However, there are several difficulties in Kemp Smith's approach and in his "naturalistic" intperpretation of Hume's philosophy. The first of these is his emphasis upon the words "nature," "natural," and "natural belief." Hume himself des not use the phrase "natural belief," and while he often uses the word "nature" in contexts that might seem to support Kemp Smith's interpretation..., he gies the term "nature" no emphasis comparable to his typographical emphasis on such words as "CUSTOM" and "HABIT"....
This is from Claudia Schmidt's David Hume: Reason in History (Pennsylvania State: 2003), p. 5. Here Schmidt is just summarizing the scholarship (Schmidt's work is very good for getting a basic impression of what Hume scholars have said). It's a common view. But I've never entirely understood it; because it seems likely to me that Kemp Smith was using 'naturalist' in his sense, not in a special Humean sense. If we look at some of Kemp Smith's other writings (which I suspect Hume scholars generally have not), we find that he occasionally divides philosophical systems into three basic types:
1. skeptical
2. idealist
3. naturalist
The skeptical type of philosophical system is exactly what it sounds like. 'Idealism' as used here is an idiosyncratic usage; by it Kemp Smith means the sort of philosophical approach that gives rational or intellectual agency an explanatory priority over everything else. Thus I am an idealist in this sense, Kemp Smith was an idealist in this sense, and, indeed, most theists are idealists in this sense. Naturalism contrasts with this; naturalists give something explanatory priority over reason and rational agency. Anyone who is what we would today call a 'physicalist' would be a naturalist. And Kemp Smith's proposal is that Hume should be considered not a skeptic (who, effectively, denies explanatory priority to anything) but as a naturalist. The reason is that Hume does attempt to explain some facets of the world, and his explanation of the world involves explaining reason and rational agency in terms of something else - instinct, custom, etc. The first clause, that he explains, is a reason to think he is not a skeptic; and the second, that he does not give first place to rational agency, is a reason to think he is not an idealist. So, naturally, he must be a naturalist.
