(1) The inability to infer a statement with an 'ought' from a statement with an 'is' is a problem that arises only within the context of moral rationalism.
(2) Hume is right that an account treating moral obligations as relations between ideas is a highly implausible account of obligations.
(3) Hume is right that an 'ought' can be derived from a certain class of facts, namely, facts about what we regard as good and bad.
(4) Much of our moral life is a matter of good or bad moral taste.
Where I chiefly disagree with Hume is in his sentimentalism; I think it leads him to draw the line between reason and passion in the wrong place, and therefore to give a misleading account of how we recognize goods, to confuse virtues and moral roles, and to take a genuine insight (that there is moral taste) too far, by treating it as covering the entire field of moral life. But to understand why I think so, it is important to take a brief detour at the beginning to discuss what Hume means by 'reason'. This is a point that trips up many amateurs reading Hume, not always through any fault of their own.
There is a very famous line from Book II of the Treatise of Human Nature: "Reason is, and ought only to be the slave of the passions, and can never pretend to any other office than to serve an dobey them" (SBN 415). The claim is easy to misunderstand if taken out of context, but in context it makes sense.
'Reason', or as he sometimes calls it, 'understanding', is a technical term for Hume. It is, specifically, the imagination insofar as it judges according to demonstration or probability: "as it regards the abstract relations of our ideas, or those relations of objects, of which experience only gives us information". The 'imagination' part of this is all Hume, since Hume thinks all operations of the mind are operations of the imagination. But insofar as it involves relations, Hume is in agreement (as far as his use of the term goes) with the rationalists. In Malebranche and Clarke, the major rationalists Hume knew, the judgment of reason is understood as the perception of relations. The precise account varies, because there is no perfection agreement about what is related by these relations. But it is a standard rationalist position that when we judge something to be the case, what we are really doing is perceiving a relation between things. So, for instance, a rationalist might hold that when we make a judgment about what 2 + 2 is, we are really not doing anything other than perceiving that the idea of 2 + 2 is related to the idea of 4 by a relation of equality and is related to the ideas of 3, 5, etc., by relations of inequality. And, of course, the use of the word "perceiving" here is quite intentional: rationalists hold that the relations are not made by us, but exist independently of us. All that's left for us to do is to perceive the relation.
So 'reason' is a technical term for the rationalists, and Hume simply takes over this sense of the term -- as I said, and as I will explain later, I think this was a mistake, but it was understandable: it was, after all, the way many of the philosophers who discussed the question used the term. The only modification made was to adjust for the fact that Hume, unlike the rationalists, did not distinguish between reason and imagination (this, I think, is another mistake, but, again, that will come up later). Hume makes his claim about reason being the slave of the passions in the context of motivation, and in particular while discussing the common trope of the struggle of reason against the passions. His point is quite clear: reason in the technical sense can't motivate any action because merely perceiving a relation is not a motivation to anything at all. It may on some occasions be an object of motivation, that is something to be motivated about, but only insofar as you have an independent aversion or inclination to it. Hume is certainly right about this: nothing can motivate except insofar as it seems good or bad. But mere perception of relation between two things is not a recognition of the relation as good or bad, nor of the objects related as good or bad.
In Hume's account we recognize objects or relations as good or bad not by perceiving relations but by the pleasure and pain caused by our passions when we are thinking about the objects or relations. Some things make us uneasy; we are carried away from those things. Some things we find satisfying; we are drawn toward those things. Therefore, since reason can't motivate, and all motivation is through the passions, the only role reason has in action is to bring things to the passions. Reason, as perception of relations, is indeed like a slave: it brings things to the passions to judge, and it is the passions, not reason, that decide what to do with them. And it really ought to be: if you tried to make it the master, nothing would get done. So, Hume concludes, there is no real sense in which anyone experiences a struggle between reason and passion, ever.
Why, then, does the trope exist at all? The answer Hume gives is that 'reason' in the rationalists' technical sense is not the only sense of the term. We have a more colloquial sense, not defined very well, and perhaps not definable at all, that is much broader than the technical sense. On Hume's view, not all passions are violent or easily noticeable. Some passions are very calm and quiet. What is more, a number of these calm and quiet passions are very powerful passions: they are stable, effective, and decisive. Because they are calm and quiet and produce no disorder in us, however, we have a tendency to confuse them with another kind of mental operation that is calm and quiet and produces no disorder: reason. In Hume's own words:
'Tis natural for one, that does not examine objects with a strict philosophic eye, to imagine, that those actions of the mind are entirely the same, which produce not a different sensation, and are not immediately distinguishable to the feeling and perception. Reason, for instance, exerts itself without producing any sensible emotion; and except in the more sublime disquisitions of philosophy, or in the frivolous subtilities of the schools, scarce ever conveys any pleasure or uneasiness. Hence it proceeds, that every action of the mind, which operates with the same calmness and tranquillity, is confounded with reason by all those, who judge of things from the first view and appearance.
These calm passions are known by their effects, which can sometimes be extensive. Examples that Hume gives are benevolence, resentment, love of life, kindness toward children, the general desire for the good, and the general aversion to evil. These things, because they are calm, are colloquially treated as if they had more to do with reason than with other passions. Therefore when people talk about the struggle between reason and passion they are really, in Hume's view, talking about the struggle between two kinds of passion: calm passion and violent passion.
This is an important point, without which Hume's view will be radically misunderstood: what Hume calls 'reason' is not what most people call 'reason'. Most people are not using the term in the technical sense Hume has in mind. 'Reason' for him means what the rationalists mean by it: perception of relations. Most of us use the term in what Hume would regard as a loose sense of the term. Some of the things we attribute to reason Hume would agree should really be attributed to 'reason' if we are going to use the term this loosely; but he thinks it doesn't belong to reason in a strict philosophical sense but to our passions and sentiments.
I've taken this detour because in any comparison between Hume's view and other views, failing to understand what Hume means by 'reason' will muddy the comparison. Hume is using the term in a technical sense, one that must be taken into account in interpreting him. It is also a sense that must be taken into account when saying what one thinks he gets right and wrong. Since this post is getting a bit long, I will do that in my next post on this subject, which should appear at some point in the next few days.