Belief is a confusing mixture of the voluntary and the non-voluntary. St. Thomas tries to explain this by saying that the knowledge of first principles and of conclusions drawn from them are not voluntary, while other beliefs are voluntary:
Faith implies assent of the intellect to that which is believed. Now the intellect assents to a thing in two ways. First, through being moved to assent by its very object, which is known either by itself (as in the case of first principles, which are held by the habit of understanding), or through something else already known (as in the case of conclusions which are held by the habit of science). Secondly the intellect assents to something, not through being sufficiently moved to this assent by its proper object, but through an act of choice, whereby it turns voluntarily to one side rather than to the other: and if this be accompanied by doubt or fear of the opposite side, there will be opinion, while, if there be certainty and no fear of the other side, there will be faith. (ST. II-II Q. 1, a. 4, corp.
However, in reality it is highly questionable whether the intellect ever assents to anything of necessity in such a way that it is impossible to doubt it. For example, if a skilled mathematician shows you a proof of some new conclusion using premises which are well known to you, you may assent to the conclusion without any doubt. But if he then says, “There is a flaw in this proof,” you are unlikely to respond, “I cannot accept that claim, as I have seen beyond any possibility of doubt that this conclusion is true.” Or if you do respond in this way, suppose he says, “In that case, I will offer to bet you $1 against $100 that there is a flaw in the proof and that I can show it to you. Since you claim that you cannot be wrong, you are bound to win the bet and gain a dollar.” Hopefully in this situation you will come to your senses and doubt the proof, rather than continuing to assert your own infallibility, an act of insane overconfidence which will surely cost you $100.
St. Thomas does point out that the act of making a statement, whether to oneself or to others, is always a voluntary act. However, he does not seem to take note of the fact that this implies that the contrary act is also possible, even if it would violate first principles or conclusions drawn from them. For example, just as I can say or write “2 + 2 = 4” voluntarily, I can equally well say or write “2 + 2 = 5”, should I so choose, and I can say this not only to others but also to myself.
Someone will respond to this that if I do say this, whether to myself or to others, I am lying. Indeed. But how is this lying detected? The main way that we would determine that someone was lying in such a case is that he would refuse to act on this claim. As an obvious example, I might say that I want to change two twenty dollar bills for a fifty (when he has one), and I would expect him to refuse. This would actually be more obvious with statements like “it is raining.” If someone believes it is raining, he will probably carry an umbrella or something of the sort. The problem with the mathematical statement is that it is so basic that it is hardly clear what it would mean to act as though two and two made five. But given that we can determine how a person believing something would act, we can find evidence that someone is lying by showing that he refuses to act in conformity with his claim, at least in certain contexts.
This suggests that there is a sense in which any belief will be entirely voluntary: just as I can voluntarily choose to make any claim, I can voluntarily decide to conform the whole of my life to the claim. In this way I am deciding to act in every way as though the claim were true, both interior and exterior, insofar as these things are in my power.
Choosing to believe, in this sense, would be rather like choosing to love someone. Just as I choose to conform my life to love, I can choose to conform my life to belief. However, there is one significant difference. There is reason to believe that one who chooses to conform his life to love is disposing himself as fully as possible toward love, such that it will always be true that he does indeed love. But there may be reason to think that, at least in some cases, it is different with belief. For example, suppose that someone were to say, “I choose to believe that I can walk out of a fifth story window without getting hurt.” If he does choose this in the manner under discussion, he will be willing to put it into practice. But even if he does actually carry it out, it is possible that he is doing this to prove that he believes, while in fact still not truly giving intellectual assent. In other words, it may be that part of the disposition to believe is in the intellect itself, and that such a disposition must be present there in advance in order for the choice to believe to be efficacious.
If this is the case, we could say that someone who “chooses to believe” when his intellect entirely lacks the appropriate disposition is rather pretending to believe, in a sense, rather than truly believing. However, this is not completely clear and consequently it remains at least possible that such a choice to believe is always efficacious.