Late Night/Early Morning

There is a paradox that says that we must both be open minded, and also stick to our guns and fight for what we believe. Well which one is it? Is it better to stubbornly continue on with your own set of hard-figured values, or is constantly considering new data and applying it to your worldview the way to go? Scientists especially struggle with this paradox, because they must except that it is never possible to be 100% sure of a fact, and yet they must act as though they know what they are talking about.