Isn't faith derived from a certain level of logic and experience? Daily we get in our cars and have faith that the other driver is paying attention and will stay in their lane. We also have faith that we can go out into society and strangers we encounter are merely going about their lives as we are and will do us no harm but of course that isn't always the case either. There is no evidence that we will be safe in either instance and as you know police reports prove that faith and trust is breached every day. Nevertheless we trust that we can safely get to where we are going and do what we wish to do unharmed. It seems to think otherwise is less rational. We would miss our entire lives and live as shut ins if we didn't have faith.

We can prove what does exist because we can see it, touch it and measure it but can we actually prove something doesn't exist? I don't think we can because one could argue that it does exist but we did not see it or was not at the proper location. For example mountain guerillas were thought to not actually exist but they do. I believe that we can only prove existence but we can't prove non-existence. I don't think that faith is not as unreasonable as you believe. You can base you beliefs on science alone but without a certain level of faith one would find no evidence because it would seem pointless to explore the unobvious. There would be no evidence because no one would bother to look for it. Those who believe in a deity or deities are no less rational than those who devote their lives looking for an unknown species or cure for a disease.

Faith isn't always emotional. Faith can be reliance on statistics and probability. For example rational people base their decision to have surgery on the probability of their survival as well as the measure of quality and quantity of life with or without it. If the probability is good then one has faith that the outcome will follow that rule. I would assume anyone view that thought process logical.

I don't believe faith is apart from logic and reason but is actually part of logic and reason.