A question for scientists

Have you ever tried to convince yourself of something, even though you know it's wrong?
For example, that tomatoes really should go with peanut butter (why? because they're two of my favorite things!) but no, tomatoes and peanut butter don't like each other (except, actually, in the rare Thai dish, crap, bad example).

Well anyway. How do you possibly know how to describe why you know something? Are feelings and convictions even describable? If we can't use logic to defend a feeling or conviction, where does that leave us?

Being an engineer, my default is to look for logical support before drawing conclusions about anything. But that doesn't actually work for every situation.

For example: 68-88% of the world's population (and ~80% of the American population) adheres to some sort of religion. However, many logical arguments could be (and have been) made to "disprove" the existence of a higher God of some sort; that is, if each person has not had a record-able, unquestionable religious encounter, it is difficult to logically prove the logical truth of the belief system.

And yet, people believe nonetheless. Many logical scientists are believers, as well. Why do we take this one exception to our "logic rule"? When we spend so much time insisting that only tangible proof, and sometimes fourfold tangible proof, is sufficient in our scientific pursuits, why do we turn to something else to prove this?

And is this the only time when such an intangible proof is sufficient? If we can use a basic "gut feeling" or "just knowing" for trusting a higher being with control of the world, however that is, can we trust that same feeling sense for other decisions? And if we can, do we need more proof? Does it make sense to ask for more when the only proof we have is that knowledge that something just is a certain way?

I leave this question for you, scientists. Do we have a way to use that gut feeling (and it is surprisingly useful in directing our research)? Can it be enough proof on its own? If it is the basis of a decision, can it by definition logically need any more proof? If the basis is not logical, can we adhere the rules of logic to it?

Maybe I should return to my small bookshelf of philosophers for this one. Unfortunately, it seems most of them were Christian... or at least the ones I have (thanks Catholic school). hmm.