Avira, gemora generally respects facts and logic. To understand your position better, I would like to see your examples of, say, Amoraim, researching facts and then paskening against the facts. I am sure there are some examples when we “do not believe our eyes”, but let’s analyze what are limits.
For example, there is a discussion between Jewish and Greek scholars whether the world was created and seemingly Greeks won the argument, but Jews are staying with our position due to the strength of the tradition (some of the conclusions may be Tosfos, not fully in Gemorah times).I understand that this is due to the incompleteness of the Greek proof. Were they to be shown a video recording of the eternal world (I guess this would have been an eternal video), they would have agreed.