How we cite our quotes: Section.Part (if applicable).Paragraph
Quote #4
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.
Quote #5
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.
Quote #6
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.