Interesting observations above. There certainly is an "unprovability" about everything, even the reality of our own existence!
However, the first thought that came to my mind when I saw this question was how I so frequently used 1 Timothy 3:16 ("all scripture is inspired of God") as proof to myself, and others, that the Bible must therefore be true! It had never occurred to me (until a few years ago) the absurdity of taking what a book says about itself as proof of anything!
Heck, I might just as well take one of Kevin Trudeau's books like Cures They Don't Want You to Know About, and then simply because he says in his book ("like I say in the book!"....one of his most common sales pitches) that everything he has written is true, that therefore I should buy into it (and, of course, also buy the book).
Self-delusion is one of the most powerful forces in this universe.