I'm going to comment on part of this:
In general, Beisner's analysis suffers from the hermeneutic of suspicion. He is so hostile to Van Tilian apologetics that he always assumes the worst interpretation of Frame's statement.
One wonders why Frame capitulates to epistemological relativism with the qualifier “for Christians, faith governs reasoning.” Does faith not govern reasoning for non-Christians? Or, is it true for Christians that faith governs everyone’s reasoning, but not true for non- Christians? Certainly Frame believes neither of these. Yet his statement implies one or the other. But presumably this is to be explained as a careless expression.
I take Frame to mean Christians acknowledge the authority of revelation whereas unbelievers do not. For Christians, revelation consciously governs their reasoning, whereas unbelievers consciously reject revelation, or they are simply ignorant of revelation.
Frame has an aggravating habit of qualifying what he says but not defining the qualifiers. For instance, he writes over and over again (not only in this essay but also elsewhere) of “human reason” and “human logic”–a habit that he shares with Van Til. “The content of faith, Scripture,” Frame tells us, “may transcend reason in these two senses: (1) it cannot be proved by human reason alone; (2) it contains mysteries, even apparent contradictions, that cannot be fully resolved by human logic. . . .”20 But what purpose does that modifier, human, serve in these statements? Is there some other reason or logic that is not human? Perhaps Frame means not reason or logic in the abstract but the attempt at reasoning by particular persons–though if that is what he means, we might plead with him to say so. But what is reason or logic other than the way God’s mind thinks? The logic humans use includes the law of contradiction; does Frame have in mind some logic that excludes it, a logic that he would describe as “nonhuman logic”? Would that even be logic? Until Frame specifies the axioms of a nonhuman logic, or of a nonhuman reason, his qualifying reason and logic with human is meaningless.
Yes, there is some other reason that is not human. For instance, there is angelic reason. More to the point, there's divine reason. God's reason is timeless, infinite, and infallible. Man's reason is temporal, finite, and fallible.
Likewise, there's a difference between "the way God's mind thinks" and human systems of logic. Human systems of logic reflect the human understanding of logic, and that evolves. Consider developments in logic in the 19C and 20C.
Does Beisner believe Skolem's Paradox is the way God's mind thinks?
I suspect Beisner's antipathy to Frame's distinctions and qualifications goes back to the Clark Controversy. Is it possible for the human understanding of logic to correspond to God's understanding of logic to a degree sufficient that human's can distinguish truth from falsehood? I guess that's what Beisner is getting at. He thinks distinguishing human reason or human logic from divine reason results in skepticism. That may be a legitimate objection to how Van Til formulated his opposition to Clark. However, Beisner is not getting that from Frame's statement.
Consider Frame’s statement that “[We] should present the biblical God, not merely as the conclusion to an argument, but as the one who makes argument possible.” The apodosis (second half) of the sentence is not properly parallel to the protasis (first half). After reading that we should present God not merely as the conclusion to an argument, we expect to read that we should present Him as the axiom (starting point) of an argument. That is, the first clause focuses on the parts of an argument, not the conditions for one. But Frame tacitly turns from the parts of an argument to a statement about the conditions under which argument can occur. God is not merely the conclusion of an argument, but “the one who makes argument possible.” Now of course the classical or evidential or cumulative case apologist will agree that had God not existed, or had God existed but never created anything, or had God created only nonrational things or only rational things that never erred, no argument could have taken place (unless of course God argued with Himself–in which case the god that existed would not be the God of the Bible). But that is surely not the point Frame wants to make…we might also wonder why, instead of writing the nonparallel sentence “[We] should present the biblical God, not merely as the conclusion to an argument, but as the one who makes argument possible” Frame did not write, “We should present the biblical God, not merely as the conclusion to an argument, but as the major premise as well.” That would balance protasis and apodosis, and it would be precisely what Frame believes. It would be unfair to assume that Frame avoided that clarity because it made the absurdity of his position too obvious, but it is not unfair to notice that the imprecision has the effect of hiding the position’s absurdity, regardless of intent.
I think Beisner misses Frame's point. Frame isn't trying to create a symmetry between the protasis and the apodosis. Rather, he's making the deeper point that if God didn't exist, there'd be no basis for rational argumentation in the first place. God is the source of human rationality. God is the source of necessary truths as well as contingent truths. God's nature is the foundation of logic. This would stand in contrast, to, say, secular Platonic realism.
It is precisely these challenges that apologetics must answer, and merely reasserting the opposite is no answer, it is again a petitio principi, an argument in a circle. There are more logic problems in them, but my primary purpose in citing these paragraphs was to point out the ambiguity of Frame’s conceding that “There is a kind of circularity here, but the circularity is not vicious.” The careless reader might think that Frame then goes on to define the “kind of circularity” he has in mind. But aside from denying that it is vicious (that is, that it is logically fallacious)–in which he is simply mistaken–Frame never does say what this “kind of circularity” actually is or how an argument can be circular but not vicious. He descends to the same ambiguity when he writes, as I cited once already, “But are we not still forced to say, ‘God exists (presupposition), therefore God exists (conclusion),’ and isn’t that argument clearly circular? Yes, in a way. But that is unavoidable for any system, any worldview” and “One cannot argue for an ultimate standard by appealing to a different standard. That would be inconsistent. [para] So there is a kind of circle here. But even this circle, as I indicated earlier, is linear in a sense.”
i) To begin with, there's a sense in which circular reasoning is a necessary condition of a valid argument. To be valid, the conclusion must be implicit or contained in the premises.
ii) Likewise, there's a sense in which many sound arguments beg the question. That's because a sound argument presumes the truth of the premises. A sound argument is not an argument for the truth of the premises, but for the truth of the conclusion. It takes the truth of the premises for granted. That's an unproven presupposition of the syllogism. In that respect, a sound argument assumes what it needs to prove. Given the truth of the premises, the conclusion is true–but unless you grant the truth of the premise, to claim the argument is sound begs the question.
iii) So what makes some arguments viciously circular and other arguments virtuously circular? There are at least two possible considerations:
a) If the truth of the premise is not in dispute, then the argument doesn't beg the question. Keep in mind that's person-variable.
b) In a deductive syllogism, the premises are reasons in support of the conclusion. They are intended to warrant the conclusion. So there's supposed to be some logical progression from premises to conclusion. If, however, the conclusion is essentially a restatement of the premises, then all it's done is to reassert the same claim. A disguised, repeated, unjustified assertion.
iv) Truth claims are ultimately circular. An appeal to reason presumes the reliability of reason. An appeal to memory presumes the reliability of memory. An appeal to testimony presumes the reliability of testimony. An appeal to observation presumes the reliability of observation. An appeal to Scripture presumes the reliability of Scripture.
Circular reasoning in that sense doesn't ipso facto mean the appeal is arbitrary. These may be necessary preconditions of knowledge. The alternative is global skepticism–which is self-refuting. Mind you, that, in itself, is a tacit appeal to reason.