The is–ought problem, as articulated by the Scottish philosopher and historian David Hume, arises when one makes claims about what ought to be that are based solely on statements about what is. Hume found that there seems to be a significant difference between descriptive or positive statements (about what is) and prescriptive or normative statements (about what ought to be), and that it is not obvious how one can coherently transition from descriptive statements to prescriptive ones. Hume's law or Hume's guillotine is the thesis that an ethical or judgmental conclusion cannot be inferred based on purely descriptive factual statements.
A similar view is defended by G. E. Moore's open-question argument, intended to refute any identification of moral properties with natural properties. Ethical naturalists view this so-called naturalistic fallacy as not a fallacy.
The is–ought problem is closely related to the fact–value distinction in epistemology. Though the terms are often used interchangeably, academic discourse concerning the latter may encompass aesthetics in addition to ethics.
Hume discusses the problem in book III, part I, section I of his book, A Treatise of Human Nature (1739):
In every system of morality, which I have hitherto met with, I have always remarked, that the author proceeds for some time in the ordinary way of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when of a sudden I am surprised to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not. This change is imperceptible; but is, however, of the last consequence. For as this ought, or ought not, expresses some new relation or affirmation, it's necessary that it should be observed and explained; and at the same time that a reason should be given, for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it.