I am skeptical that you could legitimately determine whether someone has an open mind based on the result of a debate. If at the end of the debate your opponent has not changed his or her mind or has moved on to some other topic, the most you could conclude is that your arguments have failed to persuade him or her and/or that he or she got tired of the debate; you could not logically conclude that no arguments could ever persuade him or her.
1More importantly, I don't think it's illegitimate to enter a debate with the purpose of convincing another person of the correctness of your position even if you can imagine no way of conceding to his or hers. As an example, I believe that sexually abusing a child is morally reprehensible and I do not believe that anything could convince me otherwise. If some woman were arguing the opposite, I believe that I would have a moral obligation to enter a debate with her and try to convince her that she is wrong. If she were to present an argument that is facially compelling and to which I have no immediate answer, I would not concede to her conclusion that sexually abusing a child is OK; I would simply assume that with a little more thought I could come up with a counter-argument. I do not think that debating is limited to those who are uncertain of their position; on the contrary, I believe that some
2 of the most edifying debates to watch are between two people who are both utterly convinced of their own position and completely familiar with all of the arguments for and against it.
Further, I do not necessarily see the objective of a debate as to persuade the other party to your point of view. A debate could, for instance, benefit an audience. Even without an audience, however, I would consider a debate to be with merit if you are presented with arguments against your perspective that you did not consider. Those arguments need not alter your end-position, but if it helps you understand your position in a different way, re-evaluate a weak inference, or reach your conclusion through a different chain of logic, then it has added nuance and strength to your opinion. That is true even if your opponent is completely implacable, and in my opinion, that result alone marks a successful debate.
Also, you think you are omniscent if you think you know
everything; you do not think of yourself as omniscent in any but a misleading sense simply because you believe that you know
something.
1 Unless, of course, you are of the opinion that your arguments are so convincing that no person with an open mind could ever reject them, in which case I would question whether you had an open mind.
2 Evidently, not all. See, for example, the debate between Irockman1 and NAMKCOR on water tiles in the GIAW thread. On the other hand, it is at least slightly amusing that their contrariness is mirrored by the spelling of their usernames.
To not stray too far from the topic:
Emotionally charged debates about water tiles