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Hume famously closes the section of the Treatise that argues against moral rationalism by observing that other systems of moral philosophy, proceeding in the ordinary way of reasoning, at some point make an unremarked transition from premises whose parts are linked only by “is” to conclusions whose parts are linked by “ought” (expressing a new relation) — a deduction that seems to Hume “altogether inconceivable” (T3.1.1.27). Attention to this transition would “subvert all the vulgar systems of morality, and let us see, that the distinction of vice and virtue is not founded merely on the relations of objects, nor is perceiv’d by reason” (ibid.).

Few passages in Hume’s work have generated more interpretive controversy.

According to the dominant twentieth-century interpretation, Hume says here that no ought-judgment may be correctly inferred from a set of premises expressed only in terms of ‘is,’ and the vulgar systems of morality commit this logical fallacy. This is usually thought to mean something much more general: that no ethical or indeed evaluative conclusion whatsoever may be validly inferred from any set of purely factual premises. A number of present-day philosophers, including R. M. Hare, endorse this putative thesis of logic, calling it “Hume’s Law.” (As Francis Snare observes, on this reading Hume must simply assume that no purely factual propositions are themselves evaluative, as he does not argue for this.) Some interpreters think Hume commits himself here to a non-propositional or noncognitivist view of moral judgment — the view that moral judgments do not state facts and are not truth-evaluable. (If Hume has already used the famous argument about the motivational influence of morals to establish noncognitivism, then the is/ought paragraph may merely draw out a trivial consequence of it. If moral evaluations are merely expressions of feeling without propositional content, then of course they cannot be inferred from any propositional premises.) Some see the paragraph as denying ethical realism, excluding values from the domain of facts.

Other interpreters — the more cognitivist ones — see the paragraph about ‘is’ and ‘ought’ as doing none of the above. Some read it as simply providing further support for Hume’s extensive argument that moral properties are not discernible by demonstrative reason, leaving open whether ethical evaluations may be conclusions of cogent probable arguments. Others interpret it as making a point about the original discovery of virtue and vice, which must involve the use of sentiment. On this view, one cannot make the initial discovery of moral properties by inference from nonmoral premises using reason alone; rather, one requires some input from sentiment. It is not simply by reasoning from the abstract and causal relations one has discovered that one comes to have the ideas of virtue and vice; one must respond to such information with feelings of approval and disapproval. Note that on this reading it is compatible with the is/ought paragraph that once a person has the moral concepts as the result of prior experience of the moral sentiments, he or she may reach some particular moral conclusions by inference from causal, factual premises (stated in terms of ‘is’) about the effects of character traits on the sentiments of observers. They point out that Hume himself makes such inferences frequently in his writings.

6. The Nature of Moral Judgment
On Hume’s view, what is a moral evaluation? Four main interpretations have significant textual support. First, as we have seen, the nonpropositional view says that for Hume a moral evaluation does not express any proposition or state any fact; either it gives vent to a feeling, or it is itself a feeling (Flew, Blackburn, Snare, Bricke). (A more refined form of this interpretation allows that moral evaluations have some propositional content, but claims that for Hume their essential feature, as evaluations, is non-propositional.) The subjective description view, by contrast, says that for Hume moral evaluations describe the feelings of the spectator, or the feelings a spectator would have were she to contemplate the trait or action from the common point of view. Often grouped with the latter view is the third, dispositional interpretation, which understands moral evaluations as factual judgments to the effect that the evaluated trait or action is so constituted as to cause feelings of approval or disapproval in a (suitably characterized) spectator (Mackie, in one of his proposals). On the dispositional view, in saying some trait is good we attribute to the trait the dispositional property of being such as to elicit approval. A fourth interpretation distinguishes two psychological states that might be called a moral evaluation: an occurrent feeling of approval or disapproval (which is not truth-apt), and a moral belief or judgment that is propositional. Versions of this fourth interpretation differ in what they take to be the content of that latter mental state. One version says that the moral judgments, as distinct from the moral feelings, are factual judgments about the moral sentiments (Capaldi). A distinct version, the moral sensing view, treats the moral beliefs as ideas copied from the impressions of approval or disapproval that represent a trait of character or an action as having whatever quality it is that one experiences in feeling the moral sentiment (Cohon). This last view emphasizes Hume’s claim that moral good and evil are like heat, cold, and colors as understood in “modern philosophy,” which are experienced directly by sensation, but about which we form beliefs.