The real Problem of Induction
Who has the real Problem of Induction ? The atheist, or the presuppositionalist ?
Well, I think that Christianity in general, not just presuppositionalism, is fatal to induction. As TANG proves with ironclad confidence, Christianity, and its inherent belief in miracles, contradicts the very premise of induction - that past events can be used as a guide to future events. Miracles cannot co-exist with natural law or predictability. Such laws become entirely subjective - to God's will.
Induction is only possible if the integrity of the identity of existants is preserved. This implies a self-contained (material) universe. In a self-contained universe, parts interact with each other according to their identity - causality cannot be broken. Only a transcendent ontology can break this necessity.
Even the simplest example of induction - "will the Sun rise tomorrow ?" - is contradicted by the Bible. The book of Isaiah clearly states that God stopped the Sun in its tracks. If we accept this miracle, then we must cast any affirmative answer to the question into grave skeptical doubt. A Christian would have to ask himself "how do I know the Sun will rise tomorrow ?", and to establish an answer would require one to be able to know God's will, which is strictly impossible (due to the necessity of naturalism, as well as the inevitable subjectivity of such interpretations).
What about moral induction ? Well, one example that comes to my mind is medical science. I know that my values are better fulfilled by being treated by medical science, simply because it is reality-based. But the Gospels ask us to abandon medical science for demon possession and prayer, contradicting our observation of past events. The same principle is true here. If we accept the existence of transcendent agents like gods and demons, our assumption that medical science is the best moral alternative is put into skeptical doubt.
The fact is, there is absolutely nothing in the Bible which states what induction is and why it is correct within the subjectivist Christian worldview. And even if it did, we would have to cast that passage into the same skeptical doubt that we threw everything else in. Once we take away the very basis for trust and confidence - the capacity we have to understand reality - then claims of knowledge, or even faith, become hollow.
Whether we like it or not, faith is also based on conceptualization, if only for one to know what he believes in. And adherence to religion is based on motives, values. All of these crumble in the skeptical doubt of Christian subjectivism.
A major consequence of this Christian Problem of Induction is that conceptualization itself is under skeptical doubt. Concept-formation is based on observation of a number of existants, and subsequent induction based on shared properties. If Christianity contradicts induction, then it contradicts the specific kind of induction used in concept-formation, and thus contradicts concepts.