In the usual taxonomy of mental states (usual, that is, among contemporary analytic philosophers of mind) belief is one thing, desire quite another. They play very different roles in the economy of the mind: Desires determine our goals, and beliefs determine the perceived means to achieve them, with action generally requiring the activation of a matched belief-desire pair (e.g., the belief that there is beer in the fridge plus the desire for beer). I confess I’m not much enamored of this picture.
Surely this much at least is true: The belief that P is the case (say, that my illness is gone) and the desire that P be the case are very different mental states — the possession of one without the other explaining much human dissatisfaction. Less cleanly distinct, however, are the desire that P (or for X) and the belief that P (or having X) would be good.
I don’t insist that the desires and believings-good are utterly inseparable. Maybe we sometimes believe that things are good apathetically, without desiring them; surely we sometimes desire things that we don’t believe are, all things considered, good. But I’m suspicious of the existence of utter apathy. And if believing good requires believing good all things considered, perhaps we should think genuine desiring, too, is desiring all things considered; or conversely if we allow for conflicting and competing desires that pick up on individual desirable aspects of a thing or state of affairs then perhaps also we should allow for conflicting and competing believings good that also track individual aspects – believing that the desired object has a certain good quality (the very quality in virtue of which it is desired). With these considerations in mind, there may be no clear and indisputable case in which desiring and believing good come cleanly apart.