(1) If coming to believe is an act capable of being under direct voluntary control, doxastic voluntarism is true.
: This is one form of what is called 'doxastic voluntarism', by definition.
: Note that this does not require that the voluntary control be complete, indefeasible, or universal.
: Note that the reference is to 'coming to believe' rather than 'believing'.
(2) An act is under direct voluntary control when actually guided by intention to a particular end.
: Voluntary control requires (a) voluntariness and (b) control. The former requires that there be an intention; the latter requires that this intention guide action to a particular end.
(3) Coming to believe is sometimes actually guided by intention to a particular end.
: This can be seen by the fact that we seem to be able to have a direct effect on coming to believe in at least some specific ways.
: (a) We seem to be capable of affecting our coming to believe by resolving to follow evidence or be logical. We do sometimes resolve these things. Our resolving them is best explained by the fact that we find in our experience that we can come to believe under stricter or looser regimes, i.e., holding ourselves to stricter or looser standards, and these standards are voluntarily accepted or discarded. But this means we can change our coming to believe at least in some ways by resolution, which means that intention is a causal factor in coming to believe.
: (b) We seem to be capable of suspending judgment. But to suspend judgment is both an intentional act and one that directly affects our coming to believe. Therefore intention is capable of providing at least some guidance in coming to believe.
: (c) We seem to be able to refuse to believe, for ethical reasons; thus, for instance, we talk about refusing to believe that one's spouse is betraying one, because of the ethical value of trust. But refusing to believe would be a direct intentional control of coming to believe.
: (d) We seem to be capable of deferring to others in other belief; thus, for instance, we seem to defer to experts about what to believe about specific details in matters in which we are already in agreement. But this deference is an intentional act, and it appears to guide coming to believe.
: (e) We regularly propose pragmatic reasons for believing something (e.g., that it is easier to understand or more promising for future inquiry). In other areas of life in which we propose pragmatic reasons, it is because they are capable of being acted on voluntarily.
(4) Therefore coming to believe is an act capable of being under direct voluntary control.
: From (2) and (3).
: Note again that this is a fairly minimal conclusion: it does not require that we be able to believe arbitrarily and without any regard for evidence, for instance, and it does not require that our control be perfect or easy; nor does it require that we always are able in fact to do it. One of the most common errors in arguments against doxastic voluntarism is the assumption that it requires that coming to believe be arbitrary, easy to change, or involve nothing but choice, none of which are actually required in order to hold that we can control our belief, any more than saying that you have voluntary control over your limbs means that your movements will always, or even can ever, be purely arbitrary, always easily effected, or depend solely on one's will, all of which obviously may depend on conditions.
(5) Therefore doxastic voluntarism is true.
: From (1) and (4).
: Those who dabble in philosophical discussions of doxastic voluntarism may note that this is something of a 'tollensing' of the argument against doxastic voluntarism in Dion Scott-Kakures, "On Belief and Captivity of the Will." Philosophy and Phenomenological Research 54 (1994): 77-103, with some adaptation for difference of direction.