I see no significant difference. How can physical processes produce something non-physical?
If you're saying you can't comprehend
how physical processes could produce thoughts and judgments, that's entirely reasonable; even many naturalistic philosophers say they have no answer to the "how." (If you're claiming it's impossible in principle, that's a stronger claim, which you would have to justify. If that claim is based on the principle that "no effect can possess any properties not possessed by its cause," then I think that's a false principle, for reasons I've already given.)
But if you're saying you can't comprehend
the proposition that physical processes produce thoughts and judgments, then I can't comprehend how you can't comprehend it. "A causes B" is a very simple concept, even if you think that this particular A couldn't possibly cause this particular B. For example, I don't think it's at all possible that the alignment of the stars and planets at your birth could be the cause of your personality traits, but I have no problem at all understanding that this is what astrology devotees believe.
So, if naturalists believe physical events cause brain states; that brain states cause mental states; that among those mental states are such things as "weighing evidence"; and that natural selection will result in brains which possess the capacity to bring about mental states which weigh evidence reliably... then the naturalist is not saying anything self-contradictory, and there is no reason, within the naturalist's own view, why they should not trust their own ability to weigh evidence. Your answer to that has been, "but according to naturalism,
coming to conclusions is just chemical reactions, and chemical reactions aren't valid or invalid, so conclusions can't be valid or invalid."
It's the part in
bold which is wrong. Naturalism
doesn't say that "coming to conclusions" is just chemical reactions, they say that "coming to conclusions" is a mental state which is an emergent property ultimately caused by chemical reactions.
You may believe this is wrong, even impossible; but that does not at all mean that
naturalists are inconsistent. Naturalist premises are inconsistent with
your premises; that doesn't make them internally inconsistent.
No, if the mind is not totally tied to the physical then it can operate according to non-physical laws of logic and come to beliefs based on that logical reasoning.
You say that naturalism fails here, because it posits a cause for mental activity which is different from "the non-physical laws of logic"; but you're not proposing any alternative cause which
would be similar enough to those laws in order to make things work. "It's not physical!" is not an alternative cause. Unless you're suggesting a kind of "spirit of logic" as an active cause of our thinking, I don't know what kind of cause would "operate according to non-physical laws of logic."