When you try to solve a problem the goal or the reason to reject the current solution are often vague and hard to put in words. Irrational. For example, for many years the fifth postulate of Euclid was a source of mathematical discontent because of a vague feeling that it was way too complex compared to the other four. Such irrationality is a necessary step in human thought.

Yes, that’s fair. I’m not saying there’s no value to irrational hunches (or emotions, or spirituality). Just that you should be transparent when that’s the basis for your beliefs.