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Source:: Hume discusses the problem in book III, part I, section I of his book, A Treatise of Human Nature (1739):

... But as authors do not commonly use this precaution, I shall presume to recommend it to the readers; and am persuaded, that this small attention 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 perceived by reason.

Am I right that this small attention means the problem of leaping from [is and is not] to [ought and ought not]? Even if so, how does this subvert all the vulgar systems of morality?

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Hume is using vulgar in its original sense, meaning "common." His claim is that all common systems of morality (he's probably largely thinking of Christian morality here) muddy the distinction between statements of fact like "water is wet" and statements of value like "water is good." The overall thrust of his argument is against the rationalist concept that the right moral judgment can be produced by reason (as usual, his main antagonist is Descartes). In building this argument, he leans on his empirical commitment to the idea that all statements of fact must be founded on sensory evidence.

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  • Did Christianity claim that it moves from is to ought in deductive manner and that it actually moves from is to ought? Because Hume is arguing that one can do it only inductively. And Christianity, as I see it, proclaims God in deductive manner and moves inductively to morals.
    – rus9384
    Sep 14, 2018 at 8:54
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'Vulgar' here shouldn't be taken in its usual pejorative sense; but in the pejorative sense of philosophy - of not being soundly (ie foundationally) based.

Hume's is-ought distinction, or so he claims, amplifies this; but this only if one believes principles should be 'one'; but not, perhaps if one thinks in contraries - the inner world opposed to the outer; microcosm vs macrocosm; or by a principle, that is one but has contrary manifestations - the noumenal world or Schophernian Will.

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  • I'm not convinced that vulgar does have a technical philosophical sense as delineated here. Do you have a source for that?
    – Chris Sunami
    Mar 27, 2015 at 19:43
  • @sunami: I'm not claiming that 'vulgar' is a 'technical' term of philosophy; merely that it shouldn't be taken simply as a piece of invective; but as descriptive - as in 'lacking sophistication'
    – Mozibur Ullah
    Mar 27, 2015 at 21:13

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