because there is no egocentric predicament if you’re a creationist.
…God created everything, and He created man in His image so that the fundamental biblical picture of what this world is, who we are, what our place in the cosmos is already says we’re in contact by our minds with the world that God created because God created our minds to know that world imaging Him.
In short, the point of this all is that the criticism of TAs not proving the ontological sufficiency of their arguments was originally aimed at secular TAs in the first place, secular TAs that held to the presuppositions of picture #2 above and were helplessly faced with the egocentric predicament (Grayling alludes to Neurath’s sailors). Van Til’s TA doesn’t even affirm that picture to begin with and holds to the presuppositions of picture #1. Because the presuppositions of picture 1 justify definitionally the correspondence of conceptual schemes to objects of the external world (contra secular TAs), and because the criticism of the lack of ontological sufficiency originates from the egocentric problem of picture 2, then the ontological problem of TAs is of no effect to Van Til’s TA.
And so Butler, in attempting to answer this problem, takes for granted that we’re dealing with two different plains of TAs altogether. You can’t make the assumption that all TAs are equal and therefore if one TA runs into serious problems that therefore all TAs, including Van Til’s, are also subject to the same problems. Bahnsen’s answer of the necessity of mapping out the two pictures of man and to illustrate how Van Til’s TA is starkly contrasted with historic TAs (which had an entirely different purpose altogether) is simple yet genius. Because Van Til’s TA doesn’t run into the egocentric predicament, there is no ontological problem in his argument. (But of course, Butler, who was sitting in on this entire lecture series, missed that point and decided to focus on the “inadequate” Michael Jordon analogy instead in his paper).
Bahnsen's second answer
Additionally, Butler argues that Bahnsen’s answer to Montgomery that at least one worldview must be true is “without foundation” because we can picture the world as ultimately irrational. But as Robin pointed out in his paper, this is self-defeating as it requires a rational account of what an irrational world would be in the first place. Butler’s argument falls short, therefore Bahnsen’s argument that at least one worldview must be true/“rational” still stands.
On this premise, then, Bahnsen even concedes the ontological criticism saying that even rejecting that TAG shows ontological sufficiency doesn’t negate it as an objective proof for God’s existence:
I’d like to finally point out that the transcendental method is useful on either interpretation of transcendental arguments, either the conceptual or the existential (what we might call the ontological interpretation of the argument). On the conceptual transcendental interpretation … what we say is, ‘If you wish to argue at all ... to make sense of experience, whatever, then you must presuppose the existence of the Christian worldview or God to make sense of your own argument or communicating it,’ and here the word ‘must’ is interpreted psychologically. ‘If you want to reason, to make sense of your reasoning, you must psychologically presuppose the Christian worldview.’ Now that’s not the strongest result [of a transcendental argument], I grant you, but you know if that’s all we have with what Van Til is giving us, we’ve got enough don’t we. Because basically what I’m saying to the person arguing with me is, ‘Well if you want to argue with me you have to assume that you’re wrong.’ … Through our discussion what I want to point out to him is, ‘You’re assuming the very thing you’re arguing against.’
And then later:
So you have two interpretations [of transcendental arguments], and all I’m going to get at is I think that the existential is the stronger and is legitimate. But even if somebody says, ‘Well all you’re showing is that we gotta think as Christians,’ you’ll say, ‘I’ll take it.’ That’s pretty good to tell people that if you’re going to think at all, you have to think as a Christian. See you tomorrow.
The context leading up to this point was a reiteration of the fact that there is only the non-Christian worldview and the Christian worldview. Bahnsen’s argument here, given that context, is that if you have to presuppose the Christian worldview to preserve rationality, then you must say that all other non-Christian worldviews are definitionally wrong (contra Butler), even if at a psychological level. So it seems that Bahnsen has no problem in assuming for the sake of the argument that TAG cannot answer the objection of ontological sufficiency (which he argued that it did (above)). He still believes that a conceptual proof alone is enough proof for the veracity of Christianity as a worldview, and therefore the existence of God, etc.
Chris Bolt's answer
He first starts out by differentiating how TAG is different from a TA (similar to Bahnsen’s pictures above), and then after making the distinction does he respond to Stroud’s objection:
We start from authority … we’re not just starting with this a priori analytical tool. We’re starting with the God of the Bible and His authoritative Word... We’re arguing concretely, not abstractly. We’re talking about the actual Christian worldview.
If we’re really starting with the Christian worldview, then (other than doing this conceptually for the sake of analysis) we’re not differentiating in some hard sense between the ontology of the matter and the concept of the matter anyway… We’re saying the Christian worldview is true, the Christian worldview is the reality of the matter, like this is the metaphysical scheme we’re starting with. Now of course an analytical philosopher is gonna want to try and chew that up and parse that out and tear it apart and say, ‘Oh yeah, but you know there’s a difference between metaphysics and epistemology,’ and I understand that. But we’re saying holistically we’re already starting with all of that.
[Stroud’s] argument has no teeth … one, because I’m just going to say, ‘First of all, how can you believe that God exists and also say, ‘But this doesn’t show that God exists’?’ Because when you say, ‘I believe God exists,’ you’re making a metaphysical claim. You’re professing … the truth of the matter … that God exists. What you’re telling me is you want to think about what you’ve already conceded you cannot think about, namely, that God does not exist. The other reply is simply to concede the objection and say, ‘Okay, that’s fine, Christianity may not be true, God may not exist. Now where are you?’ And they say, ‘Well I believe God exists.’