Dan Chapa seems to be confused about what Van Til meant by “presuppositions.” He makes oddball statements like “If God's existance [sic] can be demonstrated, then why presuppose it?” “Well given my observation that I have arms, my also presupposing that I have arms is minimally irrelevant, if not downright impossible.”
However, I don’t think there’s anything mysterious about Van Til’s usage. From my reading, Van Til uses “presuppositional” as a synonym for “transcendental” reasoning. Indeed, one synonym for presuppositional apologetics is transcendental theism.
So what does it mean to reason presuppositionally (i.e. transcendentally)? Well, as one scholar defines it:
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.
Van Till gives this type of argument a specifically Christian twist.