If you are not willing to be wrong about your beliefs and preconceptions, you have failed as a thinker and, even worse, as a human being.
A key part of being human is to acknowledge your own fallibility, to acknowledge that we don't know everything, and that we are oftentimes, simply, wrong.
We don't know everything, and even when we do decide that we believe something, we must also consider the multitude of people that believe the opposite of what we do, and that many of those people are not unintelligent cattle simply following a charismatic leader. Many of them are also intelligent and critical thinkers who have happened to decide that the evidence points in a different direction than you think it does.
That said, it's difficult to live a life not mired in depression and inactivity if you are constantly in a state of questioning even the most basic of your beliefs. At some point, once you've examined the evidence (as much evidence as possible), you must make some decisions about the nature of the world around you. Personally, I also think you must arrive at a metaphysical framework for the world that you believe in, to keep your mind from spinning out of control
The stronger and more well-considered the position you hold is, of course the more difficult it would be for some outside source to change your mind at some point in the future. However, if you are not even willing to change your opinion no matter how convincing the argument to the contrary is, your failure as a human being is complete. Because we are all different.
Photo by Hansel and Regrettal, via Flickr Creative Commons |