will you explain the is-ought problem and its implications?
Aw yeah, the is-ought problem. Shit's classic, bro, goes back to Hume, and it goes something like this:
Sometimes, when I'm talking ethics with my bros, they describe the way the world is. They're like, "That chair is over there. The bar closes at 4AM. The sky is blue." and I'm like, "Yup. Yup." How could I disagree? These are obviously true things. But then suddenly they're like, "Therefore, we should go on a roadtrip tomorrow." And I'm like, "woooooooooah!" How the fuck did they get from how things are, to how things should be? Those aren't the same at all. If I asked, "Where should we go?" and you told me where we already are, that wouldn't answer my fucking question.
Let's say my bro Ice and I are drinking. Ice is about to do some stupid drunken shit (as he's wont to do) and I say the following:
"You are so drunk that you could die if you tried that."
That's an is-statement. It just describes something about Ice and the thing he's about to do. Maybe you're thinking he should not do this fucking thing. But why not? "Because he'll die." So what? "Well, you shouldn't do stuff that will kill you." AHA! See, that's not an is-statement. It's an ought-statement, which describes how Ice should proceed. Before we could say that Ice shouldn't do this stupid fucking thing, we needed to say he shouldn't do stupid fucking things in general.
People typically accept that statement, and in fact, so many people accept that statement that it seems obvious, and you might miss that it's hiding in there. You might just gloss right over it.
Sometimes, though, the hidden ought isn't so widely accepted.
Next morning, Ice and I are lying around on couches, nursing hangovers, and we have this conversation:
PB: "Dude, I am so hungover." (Is-statement)
PB: "I seriously feel like I'm going to throw up." (Is-statement)
PB: "Also, I spent all the cash I had last night." (Is-statement)
PB: "Dude, we ought to never get that drunk again." (Ought-statement)
Ice: "...Wait, what?"
How did I get from those first three things to that last one? I've only described my hangover. That's all I've done. No matter how fucking miserable my hangover is, it doesn't support my conclusion that I should never drink that much again; maybe I love being hungover. (I don't.) But I accept something like the following premise, the way-too-drunk premise: "You should never get so drunk that you spend all your cash and end up super hungover the next day." BOOM. Another ought-statement. Ice is confused because he loves getting that drunk, and is willing to put up with the hangover and relative poverty. He does not accept the way-too-drunk premise, so we disagree on how we ought to act, even though we totally agree on how things are right now.
The is-ought problem arises because of a particular property of logic called conservation, which (roughly) says that whatever your conclusion is, it has to be in your premises in some form or another. It doesn't have to be obvious - in fact, often it isn't - but it is, in some form, lurking down there. (This is a really rough gloss on conservation, so bear with me here.) It's a feature that makes logic really fucking great - it tells us exactly what is and isn't supported by our premises. We want conservation in logic. Conservation is our friend. When someone objects, "Wait, your conclusion isn't supported by your premises!" she is actually objecting that I've snuck something into my conclusion that isn't anywhere in my premises, which is a no-no.
So if you start with only descriptions of how things are right now, then you can't decide anything about the way things should be. You need oughts in your premises to get them in your conclusions.
Occasionally, bros invoke the is-ought problem to argue that there is no morality at all or some similar such claim. Those bros are fucking doing it wrong. It turns out that ethical theories just are attempts to provide ways to move from is to ought. For example, utilitarianism says, at bottom, that we ought to act such that pleasure (or whatever is "good") is maximized, something like, "Whichever act creates the most pleasure is the act that you ought to do." See how that gets you from is to ought? So you know some things about which act creates the most pleasure, your is-statement; then you've got the utilitarian rule, which is an ought-statement, and that moves you to your conclusion, that you should do that act. So the is-ought problem doesn't mean there is no morality.
It is, however, a problem for deciding which moral system is the right one. The utilitarian rule is an ought-statement, too; so it helps us choose other ought-statements, but how did we get it in the first place? Usually, through some hand-waving. When J.S. Mill argues for utilitarianism, he's mostly like, "I mean, c'mon! Who doesn't like pleasure, amirite? Obviously we should maximize pleasure and minimize pain. Duh." And when Kant argues for the Categorical Imperative, he's like, "I mean, it comes from a good will, and obviously a good will can't do anything bad! So, you know, act with that shit." Some ethical theories are even more upfront about their hand-waving: W.D. Ross argues for a bunch of duties like charity and justice and stuff, and he argues for them by just saying that justice and charity and stuff are obviously things we should value.
So the is-ought problem is a problem of metaethics, the philosophy of how ethics works. Some philosophers have tried to cross the divide by giving arguments about how we can get from an is to an ought; some just argue for certain baseline oughts like charity and go from there. For example, maybe it just is the case that killing is bad. Immoral, even. Then we ought not kill. That was simple! "But why shouldn't we be immoral?!" Because that's what "immoral" means. It means don't do this fucking thing; it should not be done. (To be honest, the meaning of "x is immoral" is also hotly debated, but I'm not going to get into that here.) The point is, it might be that "x is a thing that ought not be done" might be an is-statement that also gives us an ought. That's the route that tries to cross the divide.
It's a super-interesting problem, and lots of really, really fucking cool work is being done on it. Ultimately, the problem shows us that finding out the right thing to do isn't as simple as we'd like it to be. Damn.
As usual, the Wikipedia page is pretty helpful, both in explaining and knowing where to go next.
Hume originally proposes the problem in Book 3.1 of the Treatise.