In what respect are we to understand the proposition, "I choose to believe x", and is there a significant difference between the proposition, "I choose to believe x" and "I choose to drive to San Diego this weekend"? Which epistemological systems tackle the question of the relation between belief and intention?
Both "belief" and "intentional act" are ambiguous terms, so the answer may depend on specific meanings, even for the same author. Ordinary factual beliefs, as in Plato's "knowledge is justified true belief", are typically not considered to be freely chosen, and therefore not intentional on the common meaning of "intention" (but see the last paragraph). They function rather as constraints on intentions to act, see Belief, Intention, Intentional Action by Speaks. "Choosing to believe" is quite different from ordinarily believing, try choosing to believe that the Sun will not rise tomorrow. However, "belief" is also used equivocally for "beliefs" in values ("faith"), and often both types are mixed. Values, like hope, love, etc., or some vehicles for values, like God, karma, etc., are open to choice, and on the traditional account require intentional acts, the acts of faith. There is also perennial controversy about the nature of volition ("free will"), and hence reality of "intentions", but in practical terms the difference between libertarian and compatibilist interpretations is mostly verbal.
As examples of "spiritual beliefs" indicate, it is not always straightforward to draw the line between factual and value side of beliefs. Moreover, some factual beliefs can be subject to choice, which would make their adoption an act of will (again on the traditional account). The simplest case is the liberty of indifference, when there is no preponderance of evidence for or against a belief. One is literally free to choose, and act on it. Situations of "hoping against hope", internal conflict, when core beliefs clash with acknowledged facts, etc., show that one can even choose to believe against compelling facts. Justification of willful belief choices in the face insufficient information by necessity to act is the central theme of James's lecture The Will to Believe:
"Our passional nature not only lawfully may, but must, decide an option between propositions, whenever it is a genuine option that cannot by its nature be decided on intellectual grounds; for to say under such circumstances, "Do not decide, but leave the question open," is itself a passional decision—just like deciding yes or not—and is attended with the same risk of losing truth."
In the light of recent neuroscience experiments it has also been argued that it is the action itself that is chosen, and the accompanying belief or "intention" is a confabulation (apparently, in experiments people often time their "intention to act" to after their muscles already start contracting, if not later), see How Does Neuroscience Affect Our Conception of Volition? by Roskies.
There is also a more general meaning of "intentional act", coined by Brentano (but with roots in medieval scholastics), and turned by Husserl into a centerpiece of his philosophical phenomenology. On this view all conscious activity, "the stream of consciousness", is a flow of interpenetrating intentional acts with intentional objects, at which the consciousness is directed (in reflection intentional acts themselves may become intentional objects of other acts). On this understanding all beliefs in particular are "intentional acts" (or perhaps chains of intentional acts), for the consciousness always "intends" its objects, see Consciousness and Intentionality in Phenomenology.
In psychology, I learned in a class that there's a principle of choice that divides choice into two classes: conscious choices and subconscious choices.
In my Buddhist training, I was taught that belief is nothing more than the result of our interpretations of experiences. People believe in science, for example, because science offers concrete and demonstrable examples which allow people to duplicate these direct experiences for themselves.
Most of the religious world does not do this, though until about 600 years ago (the Holy Roman Inquisition) this was in fact the norm for religion. With the rise of the Inquisition, reason was considered evidence of witchcraft, especially if it was reasoning that contradicted what the Catholic church said. The charge of heresy against the Catholic Church was not levied against anyone in history prior to the year 1156, save those who were actually clergy who were teaching things that opposed the core teachings of that faith.
Our discernment today has come a long way, but still has yet to invalidate the actual experiences that people have, because of the general tendency to be dismissive of religious beliefs as little more than a choice, rather than accepting that there may in fact be an underlying experience that the person clings to. It may be misinterpretation, but going on the offensive (from the perspective of the believer, who in today's world likely feels just as persecuted as any of our religious forebears) causes a further entrenchment into the idea that they have, and can actually inhibit the ability of the believer to reason fully and accept alternative ideas.
So yes, there is a choice that occurs. But there are actually several qualities of choice: conscious, informed, well-reasoned choices are almost always at odds with those which are spontaneous, reactive, or intuitive choices. And many choices are made before we're even aware of the choice to begin with: why did you choose the shirt you wear today? Why do you choose to buy your socks where you do? Why is one shirt preferred more than another? What will you eat for breakfast tomorrow? Hundreds of choices per day.
