[I]t is only in two senses, that any affection can be called unreasonable. First, When a passion, such as hope or fear, grief or joy, despair or security, is founded on the supposition or the existence of objects, which really do not exist. Secondly, When in exerting any passion in action, we chuse means insufficient for the designed end, and deceive ourselves in our judgment of causes and effects. Where a passion is neither founded on false suppositions, nor chuses means insufficient for the end, the understanding can neither justify nor condemn it.
On a natural reading of this passage, Hume has in mind cases like these:
False Supposition: Tom's fear of Casper the ghost. Given that there are no ghosts (and, in particular, that Casper the ghost does not exist), Tom's fear is founded on a false supposition (the supposition that Casper exists). Thus, Tom's fear can be called unreasonable.
Insufficient Means: Jane's decision to eat an apple (when motivated by her aversion to scurvy). Given that eating apples will not help one avoid scurvy, Jane's decision to eat the apple is founded on a false judgment about causes (of scurvy) and effects (of eating apples). Thus, Jane's decision (and/or action) can be called unreasonable.
Note that Hume's account of what makes for an "unreasonable" belief seems to be the following: A belief that P is unreasonable if and only if ~P. I'll come back to this point in a later post, but it is important to notice it here.
A natural criticism of Hume's position is that these cases don't seem to be cases of unreasonable emotions/decisions/actions. If anything, the false beliefs giving rise to Tom's fear and Jane's decision seem to help (rather than hinder) the reasonableness. What would be unreasonable, the thought goes, is for Tom to fear Caspar when he doesn't believe that Caspar exists (or for Jane to eat an apple as a way to avoid scurvy when she doesn't think apples prevent scurvy). To the first part of this criticism (the claim that the affections in these two cases are not unreasonable), I think Hume has room to maneuver. He even makes a point of articulating that "properly speaking" it is the judgments involved (and not the passions) which are unreasonable. So, what about the thought that there are these other cases, in which the passions are unreasonable?
Interestingly, Hume's framework leaves no room for such cases. Passions are secondary impressions (aka "impressions of reflection"), and thus, are responses to antecedent mental activity. In these cases, the passions can't be present in the absence of the relevant judgments. Setting aside the question of whether this is a desirable feature for Hume's mechanics of mind, it is, at least, an explanation of why Hume doesn't consider such cases: they are impossible, not irrational.