For a technical discussion of how we should adjust our opinions scientifically in debate with others, see Overcoming Bias. This follows an earlier post on the impossibility of disagreeing unless you (rather unreasonably) assume the other person is somehow misinformed, wrong-headed or stupid.
It does look very valuable, though I'd be grateful for a clearer explanation, notwithstanding the participants evidently think they've already given it.
There's a story about Einstein from his time at Princeton. In the lecture room, he discussed his ideas in free-ranging talks, which were so revolutionary and complex that the students begged him to put some formulae on the board so they could follow him properly. He promised he would, and next time gave another dense, extempore peroration, at the end of which he said, "It's as easy as two and two make four". He then walked to the board and wrote "2 + 2 = 4". That's mathematicians for you.