In my model of argument (ValueOfArguing) I think people start bringing different data and conjectures to the table. They naturally disagree. During the argument, they exchange proposed "facts" ie. "you're wrong because in 1856 ..."
They may, eventually end up with a common set of believed facts, but still disagree as to the generalizing conjectures they make from them. (DisagreementAndDishonesty)
But this, despite it's adversarial nature, is a collaborative research projct, which should enlighten both parties. The disagreement is a kind of potential energy.
But at some point, it's possible that consensus is reached. That the two parties do agree. This is the point I call epistemic exhaustion and I don't see it as goal of argument. It's just the point when you run out of the potential energy to do more work through argument. It's the point at which you are no longer likely to improve your knowledge through argument.
More on consensus
See also :