The more logical approach to life is to recognize that my own bounded rationality means it impossible for me to know everything. Thus, even though an idea seems wrong to me, I should give room for the possibility that I simply don't understand everything about it yet.
Permanently rejecting an idea that cannot be disproven seems little different than blind acceptance of an idea that cannot be proven. More often than not, the best answers I can give right now are "I don't know" or "I'm not completely sure."
There is One person who does know everything. When I am certain we know something in His heart, of that thing I can be perfectly confident.