To what do the "letters" in the title "a man of letters" refer?

Solution 1:

"letters" is a rather archaic term for what we would today call "literature".

For example, my mother got her PhD through the English department. Her degree reads: "PhD in English Letters". I remember her doing a lot of work on James Joyce.

Dictionary.com doesn't have this in their definition of letters, but they do say the following at the end:

Origin: 1175–1225; Middle English, variant of lettre < Old French < Latin littera alphabetic character, in plural, epistle, literature

(emphasis mine)

Of the three options you listed, I'd say #3 was the closest to correct.

Solution 2:

"Lettere" in English is what you would call "Humanities" (meant as "studies").

In Italian, "Lettere" is a university faculty where you study those subjects that refer to man and the human condition.

The main disciplines include Literature, Visual Arts, Performative Arts, linguistic disciplines, like Linguistics, Philology and Semiotics, historic disciplines, like History and its subdisciplines, Philosophy, Religion and Law.

So I'd say that "Man of letters" is someone who had to study any of those disciplines or had an academic career in those fields.

In the NOAD, it says "man of letters: a male scholar or author."

Solution 3:

The way I consider the phrase 'man of letters' is the most basic meaning of letters, as building blocks of any kind of writing.

Usingenglish.com, explains the idiom as

A man of letters is someone who is an expert in the arts and literature, and often a writer too.

ngram search shows that in books the phrase is used also specifically to talk about correspondence, but I take that as play on words.

EDIT: Wikpedia's entry gives etymology

The term ‘Man of Letters’ (‘belletrist’, from the French belles-lettres), has been used in some Western cultures to denote contemporary intellectual men; the term rarely denotes ‘scholars’, and is not synonymous with ‘academic’. Originally, the term implied a distinction, between the literate and the illiterate, which carried great weight when literacy was rare. It also denoted the ‘literati’ (Latin, pl. of literatus), the ‘citizens of the Republic of Letters’ in seventeenth- and eighteenth-century France, where it evolved into the salon, usually run by women.