This blog post raised an interesting question--whether or not someone is unreasonable if there is no amount of evidence that could make them change their mind about something. Of course, at first blush, by definition if your mind is unwilling to allow any new facts to change it, you are beyond reason and therefore unreasonable.
However, I think most of us--myself included--would answer "of course I'd be willing to change my mind if new facts came out that challenged my beliefs! I just haven't seen such facts, yet, which is why I still firmly believe [abortion is murder; we shouldn't have a death penalty; Obama was born in China; the Redskins still suck]." Our unwillingness to change our minds is not so much that we're so dogmatic we refuse to listen to new facts, but rather that our worldview makes us look at those new facts differently. Facts that challenge our firm beliefs are either discredited or reinterpreted to fit our existing worldview. Consider these examples:
1) I think the Redskins suck because owner Dan Snyder is a moron who meddles in the team creating instability and he's just a rotten guy who makes the team suck and they still have a racist name even in 2012. If suddenly Dan Snyder donated his whole fortune to cancer research and lived the rest of his life like a monk in a broom closet at Fed Ex Field, and Coach Shanahan, free from Snyders meddling, traded for some good players and made some smart draft picks and the team had a winning season, I'd probably assume all that new information was just an Onion spoof article.
2) A strict gun control advocate who sees data that shows crime rates dropping in a town that recently relaxed its gun laws would assume the dropping crime rates are due to other factors, as there's no way this could be due to criminals being deterred by a more well-armed citizenry. If the crime rates went up in that town, the gun rights advocate would believe some other factor was causing the rates to rise, and that those rates would have gone up even further if not for the deterrant of the well-armed citizenry.
3) I think IHOP is disgusting. If I found myself eating at one that was clean, well-run and had decent food, I'd assume I walked into a Cracker Barrel by accident.