I recently saw the question posed whether it is possible to choose what one believes. The answer is obviously not. Having said that, it clearly is possible.
Before I get into either answer, I want to briefly define what I will mean by the word reality. It is that which, when you stop believing in it, doesn’t go away.
It is clear, then, that it is not possible to choose what one believes because belief is, simply, what reality appears to be. Beliefs are, in this sense, passive, like sight or hearing. We cannot choose what we see—we look and there it is.
But even in saying that, we can begin to see why it is possible to choose our beliefs: You can choose where you look.
If you hear a belief proposed which depends for intelligibility on knowledge which you don’t at present have, the belief will necessarily not be believable. You might have no reason to disbelieve it, or you might take it on the authority of whoever told you as likely to be true (whatever it means), but you will not actually believe it. To give a concrete example, suppose someone is telling you something about relativity, and says that some property is true of the Lagrangian near massive bodies. If you have no idea what the Lagrangian is, you can trust that he isn’t wrong, but you can’t believe what he’s saying because you don’t know what it means. For you to believe it, it must seem to you an accurate description of reality. Until you understand it, to you it is not in fact a description of anything at all. Now, it is quite possible to, by choice, refuse to ever learn any of the base knowledge necessary for the belief to be believable. If you did this, you would be choosing not to believe the belief.
A practical case I deal with all the time is that young children will not listen to any evidence about the toy store being closed because they are unwilling to believe the necessary corollary to it: that they cannot go to the toy store right now. Toy stores can’t close, and I’m a monster for not taking them there, now. It is true that they don’t believe the toy store is in fact closed, but in shutting themselves off from all evidence because they can’t deal with the consequences, they are clearly choosing to believe that the toy store is in fact open. (To be clear, I picked this example because it should be familiar to everyone and is ready to hand, I am not trying to subtly call all atheists children, nor anything like that. I do my best to restrict rhetoric to posts in the rhetoric category and with a warning up top about how to read them. I believe in active aggression, not passive aggression.)
In a similar way, it is also possible to choose to believe something: in the spirit of inquiry, one could seek out all of the knowledge necessary for a belief. Properly, one would be attempting to believe it. There is an asymmetry here, because the best one can do is try to believe something whereas ignorance can be guaranteed. It is always possible that, having all the necessary groundwork for a proposed belief to be believable—in other words, fully understanding the idea—it still does not seem to be an accurate description of the world. This is always going to be true of false beliefs, like the terrorist attacks of 9/11 on the world trade center being an inside job or the one-gene-one-protein theory which was recently chucked into the dustbin of biology. It may even be the case of true beliefs where we don’t understand them well enough, like people who rejected the Monty Hall problem despite knowing a lot about probability and thinking they fully understood the problem specification.
But it is very important to note that what constitutes attempting to believe a belief is not purely an act of will. It is the will directing the intellect where to look. That is as far as the will can go; the intellect will see what it sees, just as will can literally make your eyes look at something but your eyes then see what they see, and not what you wished to see. It is a question of the will overcoming laziness or fear and putting in the work of learning, not a matter of the will overcoming the intellect and creating something in it. Human will is a powerful thing, but it cannot do the impossible, and it is not possible to create impressions upon the intellect through sheer will. The intellect is always fertilised by the reality it perceives. Will can no more create a belief in the intellect than a man can impregnate the color blue.
Update: My friend Eve Keneinan pointed out that I didn’t address the complication that we can choose to look at our imagination rather than at reality or nothing at all. I’ve fixed that in its own blog post.