First Person (Central Narrator)
When you're reading this book, it doesn't immediately leap out as being in first person. In other kinds of texts, this is often way more obvious: with an autobiography, journal, or piece of travel writing, we can often tell right off the bat that we're in first-person mode. Likewise, in poetry and fiction (especially stream of consciousness stuff) we can identify the perspective pretty quickly. How do we know that something is first person? There's one major thing to look for, and that's the use of the term "I" as in "I think" and "I saw," etc.
There's no reason why a philosophical work can't use the first-person tense in this way, but with the Enquiry, ittakes us a while to find our feet. The thing to remember is that this is a serious, academic work. Sure, Hume tries his best to make it accessible, and he does a good job. The thing is, though, that scholarly works can often be more detached and formal than some other kinds of writing. Have you ever been told not to use "I" in academic writing? There's no hard and fast rule, but some folks believe that writers should stay invisible in this sort of material.
When the Enquiry begins, we could be forgiven for thinking that it's in the third person. The first-person POV isn't as in-your-face as it may be in some other texts, but don't let that fool you. Around halfway through the first section, Hume utters the magic word "I." Here's the quote in full:
These arguments on each side (and many more might be produced) are so plausible, that I am apt to suspect, they may, the one as well as the other, be solid and satisfactory, and that reason and sentiment concur in almost all moral determinations and conclusions. (I.9)
Up to this point, Hume has used the kind of language that we'd expect to find in an academic essay, and he carries on in this vein. Still, there are moments when he draws attention to his own status as a narrator: at one point, he curbs his train of thought to tell himself:
But I forget, that it is not my present business to recommend generosity and benevolence, or to paint, in their true colours, all the genuine charms of the social virtues. (II.I.4)
Later, he writes:
[I]t will readily, I believe, be admitted, that the strict laws of justice are suspended, in such a pressing emergence, and give place to the stronger motives of necessity and self-preservation. (III.I.8)
We could give loads more examples, but you get the gist. Hume stays formal and in essay mode, but sometimes he'll talk in a direct, one-to-one way about his convictions or doubts. That's when we think, "a-ha! This is first person!" Not only this, it draws us in and helps make the Enquiry accessible.
Another thing we can tell is that Hume is a central narrator. Again, the language may not be as personal as in some other kinds of texts, but the Enquiry is made up of Hume's thoughts, criticisms, arguments, etc. Yep, he's definitely the main man here.