Complex ideas may, perhaps, be well known by definition, which is nothing but an enumeration of those parts or simple ideas, that compose them. But when we have pushed up definitions to the most simple ideas, and find still more ambiguity and obscurity; what resource are we then possessed of? By what invention can we throw light upon these ideas, and render them altogether precise and determinate to our intellectual view? Produce the impressions or original sentiments, from which the ideas are copied. These impressions are all strong and sensible. They admit not of ambiguity. They are not only placed in a full light themselves, but may throw light on their correspondent ideas, which lie in obscurity. And by this means, we may, perhaps, attain a new microscope or species of optics, by which, in the moral sciences, the most minute, and most simple ideas may be so enlarged as to fall readily under our apprehension, and be equally known with the grossest and most sensible ideas, that can be the object of our enquiry.--David Hume, first Enquiry, 4.7
In my interpretation, Hume's 'new microscope' represents (recall) a partial departure from his method in the Treatise. On my interpretation, in the Treatise, Hume embraces a normative theory of proper cognition (I have defended that here, here, and, especially, here). We can't really think without adequate ideas. I think this idea is represented best in this passage: "Tis impossible to reason justly, without understanding perfectly the idea concerning which we reason; and ‘tis impossible perfectly to understand any idea, without tracing it up to its origin, and examining that primary impression, from which it arises. The examination of the impression bestows a clearness on the idea; and the examination of the idea bestows a like clearness on all our reasoning." (22.214.171.124) In the Treatise, Hume presupposes what has come to be known as his 'copy principle.' And he suggests, I argue, that as part of genuine reasoning one must go, as it were, meta and introspect on the source of one's ideas. And then only so-called adequate ideas are "the foundation of all human knowledge." In my interpretation, Hume thinks (and I believe he is very indebted to Berkeley on this point) that much that passes for reasoning even in the sciences is a kind of ersatz-reasoning impressing the learned and gullible alike.
But in the first Enquiry, Hume backtracks a bit. In particular, I think the normative theory of proper cognition with clear ideas is dropped as a general principle. This is not to deny that some of it is still presupposed; after all, Hume continues to rely on the fact that in normally functioning human impressions are faithfully copied into ideas. That is, the strategy of Hume’s science of man remains the same: trace ideas back to simple impressions (or original sentiments) and inspect these under the (mental) “new microscope.” However, the domain of application is now limited to the “moral sciences” and not “all knowledge” (as promised in introduction of the Treatise).
This last point is crucial. In the first Enquiry, Hume makes a distinction between the epistemology proper for natural philosophy and the one in the moral sciences. For, in the study of natural philosophy Hume allows that in “almost in every part of nature, there is contained a vast variety of springs and principles, which are hid, by reason of their minuteness or remoteness… that it is at least possible the contrariety of events may not proceed from any contingency in the cause, but from the secret operation of contrary causes.” (EHU 8.13)* The quoted sentence is very important in the so-called 'New Hume' debate, but here I ignore (as is my usual practice) that debate.** But Hume's claim entails that natural philosophy can almost never produce secure knowledge of hidden reality.
But according to the 'new microscope' passage, in social science+ “the most minute” ideas can be made to “fall readily” under our apprehension. So, in one sense the scope ofHume’s ambitions have been dramatically curtailed. The science of man does not provide a mental microscope for all the natural sciences (nor natural religion and mathematics). But Hume continues to imply -- and here comes rather close to the kind of reasoning we now tend to associate with Vico -- that due to the mental microscope the moral sciences are, in principle, in better epistemic shape than the natural sciences. Original sentiments are human, and so knowable. This is why the “true and proper province,” of “natural and unassisted reason” ends up being restricted to “common life.” The real target here is, as becomes clear in chapter 11 in the first Enquiry, the Newtonian attempt (as exemplified by Newton’s correspondence with Bentley and Clarke’s writings more generally) to make cosmogony an integral part of natural philosophy, but that's for another occasion.