Also keep in mind that it's more important to make your beliefs as correct as possible then to make them as consistent as possible. Of course the ultimate truth is both correct and consistent; however, it's perfectly possible to make your beliefs less correct by trying to make them more consistent. If you have two beliefs that do a decent job of modeling separate aspects of reality, it's probably a good idea to keep both around, even if they seem to contradict each other. For example, both General Relativity and Quantum Mechanics do a good job modeling (parts of) reality despite being inconsistent and we want to keep both of them. Now think about what happens when a similar situation arises in a field, e.g., biology, psychology, your personal life, where evidence is messier then it is in physics.