Frankly, I'm not impressed with Kline's arguments. To boil all the wordy verbiage away, his position is that you can't really prove anything, therefore religion (more specifically, if math and science cannot be proven, the criticisms towards religion cannot be proven either, therefore religion stands uncriticized). The problem is that this begs the question. Even if you can't prove some mythical "independent existence" for math or science, which are objective in nature, how much less can you prove the "independent existence" of something that's entirely subjective, like a religious belief in some deity?
Simply put, you cannot. You can't even know where to begin to look, let alone how to actually prove it. Therefore, your only option if you don't want to admit that you might be wrong is to attack the foundations of scientific reason and knowledge, so that you can pretend that your belief is untouchable by science. Except that this is pure sophistry. It's not even good sophistry. It's basically the equivalent of sticking your fingers in your ears, going "lalalala I can't hear you", and then claiming that your belief is untouched because you drowned out the criticisms against it.
It doesn't work, Olivianus. You're just wasting our time and yours. Though, frankly, you're wasting much more of your time than ours. It took you what, 35 hours to read that book, and another several to write up your post on it? It took me about 10 minutes to read over your post and then another few to get at the essential part of it. But hey, if you want to waste your time like that, don't let me stop you. Just don't expect it to be convincing, anymore than arguing that science is somehow based on "atomism" or "monism", neither of which it is actually based on. You see, science is nothing more than a set of tools we use to examine the universe. It doesn't need to have some "independent existence" that we have to waste time trying to divine, anymore than I have to try to figure out if a hammer "independently exists" before I use it to pound in a nail.