Russell introduces the standard view of Hume's thought - as the principal source for "classical compatibilism" - one that he hopes to correct:

Hume's discussion of the problem of "liberty and necessity" was first presented in the Treatise (II, iii, 1-2) and, then, in a slightly amended form, in the first Enquiry (Sec. 8). It is widely held that what Hume has to say on the subject of the nature and conditions of moral responsibility is very largely limited to these important sections of his work. More specifically, Hume's concern with the problem of moral responsibility is generally interpreted in terms of his discussion of the nature of "liberty," or moral freedom, and the way in which it is related to causation and necessity. From this perspective, once we have acquired a proper grasp of Hume's arguments that show how liberty and necessity are related (i.e. that they are compatible), there is little else to learn from him about the nature and conditions of moral responsibility.

This general perspective on Hume's views on responsibility suggests that Hume, like many other philosophers writing on this subject, believes that the problem of responsibility just is the problem of "free will and determinism". According to this approach, any adequate interpretation and discussion of moral responsibility must begin with, or develop out of, some relevant and appropriate account of the nature of moral freedom. I believe that this perspective on Hume's views on responsibility fundamentally misrepresents his approach.
(Freedom and Moral Sentiment, p.11)

In the Treatise of Human Nature, Hume identified the "voluntarism" of Thomas Hobbes with the liberty of spontaneity. Hume contrasted this with the liberty of indifference, which he took to be synonymous with chance and absence of causes in our actions.

Russell is concerned that as the question of free will and determinism has become clouded in recent years, it is worth noting that Hume had a separate defense for morality. Hume's project to reconcile liberty and necessity depends critically on moral sentiments and Hume's naturalistic account of moral responsibility.

It is of some contemporary importance that Hume continues to be interpreted in this manner. The reason for this is that there is an increasing consensus among philosophers in the field that the classical compatibilist strategy has now been effectively discredited or surpassed by more recent developments in compatibilist thinking. Insofar as Hume continues to be read as holding to the classical compatibilist position, his views will inevitably be judged as of less immediate contemporary interest and significance. In other words, if the classical reading of Hume's compatibilism is indeed correct and it is also true that compatibilist thinking has now advanced well beyond the confines of this general strategy, then we must conclude that Hume's thinking on this subject is now somewhat dated and passé. The crucial question, therefore, is whether or not Hume has been properly interpreted by his commentators.
(Freedom and Moral Sentiment, p.4)

Modern followers of Hume are sometimes called the "new compatibilists," perhaps starting with Peter Strawson, who argued that whether or not determinism is true, we can defend morality on the basis of universal "reactive attitudes" to actions. We cannot fail to assign praise and blame to others. And we feel guilt and pride in our own actions. For some thinkers, this is freedom enough.

Russell is a critic of these "new compatibilists." He is correct that Hume's insight into moral sentiments has made an enormous contribution to the modern debate, especially via Strawson. But by conflating the question of moral responsibility with freedom of the will, many of these modern thinkers, including Russell, commit what we call the ethical fallacy, which confuses all responsibility with moral responsibility. We cannot defend freedom of action simply because we are observed experimentally to act morally. Nor can we say the free will is merely "the control condition for moral responsibility," as has become popular lately.

Some new compatibilist philosophers argue for moral responsibility even if determinism is true. The weakness of their argument is perhaps seen in the fact that some of their incompatibilist skeptic colleagues deny moral responsibility on the very same grounds - the standard two-part argument against free will.

The general claim that the project of the Treatise should be understood in terms of "Hume's ambition to be the Newton of the moral sciences" is now a commonplace in introductory textbooks and general histories of philosophy." Moreover, Hume's "Newtonian" project in the Treatise has produced several studies that are devoted to a detailed analysis and exegesis of this aspect of his thought. Even those who accept Kemp Smith's (Hutchesonian) naturalistic interpretation are generally willing to place equal emphasis on Hume's "science of man" as inspired (supposedly) by Newton. There is, however, a fundamental difficulty for views of this kind. How do we reconcile Hume's ambitions to be the Newton of the moral sciences, not only with his skeptical principles, but with a form of "naturalism" that teaches "that reason, as traditionally understood, has no role in human life" — a claim that, on the face of it, sits uncomfortably with Hume's (Newtonian) "scientific" ambitions.

The skeptical/naturalism divide in Hume's intentions gives his whole project a Janus-faced appearance. Indeed, the situation is more problematic than this, since it may be argued that the whole project in the Treatise is actually broken-backed. That is to say, both the skeptical and naturalistic dimensions of Hume's thought seem to be equally essential to what he is trying to achieve but are nevertheless inherently opposed and irreconcilable."
(The Riddle of Hume's Treatise, 2008, p.7)