In his discussion of natural virtues and vices (T 3.3.1.4-5, SBN 575), Hume has an argument that I think deserves a lot more consideration than it is usually given:
If any action be either virtuous or vicious, 'tis only as a sign of some quality or character. It must depend upon durable principles of the mind, which extend over the whole conduct, and enter into the personal character. Actions themselves, not proceeding from any constant principle, have no influence on love or hatred, pride or humility; and consequently are never consider'd in morality.
This reflection is self-evident, and deserves to be attended to, as being of the utmost importance in the present subject. We are never to consider any single action in our enquiries concerning the origin of morals; but only the quality or character from which the action proceeded. These alone are durable enough to affect our sentiments concerning the person. Actions are, indeed, better indications of a character than words, or even wishes and sentiments; but 'tis only so far as they are such indications, that they are attended with love or hatred, praise or blame.
The claim here is remarkable -- that it is self-evident that actions themselves are never considered in morality; actions are only considered in morality insofar as they are signs of something durable. Love, hatred, pride, and humility, are sentiments that do not consider transient and passing actions, and since Hume's version of moral sentimentalism takes all attributions of virtue and vice to depend on these, we can only get morality where those passions reach.
This is perhaps not what one would have expected from Hume's original set-up (T 3.1.2), where Hume (twice!) refers to actions in moral contexts. But, of course, the claim here is not that actions are not relevant to morality at all, but that when they are relevant, it is because they are taken as signs of 'qualities' that are lovable or hateable (if we are talking about others) or able to be objects of pride or humiliation (if we are talking about ourselves). That this is the case is clear when Hume begins talking about justice (T 3.2.1.2-3, SBN 477-478):
'Tis evident, that when we praise any actions, we regard only the motives that produced them, and consider the actions as signs or indications of certain principles in the mind and temper. The external performance has no merit. We must look within to find the moral quality. This we cannot do directly; and therefore fix our attention on actions, as on external signs. But these actions are still considered as signs; and the ultimate object of our praise and approbation is the motive, that produc'd them.
After the same manner, when we require any action, or blame a person for not performing it, we always suppose, that one in that situation shou'd be influenc'd by the proper motive of that action, and we esteem it vicious in him to be regardless of it. If we find, upon enquiry, that the virtuous motive was still powerful over his breast, tho' check'd in its operation by some circumstances unknown to us, we retract our blame, and have the same esteem for him, as if he had actually perform'd the action, which we require of him.
Hume is significant in being the primary early modern virtue ethicist -- even the scholastics in the period usually seem to think of morality in terms of moral law and duty, but moral law plays no role, and duty a very secondary role, in Hume's account of morality. Unlike Aristotelians, he can't take character or second nature as an inhering quality. Indeed, it seems Hume is committed to holding that character is not something you can really have. Nonetheless, character is something attributed to a person, and we attribute it by classifying actions and words based on whether they regularly give pleasure or pain and on whether they regularly turn out to be useful or the opposite. Someone whose words often cannot be relied on (thus highly defective in their usefulness and often displeasing) is assigned the vice of dishonesty; someone whose actions are like those of other dishonest people is assigned the same vice. We hate dishonesty and are humiliated if we find ourselves in a situation where our actions suggest, to our own consideration or to the consideration of others in a way we find plausible, that we are dishonest.
Thus when Hume talks about 'natural virtues and vices', he is not talking about inherent virtues and vices but attributed virtues and vices, and the primary features of Hume's ethics arise from the fact that on his account morality is a system of classification based on diagnostic actions. Unlike Aristotelian virtue ethics, which is agential (the virtues or vices are about how your passions tend to affect your choices), Humean virtue ethics is spectatorial (the virtues or vices are about how you tend to appear to yourself and others). Being moral is primarily an attempt to communicate that you are pleasant and useful. Hume has no strict agential component, I think. The reverse is not true -- Aristotle does think that communicating character is morally important (it's something you do in friendships, for instance, and friendship is a central pillar of the Aristotelian account of ethics), but it is a very secondary role. In fact, the doctrine of the mean directly implies that a Humean account would be inadequate, because with the doctrine of the mean, Aristotle famously establishes that there can be (for various incidental reasons) virtues and vices for which we have no words -- i.e, that are not included in our standard classifications. In Aristotle's account, virtues admit of a wide range of variations, but they are real and can be discovered even if we don't have a way of classifying them yet; but in Hume's account, something's being a virtue follows on its being classified a certain way.
When I teach virtue ethics in a survey course, I typically (as is fairly common) divide kinds of virtue ethics according to whether they are sentimentalist (like Hume) or rationalist (like Aristotle). But I think one could argue that classification is the more fundamental issue, and whether virtues and vices are inherent or attributed might perhaps be the most fundamental divide. (A potential advantage of this is that Confucianism as a whole straddles the sentimentalist/rationalist distinction in a very awkward way, whereas it sits very comfortably on the inherent side of the divide, for very much the same reasons Aristotelianism, Neoplatonism, and Stoicism do.)
