You don't need specific empirical data to back up the point of saying that claims without empirical data are not reliable enough. We have the scientific revolution to back that point up.
I think it's worth noting the irony in that you seem to believe in solving everything rationally except for the value of rationality.
One thing that scientific research has elucidated is that gut feelings aren't useless, and in fact can be very useful in evaluating people. The thing is that we take in so much data via our senses and the conscious mind is only capable of handling a very small amount of those signals. The unconscious mind picks up on these things and surfaces them as intuitions.
