Hume's naturalism rescues him from this extreme skepticism. While neither our belief in an external world nor our belief in necessary connection are rationally justified, custom and habit lead us instinctually to accept them. Skepticism is useful in that it places limitations on our reason and makes us doubt what we might otherwise take for granted, but it is ultimately unlivable. I can doubt all I please in the comfort of my study, but in order to get by in the world I must as least assume that there is an external world and that my judgments and actions in that world make some sort of difference.
Naturalism makes skepticism livable by reinstating certain kinds of thinking and reasoning as acceptable and trustworthy. Importantly, though, naturalism only reinstates relations of ideas and matters of fact, leaving metaphysics a little empty. Relations of ideas deal only with mathematical truths and matters of fact must be grounded in experience. Thus, a great deal of the subject matter of rationalist metaphysics--the existence of God, the immortality of the soul, the nature of matter, etc.--is discarded. We cannot answer such questions through reason alone, as a rationalist would want, and there is nothing in experience that can point us fruitfully toward any satisfying answers. Thus, in the closing line of the Enquiry, Hume recommends that we commit to flames all books that engage in such empty, metaphysical speculations.