On the subject of belief, my belief anyway, I've always tried to be clear. But the comments below and on Twitter show me I haven't succeeded. So let's try again.
As the dictionary defines it, belief is a state or habit of the mind. Sometimes, beliefs are based on evidence --but not always. You can end up with a belief thanks to education or upbringing or even bad brain wiring. A case of indigestion can be interpreted as an apparition and produce a belief in space aliens. The way your father spoke about black people might be why you believe they are inferior. Or perhaps your inability to resolve your own sexual tendencies has left you believing that homosexuality is immoral. The point is beliefs need not be based on anything. They just are. Like any other habit, this habit of the mind is something we fall into for one reason or another. Sometimes the reason is a good one. Sometimes it isn't.
Habits can be hard to break, but we aren't their prisoners. When introduced to clear evidence, intelligent people will attempt to break their old habit of believing in something that clearly isn't true. And I have done this. Once upon a time, I was firm in my belief that every word in the Torah, as we have it today, was given by God to Moses. Having encountered reams of evidence for things like scribal errors, I no longer believe in the Immutability of the Torah. When evidence speaks, I try to listen.