What is honorable, what is fair, what is becoming, what is noble, what is generous, takes possession of the heart, and animates us to embrace and maintain it. What is intelligible, what is evident, what is probable, what is true, procures only the cool assent of the understanding; and gratifying a speculative curiosity, puts an end to our researches. (I.7)
Here we have it folks—the perfect summary of Hume's moral theory. Hume isn't down on facts and reason, he just thinks that we use both our head and our heart when making moral judgments. Reason is cool and clinical, which is fine (it never did Sherlock Holmes any harm, right?), but it's our natural sentiment that spurs us on and shapes our ideas about what's right and good.
Extinguish all the warm feelings and prepossessions in favor of virtue, and all disgust or aversion to vice: render men totally indifferent towards these distinctions; and morality is no longer a practical study, nor has any tendency to regulate our lives and actions. (I.8)
So, imagine what it would be like if we didn't use sentiment in our moral judgments. Could we even make moral judgments? Hume suggests that we could discuss morality in theory but it would be detached from real life. In other words, it'd be pretty much useless. It's only when we feel a reaction to virtues/vices that morality comes to life.
Celibacy, fasting, penance, mortification, self-denial, humility, silence, solitude, and the whole train of monkish virtues […] neither advance a man's fortune in the world, nor render him a more valuable member of society; neither qualify him for the entertainment of company, nor increase his power of self-enjoyment? (XI.I.3)
Some philosophers (especially religious ones) may believe that self-denial is a virtue. Even outside philosophy, people sometimes admire those who embark on periods of fasting, silence, or solitude. Hume, however, isn't on board with this idea. In his eyes, these things aren't useful or agreeable to anyone, so how can they be virtues? Hello?
Utility is only a tendency to a certain end; and were the end totally indifferent to us, we should feel the same indifference towards the means. It is requisite a sentiment should here display itself, in order to give a preference to the useful above the pernicious tendencies. This sentiment can be no other than a feeling for the happiness of mankind, and a resentment of their misery. (AI.3)
We shouldn't overlook the importance of reason, as it helps us size up whether something's useful or harmful. But what next? If we only used reason then we'd be like robots—we wouldn't feel anything and wouldn't care about anything. This is hardly the ideal way to view humanity, and that's why sentiment is so important: it gives us our motivation.
When it is affirmed that two and three are equal to the half of ten, this relation of equality I understand perfectly […] But when you draw thence a comparison to moral relations, I own that I am altogether at a loss to understand you. A moral action, a crime, such as ingratitude, is a complicated object. (AI.8)
When we're calculating a sum, we're dealing with hard facts and our answer is either right or wrong. Some folks have acted as though we can take the same approach to morality, but Hume sees this as a big no-no. Morality is way more complex and doesn't always stay the same in different eras and places. There are no grey areas in math but philosophy's a whole different ball game.
The hypothesis which we embrace […] defines virtue to be whatever mental action or quality gives to a spectator the pleasing sentiment of approbation; and vice the contrary. We then proceed to examine […] what actions have this influence. We consider all the circumstances in which these actions agree, and thence endeavour to extract some general observations. (AI.10)
Here, Hume recaps and builds on his main ideas. He's already argued that morality is a matter of sentiment (rather than reason alone) and that virtue is swell; now, we need to look at real-life examples. By doing this, we can come up with some more general thoughts and remarks on the wide world of morality.
While we are ignorant whether a man were aggressor or not, how can we determine whether the person who killed him be criminal or innocent? But after every circumstance, every relation is known, the understanding has no further room to operate […] The approbation or blame which then ensues, cannot be the work of the judgement, but of the heart. (AI.11)
This quote highlights why we need start out by getting the facts. In any criminal case, it's important to try to find out exactly what went down rather than be ruled by our emotions. But once we've done that, there's no more to understand: intellectual inquiry hits a brick wall and our sense of humanity comes to the rescue.
Ask a man why he uses exercise; he will answer, because he desires to keep his health. If you then enquire, why he desires health, he will readily reply, because sickness is painful. If you push your enquiries farther, and desire a reason why he hates pain, it is impossible he can ever give any. This is an ultimate end, and is never referred to any other object. (AI.18)
Hume takes a moment here to show how reason can only go so far. If we ask someone why they exercise and they tell us it's for health reasons, that's our question answered. But if we start asking why they want to be healthy and why they hate pain, they're gonna struggle to answer (and get pretty cheesed off). C'mon, you don't have to be Einstein to see that hating pain is a natural response—not an intellectual thing.
Thus the distinct boundaries and offices of reason and of taste are easily ascertained […] The one discovers objects as they really stand in nature, without addition and diminution: the other has a productive faculty, and gilding or staining all natural objects with the colours, borrowed from internal sentiment, raises in a manner a new creation. (AI.21)
Reason and taste work in different ways, with reason giving us the lowdown on what's true/false and taste guiding our overall moral outlook. Reason focuses on things as they are but taste brings something new to the table. Hume conjures up the image of a paint brush sweeping across the landscape, adding color to the world. Like a finished artwork, sentiment builds on reason to create something new.
Should we affirm that the qualities alone, which prompt us to act our part in society, are entitled to that honourable distinction; it must immediately occur that these are indeed the most valuable qualities, and are commonly denominated the social virtues; but that this very epithet supposes that there are also virtues of another species. (AIV.2)
Okay, so we know there are virtues and vices, but are there different kinds of virtues and vices? Hume's answer is a definite "yep." Take virtues: some varieties are useful to society and are valued because of this. By using the heading "social virtues" for this category, Hume gives us a heads-up that there are other kinds of virtue worth checking out, too. Makes sense, right?