There are conscious choices. There are unconscious choices. There are choices that are preferences. There are choices we must choose for the sake of self-image. There are choices for health, just as there are choices for the lack of it. Every choice brings an experience.
Experiences result in analysis (where lots of people are lacking, including those who really shouldn't be). The result of analysis is a belief. We then build our thoughts on those beliefs, which create ideas. The ideas further what we look at in the world (e.g., perceptions), and these in turn motivate us to take actions. The graphic below should illustrate this paragraph.
My approach to this would be to use a synonym to: "I believe."
I believe that "I am convinced" is pretty much the same thing as "I believe."
The Merriam Webster dictionary also shows belief to be a synonym of conviction.
not credible or plausible
Plausible in turn is defined as:
having an appearance of truth or reason;
Meaning if something is reasonable, agreeable to reason or sound judgment, it is useful for convincing somebody enough that they eventually believe you.
Now if you convince yourself through your own experience or you experience somebody else convincing you is just a difference in semantics.
So in the same way you can choose to be convinced by something or chose to intentionally ignore sound reason.
Most beliefs, like love and hate, are spontaneous: it is as impossible to believe the sort of thing one does not believe as to love those things that inspire hate. Yet, there are chosen beliefs, but beliefs that are chosen are actually entirely different from the spontaneous ones. The difference is such as between "p" and "p is true."
A belief, in the case of a man, is a mental state.
A proposition expresses a mental state.
Given a proposition p, when a person is in a state of mind which can be expressed as p, we say this person believes p; otherwise this person does not believe p.
In the case of "Robert chooses to believe p," when Robert is not in the state of mind that can be expressed as p, Robert actually believes "p is true" in which p is merely verbal.
4.1 Let p = "there is a monster standing behind my back." If one believes p, he should have many bodily reactions that do no submit to the command of will, such as hair standing on end, goosebumps, chill, alertness and nervousness. If this person does not have this set of reactions, he is merely believing "there is a monster standing behind my back is true."
4.1.1 Let p = "I am sitting on the edge of an overhanging rock cliff," and ask yourself if you are believing p or "p is true."
4.1.2 Let p = "A yellow bird is about to swoop down on me." It is very likely that the accusers in Salem witch trial believed p, not "p is true," because they had all the unconscious reactions that corresponded to this belief; they are marvellous pretenders, but nevertheless they believed p, not "p is true."
4.1.3 It is very likely that Emily Rose saw something that others could not see. She believed p, not "p is true." Sincerely yours had often walked alone in the Black Forest during the darkest hours, bypassing the most Gothic cemetery and wondering why he was not slightly spooked. This sense of security was forever lost after he watched *The Exorcism of Emily Rose."
126.96.36.199 A false believe can nevertheless be an existent belief, i.e. a full-blown mental state; hallucination is a case in point.
188.8.131.52 The belief caused by hallucination is not true but real, so are the concomitant anguish. That is why, when there are signs of intention and skill of psychological abuse, a sensitive person should extract himself from such an environment as soon as possible instead of toughing it out because it takes only a few quiet snyde remarks to trigger schizophrenia in an otherwise normal person. American military explicitly asks their leaders to talk straight because, when the leader is snyde, those who look up to him are always snyder.
4.1.4 John Nash later in life said he still saw those things but he chose to ignore them. This attitude is similar to that of a normal person's towards his own reflection in a mirror.
4.2 Most of the knowledge passed down from books are actually of the type "p is true" where p is merely verbal; the most familiar beliefs of this type are those listed in the multiplication table. See what's the difference between p and p "is true"?
4.2.1 Take addition for example, when dealing with scalars, e.g., weight, we choose to follow arithmetic rules; when dealing with vectors, e.g., speed, we choose to follow the parallelogram rule.
Since beliefs are mental states and most beliefs are formed spontaneously, it is possible that a belief can be planted in a person's head before his conscious judgement; this is why brainwashing can be so effective, and why the likes of Honest Iago have been so successful in human history.See politically motivated movies.
This answer demonstrates how modern philosophers do philosophy.