Machiavelli said:
I must admit, I find it hard to get my head around this whole issue.
I guess to answer your question (which may in itself be an article of faith) my question may not intrinsically be either an article of faith, nor necessarily a product of logical process. However, I think that it is probably true that the question I ask does carry certain presuppositions about what logical process is and what an article of faith is. Perhaps it would help if I was to provide my understanding of the four epistemological foundations.
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Arggh, my head is beginning to spin again ...
OK, I'd hate to make it spin more but it sounds like you're looking for philosophical basis. (and ... Hi! That interests me, too.) That's fine.
The basic problem with questions of revelation and inspiration is that they all consist in presuppositions. So the inevitable answer to any such question is, "Of course they have assumptions associated with them."
To get to special revelation there's a minimum of assumptions to deal with, so let's at least get our heads around that. Special revelation results from the existence of God (an authoritative creator) and second, the desire of God to communicate some kind of information with His creatures.
Without that desire, you end in Deism or agnosticism. With that desire, you end in revelatory theism.
The conclusion that God is interpersonal (and not pantheistic or apersonal) is concluded from the assumptions that persons are created as well: an assumption that some deny. These feel that personhood is only ephemeral, and thus not "real".
Inspiration (God-breathedness) is concluded from the existence of special revelation. I'm not sure how special revelation could be something other than directed by God, if God sought to communicate with His creatures.
Inerrancy/infallibility is a tougher issue, it seeks an extended assumption that God desires to communicate some message with unerring authority among those in His creation.
But to my knowledge that's essentially how the "end" theology is constructed. Proof (or confirmation or demonstration) of these assumptions from empirical data or from other assumptions via logic, there are people who will bring out evidence of such. But they seem to exist to support the hypothesis, not to require the assumption. Often they are practically overwhelming, though. The prophetic claims for Isaiah and Ezekiel are impressive, for instance.
I'm not sure if this is what you want ... it's a more philosophical side of things, which is what I normally get my head around.