In a heated argument, I can find it very easy to think that my opponent is simply being unreasonable. This may actually be the case, as we humans are not perfectly rational beings even on our best days. But if the topic of discussion is a matter of fact rather than opinion, then it can hardly be reasonable to agree to disagree. In fact, Aumann’s agreement theorem demands this, for rational persons under certain restrictions. It’s not practically applicable in everyday life, but its conditions suggest other sources of disagreement.
One possible source of disagreement is a difference in experience. Two parties may have seen entirely different evidence, or there may be subjective elements involved which prevent evidence from being shared or accepted. The evidence may be subject to interpretation or may meet one party’s standards of evidence but not the other’s. Prior beliefs may also be a source of disagreement, especially with weak evidence which may not suffice to change one’s position on a topic. And, of course, one or both parties may be acting irrationally. There are numerous biases that make it hard to change minds.
Part of why I’ve been thinking about this is that I have enjoyed debate for as long as I can remember. I think I may have felt for some time that consensus is the proper result of discussion and that leaving with a disagreement is something of a failure, although sometimes unavoidable. Hopefully examining the cause of disagreement, especially in myself, can help lead to better understanding with others.