James Anderson on presuppositionalism

Here's an outstanding exposition and defense of Van Tilian presuppositionalism: 

https://www.youtube.com/watch?v=EguVuY5HVkA

I'll venture a few observations:

1. Let's begin with some definitions:

As standardly conceived, transcendental arguments are taken to be distinctive in involving a certain sort of claim, namely that X is a necessary condition for the possibility of Y—where then, given that Y is the case, it logically follows that X must be the case too.

https://plato.stanford.edu/entries/transcendental-arguments/

Transcendental arguments are partly non-empirical, often anti-skeptical arguments focusing on necessary enabling conditions either of coherent experience or the possession or employment of some kind of knowledge or cognitive ability, where the opponent is not in a position to question the fact of this experience, knowledge, or cognitive ability, and where the revealed preconditions include what the opponent questions. Such arguments take as a premise some obvious fact about our mental life—such as some aspect of our knowledge, our experience, our beliefs, or our cognitive abilities—and add a claim that some other state of affairs is a necessary condition of the first one. Transcendental arguments most commonly have been deployed against a position denying the knowability of some extra-mental proposition, such as the existence of other minds or a material world. Thus these arguments characteristically center on a claim that, for some extra-mental proposition P, the indisputable truth of some general proposition Q about our mental life requires that P.

https://www.iep.utm.edu/trans-ar/

2. Apropos (1), Anderson defines presuppositionalism partly in terms of presenting an internal critique of non-Christian worldviews. One way of putting this is that non-Christian worldviews lack the metaphysical resources to provide the necessary enabling conditions for coherent experience or the possession or employment of some kind of knowledge or cognitive ability. 

3. Is presuppositionalism circular? In a sense, but not viciously so. Take a transcendental argument which posits that knowledge/truth/human rationality possible, and Christian metaphysics provides the necessary enabling conditions. That's circular in the sense that it takes for granted the possibility of knowledge/truth/human rationality, but there's nothing fallacious or question-begging about that assumption. After all, what's the alternative? How would a critic argue that knowledge/truth/human rationality are impossible? Such a denial would be self-refuting. Although you can debate the degree to which knowledge is obtainable, or the degree to which human reason is truth-conducive, it would be self-referentially incoherent to deny those claims wholesale. 

4. Anderson classifies transcendental arguments as deductive arguments. Once again, let's provide a definition:

A deductive argument is an argument that is intended by the arguer to be deductively valid, that is, to provide a guarantee of the truth of the conclusion provided that the argument’s premises are true. This point can be expressed also by saying that, in a deductive argument, the premises are intended to provide such strong support for the conclusion that, if the premises are true, then it would be impossible for the conclusion to be false. An argument in which the premises do succeed in guaranteeing the conclusion is called a (deductively) valid argument. If a valid argument has true premises, then the argument is said also to be sound. 

An inductive argument is an argument that is intended by the arguer to be strong enough that, if the premises were to be true, then it would be unlikely that the conclusion is false. So, an inductive argument’s success or strength is a matter of degree, unlike with deductive arguments. 

Although inductive strength is a matter of degree, deductive validity and deductive soundness are not. In this sense, deductive reasoning is much more cut and dried than inductive reasoning. Nevertheless, inductive strength is not a matter of personal preference; it is a matter of whether the premise ought to promote a higher degree of belief in the conclusion.

Because deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises, if the argument is a sound one, then we say the conclusion is “contained within” the premises; that is, the conclusion does not go beyond what the premises implicitly require. 

Because the difference between inductive and deductive arguments involves the strength of evidence which the author believes the premises provide for the conclusion, inductive and deductive arguments differ with regard to the standards of evaluation that are applicable to them. 

https://www.iep.utm.edu/ded-ind/

5. This is often a sticking point between evidentialists and presuppositionalists. For instance, Bahnsen is highly critical of the fact that inductive arguments only yield degrees of probability. They fall short of certainty. But a basic problem with Bahnsen's position is that inductive and deductive arguments from Christianity differ in scope. Inductive arguments include the Resurrection, the canon of scripture, the argument from prophecy, the biographical accuracy of the Gospels, the reliability of the Greek/Hebrew text of Scripture. Christian apologetics can't afford to eliminate inductive arguments of this kind. Christian transcendental argument are limited in scope. So Christian apologetics requires a combination of inductive and deductive arguments. 

6. That may seem to leave a unsatisfying gap between the two kinds of argument. However, they're not essentially at odds or separate. Christian transcendental arguments provide the necessary backing for Christian inductive arguments. They justify the enabling conditions on which inductive arguments depend. So you can still have certainty at that foundational level. 

7. Finally, Anderson draws a distinction between knowledge and proof. Due to natural revelation, we intuitive know certain things independent of formal argumentation. So there's a kind of certainty that's not contingent on our ability to formulate sound arguments.