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Let me phrase it as a question. Can we have justified true beliefs about the nature of God?
With the usual definitions I would say the answer is no, or else there would be no faith.
Although (perhaps paradoxically) I think faith leads to its own justification. I've said before that I think the purely epistemological definition of faith, at least within a naturalistic framework, doesn't capture the essence of faith as a Christian virtue.
A rather poetic way of trying to capture the idea that I have is that my favorite definition of love is that it is the going out of the lover to the beloved. Not just in metaphor but as a real ontological act.
There is an asymmetry to our knowledge where we seem to have much greater access to our internal experiences then the world "out there". Philosophically it either leads to solipsism or making axiomatic the existence of external realities. Given that axiom, there are certain kinds of phenomena which have properties that make them amenable to scientific methodology, which justifies them by inductive reasoning (and I think "justifies", in the sense of making plausible, the choice of axiom as well, but that's another philosophical topic).
Christians, by faith, begin by also assuming the existence of other realities that are not so amenable to science. Love, according to the definition, is what allows unmediated knowledge of those realities. But prior to bridging that gap, there is no "justified" belief that the endeavor will succeed. There is a leap of faith. The expectation that love is such a bridge, that God is love (and thus not EvilGod), that the other side is reachable, is fundamental to understanding Christianity "from the outside", in my opinion. But when one experiences love in that ontological sense, experiences God, then there is something that we would feel free to call knowledge. I know that God is.
But the truth of that is unprovable within the normal framework of epistemological justification. And that is why we say faith is necessary.
I'm drifting further and further off topic here, and my thoughts are fairly muddled, so augie I'm sorry about that. And of course I realize I've also constructed an edifice that is impervious to refutation, which is the point you are trying to make about "God is mysterious" to begin with. I think your point is granted but I'm just trying to explain how I reconcile understanding that "God is mysterious" is an uncompelling response, with my own experience of God and how I read the Bible and other Christian authors.