There's a reason practitioners of presuppositional apologetics (PA) use the word "presupposition". They presuppose not only the existence of the Christian God (which to an unbeliever is a frankly laughable methodology), but also that logic and reason are in some sense supernatural or "transcendent". That's why PA is based on the TAG — the transcendental argument for God.
The presuppers admit their argument is circular, but claim everyone else's is circular too, challenging people to account for their ability to reason, but without using reason to do so. Another ploy is to demand people explain how it is possible for them to know anything, if they don't claim to have absolute certainty: "Is it possible that you could be wrong about everything you claim to know?" Any claim that absolute certainty is impossible is met with "Are you absolutely certain of that?" — to which the answer, logically, is no. It all boils down to basic epistemology: how do you know anything?
At bottom, the only thing that anyone can claim to know with anything approaching certainty is that "thinking" is going on somewhere, somehow — because the acknowledgement of that fact is simultaneously its demonstration. Beyond that, we have only inferences from our perceptions to guide us in assessing the reality of the external world.
We could indeed be wrong about the external world, and it seems likely that we have been wrong about it in the past and to a certain extent remain wrong about it in the present. But we use our perceptions to build mental models of reality that appear to be largely self-consistent. This doesn't of itself make the models "true" — in the sense of being accurate representations — but Okham's razor demands that we do not multiply entities unnecessarily. Okham's razor is also why we do not unnecessarily posit supernatural agency in the absence of evidence for such agency.
Similarly, if we hypothesize that we are living in the Matrix — which is a possibility that cannot be definitively refuted — we have multiplied entities unnecessarily in order to explain our perceptions: we have the world as we perceive it (which gives us the illusion of reality) plus the world of the Matrix in which our reality is but a simulation. Our mental models fit both these "realities", and Ockham's razor should encourage us to discard the one that includes the superfluous entity. (It doesn't stop with the Matrix — the world of the Matrix could itself be a simulation within another world, which could be a simulation within yet another ... and so on. Ockham is our essential friend here.)
Parallels can be drawn with the Christian theistic worldview, in which we have the world as we perceive it, plus the world containing such additional entities as God, the Devil, angels, demons, miracles, Heaven and Hell. The world "as we perceive it" does not include these additional entities, because they don't actually impinge on our senses (that is, there's no evidence for them), and so positing them as part of a worldview is a gratuitous violation of parsimony — to which Ockham shall apply his blade.
The central foundation of PA, and its fundamental misconception, is the
matter of absolutes. The TAG is based on absolutes and that's why it
fails. Logic and reason are not absolute, objective entities existing "outside" of the Universe — they are intrinsic to existence, to cause and effect, and therefore to ask someone to "account" for logic and reason without "using" logic and reason is like asking someone to describe something without using adjectives, or to speak without speaking, or to think without thinking. The point here is not that these things can't be done — the point is that they're not necessary.
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