"Chances are you've disagreed with someone today, and walked away without settling your differences. I'm forced to conclude that at least one of you is not an honest truthseeker."
- from Chapter 8 (Diogenes' Nightmare) of the book titled "The Big Questions" by Steven E. Landsburg, Ph. D. - Professor of Economics at University of Rochester.
To read more, Google for the keywords "Aumann" and "agreeing to disagree".
For a good account of the theory behind "disagreements" and "honesty", you can refer to Robin Hanson's PPT titled "The Irrationality of Disagreement": http://www.fhi.ox.ac.uk/__data/assets/powerpoint_doc/0005/8762/Deceive-07.ppt.