Aumann’s agreement theorem, roughly speaking, says that two agents acting rationally (in a certain precise sense) and with common knowledge of each other’s beliefs cannot agree to disagree.
In other words, when two truth-seeking individuals share information, they approach the same beliefs.
Sometimes, when I’m in a discussion with others, I remember Aumann's agreement theorem. To me, it’s an ideal: Whenever we discuss facts about the world, we should approach agreement. Otherwise, we're failing. This ideal assumes that we are: