Let's say, for the sake of argument, that I live in a world divided into tribes with strongly-differing views. My tribe says that many of our opponent's values are immoral and much of their leadership is corrupt; they say the same about us. My tribe says that our opponents often make up falsehoods easily refuted by known facts; they say the same about us. My tribe says that our arguments are based on principles of logic that have been accepted for millennia, while theirs appear to be absurd gobbledygook; they claim the opposite is true.
No one that I know of, on any side, has found a way to reconcile these differences or devise a compelling alternate viewpoint. One of the things we all agree on is that one side must be predominantly in the wrong, and the other side right.
I sincerely believe the key elements of my position; therefore I infer that my opponents are lying and/or insane. I consider myself to be a rational person who follows the scientific method; therefore I must test the possibility that I am wrong and attempt to find errors in my hypotheses.
Is there any way for me to determine whether or not I am insane, my perceptions are faulty, and/or my entire method of reasoning is fallacious?