Presuppositionalism (in some forms) hangs on the problem of induction. We cannot ultimately justify any of our beliefs without first making some assumptions, otherwise we end in solipsism. Christianity, then, justifies itself not on evidence, but on internal consistency. It is ok for an argument to be ultimately circular, because all arguments are ultimately circular. Christianity alone maintains perfect worldview consistency when examined through this lens, and is therefore correct.
Presuppositionalism is pretty generally based on the universality of bias, not the problem of induction; the problem of induction is not sufficiently extensive enough to ground the sort of argument presuppositionalists want to make. Van Til (although pretty much alone among presuppositionalists) does regard all arguments as circular; this is an adaptation of a point by Mill. However, presuppositionalists do not generally regard worldviews, even Christianity, as self-justifying (and, indeed, it is fairly common for presuppositionalists to argue that the most that can be established for any worldview is relatively greater probability); rather, one can say they focus on worldview self-defeat, and are only primarily concerned with internal consistency in a sense of internal consistency that would include transcendental arguments. That is, after all, why it is called 'presuppositionalism': its focus is on the consistency of the presuppositions we use in interpreting facts. The presuppositionalist denies that any of these presuppositions are 'neutral'; our biases are instead built into the interpretation of facts from the get-go, and to handle this systematic error, we are forced to root out bad presuppositions on the fly. This cannot be done by evidence alone; a sufficiently resourceful and ingenious interlocutor can re-interpret small collections of facts that (on your interpretive assumptions) are disconfirming according to his own interpretive assumptions, in light of which they would not be disconfirming -- since evidence is made to conform to assumptions used in interpreting them rather than vice versa, simply throwing evidence at an assumption is not going to do anything. The way we manage it is by pinning down the nature of our presuppositions and tracing out their ramifications to see if and when, in interpreting the massive volume of facts we have to use them to interpret, they (1) contradict each other; or (2) lead inexorably to skeptical breakdown; or (3) leave massive lacuna that make it impossible to defend important rational activities, like scientific inquiry or logical reasoning, from skeptical attack. That is the presuppositionalist theory, in any case; presuppositionalist practice is often less than optimal even on its own theoretical terms.
