Published posthumously in 1777, the text remains lucid:
Every one will readily allow, that there is a considerable difference between the perceptions of the mind, when a man feels the pain of excessive heat, or the pleasure of moderate warmth, and when he afterwards recalls to his memory this sensation, or anticipates it by his imagination. These faculties may mimic or copy the perceptions of the senses; but they never can entirely reach the force and vivacity of the original sentiment. The utmost we say of them, even when they operate with greatest vigour, is, that they represent their object in so lively a manner, that we could almost say we feel or see it: But, except the mind be disordered by disease or madness, they never can arrive at such a pitch of vivacity, as to render these perceptions altogether undistinguishable. All the colours of poetry, however splendid, can never paint natural objects in such a manner as to make the description be taken for a real landskip. The most lively thought is still inferior to the dullest sensation. - Paragraph 11It is common in everyday speech to separate the empirical (the things we experience in the world of the five senses), from the rational (the things that happen inside our minds). But isn't it better to consider every aspect of experience as constituting empirical fact?
If so, thought and imagination should also be considered empirical. We make discoveries in our minds by way of reason and explanation, and we remember our thoughts much the way we remember a day at the beach.
Breaking down the artificial separation between the rational and the empirical is liberating. As Hume explains above, our liberation costs us nothing in our ability to distinguish imaginary things from physical things.
However, we must surrender absolute certainty in making our escape:
There is a species of scepticism, antecedent to all study and philosophy, which is much inculcated by Des Cartes and others, as a sovereign preservative against error and precipitate judgement. It recommends an universal doubt, not only of all our former opinions and principles, but also of our very faculties; of whose veracity, say they, we must assure ourselves, by a chain of reasoning, deduced from some original principle, which cannot possibly be fallacious or deceitful. But neither is there any such original principle, which has a prerogative above others, that are self-evident and convincing: or if there were, could we advance a step beyond it, but by the use of those very faculties, of which we are supposed to be already diffident. The Cartesian doubt, therefore, were it ever possible to be attained by any human creature (as it plainly is not) would be entirely incurable; and no reasoning could ever bring us to a state of assurance and conviction upon any subject. - Paragraph 116[Hmmm. Perhaps it is time to change my blog subtitle!]
Hume's skepticism does not deprive us of logic, mathematics, science or meaning. Hume's philosophy is infused with practicality. It merely admits that all conclusions we might reach in these endeavors have some degree of uncertainty. With diligence and repetition, the uncertainties of constructions like logic, mathematics and meaning can be made arbitrarily small.