Most traditional interpreters of Hume have read his language of "impressions" as Cartesian/Lockean, in the sense that he is wedded to a representational view of mind such that skeptical doubt is an inevitable (albeit perhaps trivial) problem. Thus the empiricist is a kind of cheerful skeptic, suggesting (as Hume does) that rationalist approaches overstep their bounds in the face of inscrutable nature. I've been wondering if Hume wasn't perhaps closer to Wittgenstein, with his idea that skepticism is a kind of pseudoproblem, than he was to early 20th century "analytic" philosophers, like Russell and the "phenomenalists" of early 20th century philosophy of science. So I was pleased to see that one of the selections in my Intro anthology was "Of scepticism with regard to the senses," Book 1 Part 4 Section 2 of the Treatise. Three paragraphs in we find "For as to the notion of external existence, when taken for something specifically different from our perceptions, we have already shown its absurdity" and we get a footnote directing us to "Of the idea of existence, and of external existence," Book 1, Part 2, Section 6.
Hume writes, "The idea of existence, then, is the very same with the idea of what we conceive to be existent. To reflect on anything simply, and to reflect on it as existent, are nothing different from each other. That idea, when conjoined with the idea of any object, makes no addition to it. Whatever we conceive, we conceive to be existent. Any idea we please to form is the idea of being; and the idea of being is any idea we please to form."
The Cartesian reading of this sort of thing is that we cannot get around our "ideas" or indeed past our "impressions" in order to know the external world directly. For all we know the external world might not exist, but there's simply no sense playing philosophical parlor games. Beyond experience lies the unknown. (I noticed reading Bryan McGee's Confessions that he was particularly enamored of this sort of idea, which he attributed to Kant.) But it looks to me that there is a much more powerful argument here, one that does aim to defeat Cartesian skepticism. On this more Berkeleyan reading the external world just is experience just is the external world. There cannot be any "abstract idea" (Hume thinks that the problem is that these are fishy abstract ideas) of an existing thing apart from our actual experience. So skepticism is a pseudoproblem motivated by a misconception of the meaning of "being." Experience is the ground of conception, so there are not any genuine concepts that extend beyond experience. This I take to be broadly equivalent to Wittgenstein's diagnosis. It is not a mere throwing up of the hands of an empiricist: I think that Hume positively rejects the Cartesian possibility as a demonstrable error. One can not be said either to "know" or to "not know" about the existence of the external world. Wittgenstein is making the same argument with his appropriation of the word "solipsism" at the end of the Tractatus.