I often see it claimed that you can't derive an "ought" from an "is", and I have some sympathy for that view, which is often referred to as "Hume's Law". But I'm reminded by a discussion on Facebook, where I just chipped in, that Hume's point was more subtle.
His complaint seems to be that many philosophers go along piling up "is" statements; then you notice that somewhere along the way they've slipped into "ought" language. But how is that possible? As we'd put it in modern lingo, it seems that no number of statements using the copula "is" can ever (just as a matter of propositional logic) entail a statement with the copula "ought". So it appears that, if these philosophers have arguments that are valid (just as a matter of propositional logic), then they must be relying somewhere on one or more unstated premises that contain "ought". But, I take it Hume is suggesting, such premises are likely to be controversial. Accordingly, we shouldn't be persuaded by the arguments of these other philosophers.
But I think it can be taken a bit further when the famous passage in Hume's Treatise of Human Nature is read in the context of the entire meta-ethical discussion that precedes it. It appears that Hume believes you can derive an "ought" from an "is" in some cases. You can't do it as a matter of propositional logic, but if you understand the meaning of "ought" you can do it as a matter of semantics.
Compare the following:
Premise: Foo is a bachelor.
Conclusion: Foo is male and is not married.
Given the meaning of the word "bachelor", this deduction is perfectly valid. It's a matter of semantics - of meanings - not a matter of using the rules of propositional logic, such as modus ponens, modus tollens, etc.
Hume seems to have a similar idea about how we ground "ought" statements. For Hume, the meaning of "ought" is such that the following (or something like it) is a valid argument:
Premise 1.: Professor Snark has a desire for chocolate.
Premise 2.: Professor Snark believes (or should it be "correctly believes"?) that there is chocolate in the cupboard.
Conclusion: Professor Snark has a reason to go to the cupboard to find the chocolate.
Further conclusion: All other things being equal, Professor Snark ought to go to the cupboard to find the chocolate.
I.e., for Hume to say that somebody "ought" to do something is just to say that they have a reason to do it, or perhaps a reason that actually prevails over any contrary reasons that they might also have.
And we can then look at various kinds of "oughts". Perhaps, for Hume, a moral ought is a reason that is based not just on any old desire but a desire for the welfare or the non-suffering of others, a kind of sympathy for others' pain. Thus, Hume would probably accept something like this as a valid argument.
Premise 1.: Jill Bloggs sympathises with the suffering of Joe Sixpack.
Premise 2.: If Jill Bloggs stops the torturer stretching Joe Sixpack on the rack, Joe Sixpack's suffering will be relieved.
Conclusion: Jill Bloggs has a (moral) reason to stop the torturer stretching Joe Sixpack on the rack.
Further conclusion: Jill Bloggs (morally) ought to stop the torturer stretching Joe Sixpack on the rack.
Obviously, things get a bit more complicated than this. What if Jill doesn't feel any sympathy Joe? We might still want to say that she ought to do what she can to prevent his torture. I think that Hume, at least in his later work, realised that it gets a bit messy, and that the above analysis might be too simple. But he'd still insist that somewhere along the line the various kinds of "oughts" that we recognise will always involve something like a desire and that moral "oughts" will always involve something like sympathy (or desire for another being's non-suffering).
This is all putting the point in modern language, and of course I don't know exactly how Hume would phrase things if he had absorbed modern ways of discussing such issues, but I'm confident that he'd consider the above to be at least a reasonable first approximation of his position. His real point is not to say that "ought" claims are totally ungrounded, but to say that we need to understand the character of "ought" claims and to see how they can't be grounded in just any old "is" ... but must be grounded in certain contingent features of human psychology such as desire and sympathy. He'd insist that morality could never motivate us unless it were grounded in desires (in a broad sense) as well as reason.
Although the theory says that oughts can be grounded, and are not just mysterious, it's importantly a subjectivist theory. Hume doesn't think "ought" claims are altogether ungrounded, but he thinks that they are grounded in the desires and so on that people actually have, so some reference will need to be made to those people and their psychological characteristics. There are no objective "ought" statements in the sense of "ought" statements that are true, totally independently of the psychological characteristics that various human subjects actually have. On the other hand, he thought we were sufficiently similar psychologically to be able to reach agreement on what people (morally) ought to do in various situations. He'd have loved the modern idea that there is an evolved human psychology that underpins our responsiveness to other human beings and our sympathy towards any creature that we can imagine suffering pain.
I happen to think that the views that I've attributed to Hume are more or less correct, but that's not such much my point. My point is more to emphasise that Hume was saying something much richer - more subtle and complex - than just the fact that you can't, as a matter of propositional logic, deduce an "ought" statement from an "is" statement.
But, of course, he realised that too.