Is-ought problem
In ethics, the is-ought problem was raised by David Hume (Scottish philosopher and historian, 1711-1776), who noted that many writers talk about what ought to be on the basis of statements about what is. But there seems to be a big difference between descriptive statements (what is) and prescriptive statements (what ought to be).
Hume's classic formulation of the problem is found in book III, part I, section I, of his G. E. Moore's 'open question argument', intended to refute any identification of moral properties with natural properties -- the so-called 'naturalistic fallacy'. And, like the naturalistic fallacy (which is often misunderstood to involve the arguably fallacious inference from 'this is (un)natural' to 'this is (im)moral'), the is-ought problem has been misunderstood as related to a less deep, but more common issue: many people use 'is-ought' talk in making the arguably true claim that, just because something is the case, that doesn't mean that it ought to be the case. On this misunderstanding, Hume was arguing against those complacent moralists who hold that the world is just fine as it stands, and needs no improvement. This is, of course, not Hume's point -- he meant to challenge the hasty transition whereby theorists move to prescriptive claims directly from descriptive claims. This is a very general and very deep challenge to any descriptive account of moral thought, a challenge that is in keeping with Hume's anti-rationalist bent as a moral theorist.
Many people find Hume's question unanswerable, and see no hope for grounding moral statements in purely descriptive ones. A handful of arguments have been proposed which claim to show that an "ought" can actually be derived from an "is". John Searle designed such an argument. Basically, it tries to show that the act of making a promise places one under an obligation by definition, and that such an obligation amounts to an "ought". See one to this.
Connections to the rest of Hume
The apparent gap between "is" statements and "ought" statements, when combined with Hume's fork -- the idea that the only meaningful statements either follow from logic or make particular claims about the physical world -- renders "ought" statements of dubious validity. Since "ought" statements don't seem to be either analytic or synthetic, and these are the only ways a statement can be meaningful, moral statements seem to be meaningless. Two responses to this are moral skepticism and the alternatives known collectively as non-cognitivism.
