This is really interesting to me so thanks for posting it and bringing it to my attention. I've never read any of Jaspers but the quoted part immediately made me think of Kierkegaard's God which I guess is no surprise as Jaspers seems to have been heavily influenced by him. My eyes get strained if I read on a computer screen for too long but I think I'll pick up a paper copy of this as I'm really intrigued by how he'll frame and develop the point. I had some thoughts myself though...
I think the "assertion" itself is based on a kind of holistic self confidence, not of personality but of one's total being. I guess that is the existential in Jaspers or a reflection of my own biased reading! The obvious critique that jumps to my mind is the following:
If, as Jaspers suggests, we take belief in God as "to live by something which is not in the world", there is the potential for our acting outside the realms of discourse and debate. And that, socially speaking, is a bit scary. Because immediately self doubt and fear arise about one's ability to "be good", just, fair, kind, reasonable etc etc without "calculable knowledge" as its basis. And this is as a total way of life. The same doubt is magnified many times over for your neighbours ability to do it. It's important we're always acting in accord with
something so we can negotiate on some common ground.
On the other hand, it's beyond my conception of a man to live by such a faith alone. His being "in the world", engaged with language, necessarily means that this faith has to be reconciled with reason. So perhaps this conception of faith is only for those with sound reason to begin with, as a necessary counter balance. The next question is why not just drop the faith altogether but obviously these same individuals don't
want to do that.
Hope that made some sense anyway. Now to read the book...