Many state blithely that they choose to believe this or that. The statement, on the face of it, is absurd. It is impossible for most of us to believe, for example, that 2 + 3 = 6. This proves easily that some beliefs are impossible, but it does not prove that it is impossible to choose some beliefs. Some people believe blue is attractive and other find it much less attractive. If I am forced to live or work in an environment where nearly every thing around me is blue, it is in my interest to believe that blue is attractive. It may or may not be possible for me to choose to be attracted to blue, but it does not really matter as this does not seem to be a belief in the important sense most people want to assign to belief.
When people say they choose to believe something, they are generally talking about something like the existence of moral value or God or mathematics. William James famously declared that our first act of free will is to believe in free will. His point is well taken, by some anyway. Life is filled with choices, and we make choices based on our beliefs. If we do not believe we have control over our beliefs, then we do not believe we have control over our choices. If we do not believe we can make choices, we are rather stuck in the mud. The fact that we carry on with our lives is evidence that most of us at least behave as if free will is possible.
Of course, free will, and freedom of belief are hardly one and the same. Is it possible for someone who believes recreational homicide is wrong to come to a different conclusion by an act of will? It is conceivable (though just barely) that some argument or experience might change ones mind, but this is not an act of will. If I move to a society where disbelief in Odin is punishable by death (no, I am not aware of any such society), I would certainly choose to avow publicly that I believe in Odin, but this avowal would be made much easier by actually being able to believe in Odin, for it is easiest to avow an occurrent belief.
Perhaps if we cannot simply choose a belief, we can choose to examine a belief in more detail in order to move closer to a new belief. I live where belief in Odin is required, but I do not as yet believe in Odin. In fact, I do not have the requisite experience or knowledge to believe in Odin, so I may begin to read texts on the basic tenets of Odin’s followers. I may attend worship services devoted to Odin. I may mimic prayers and sacrifices to Odin, if such are appropriate. I may discuss the virtues of Odin belief with his followers. When I come to understand Odin better, I may come to believe in Odin and declare honestly and proudly, “I choose to believe in the infinite power and mercy of Odin.” I may congratulate myself on discovering ways to choose beliefs. Now, I need only to define a belief.