University Diaries has this post about "going cosmic." One way to know that an academic has lost an argument (and knows it) is that they go cosmic -- in my field, generally arguing that truth is a construct.
It's the rhetorical version of a scorched earth strategy in war. I spend 20 minutes arguing that my position is right (implicitly acknowledging you should value the truth of my position), and when I realize I am wrong, I burn the earth behind me, declaring that I might be wrong, but you are wrong too because there is no truth, etc.
The biggest mistake people make when confronted with this policy is to pursue the argument further, taking seriously the position that there is no truth (made by a person earnestly telling you that this is an indisputable truth). Once you've done that, you've playing into their hands, playing toward a draw in a game you've already won.
No, the best thing you can do at that point is smile politely and end the conversation. By doing this you bring the argument to an end (with yourself as the victor) and allow the other person to save face, perhaps creating enough doubt that they will reconsider their original position.
By the way, a great example of going cosmic is found in Pilate's interrogation of Jesus. Pilate has to figure out if Jesus is some kind of rebel against Rome, a rather straight-forward legal and political question. He asks Jesus, "Are you king of the Jews?" In his answer, Jesus says that he came into the world to testify to the truth, and that everyone on the side of truth listens to Him.
Pilate responds, "What is truth?" and proceeds to have Him executed when it is clear that it's the politically expedient thing to do. He'd have made a great academic.