What does the epigraph in "The Love Song of J. Alfred Prufrock" mean?

The epigraph to “The Love Song of J. Alfred Prufrock” comes from Dante's Inferno, a work of literature that had particular resonance for T. S. Eliot throughout his life. The words are spoken by Guido da Montefeltro, a character stuck in the eighth circle of hell for all eternity:

If I but thought that my response were made
to one perhaps returning to the world,
this tongue of flame would cease to flicker.
But since, up from these depths, no one has yet returned alive, if what I hear is true,
I answer without fear of being shamed.

Essentially, what this means is that Guido feels able to tell his story to Dante's protagonist—a fictional version of Dante—because he is sure that the poet will never leave hell and so will be unable to tell anyone else about all the horrible things Guido did that put him in hell in the first place. Guido, however, is profoundly mistaken. Dante is indeed passing through, and he will eventually make it out of hell and tell the story of what this wicked man did when he was alive.

The relevance of the epigraph to “The Love Song of J. Alfred Prufrock” is not immediately apparent. It seems to be the case that Prufrock believes that by singing his song, no one else will ever hear it. It is as if he were sharing a confidence with the addressee—who is arguably himself—about all his insecurities, neuroses, and anxieties, safe in the knowledge that no one will divulge the information.

One could also say that Prufrock, like Guido from Inferno, lives in a kind of hell from which it is impossible for him to escape.

What is the significance of the epigraph in Eliot's "The Love Song of J. Alfred Prufrock?" What commonality do these voices share?

Eliot often uses allusions and intertextuality of this kind in his poetry and, indeed, often uses text in foreign languages without translating it. In this way, he rewards the more diligent reader: anyone who is actually familiar with Dante's Inferno will immediately have a better understanding of this poem's context than someone who does it.

The epigraph's lines from Dante can be translated as follows:

If I but thought that my response were made
to one perhaps returning to the world,
this tongue of flame would cease to flicker.
But since, up from these depths, no one has yet
returned alive, if what I hear is true,
I answer without fear of being shamed.

That concept of "fear of being shamed" and the circumstances in which that fear might disappear are pivotal to the poem. Prufrock lives his whole life in fear of being shamed: he does not know what is expected of him or what would be the best course to take, and is perpetually wracked by "decisions and revisions." He is an outsider everywhere he goes: "the women" in the poem are unnamed and unknown to him, and he dares not "presume." In some ways, he has "known them all already," the people he meets, but they do not know him. In the act of telling this story of his inner life to someone—the act of speaking as he does in this poem—Prufrock is stepping outside of himself. He is delivering a monologue that is so revelatory, he would never be able to do it except under extraordinary circumstances.

In this way, he is not dissimilar to the speaker in the Dante quotation: these words are spoken aloud only because Dante, in purgatory, can be trusted never to return to the surface of the earth alive and repeat what he has heard. Dante hears truths from the spirits he meets in the underworld which no living soul has ever heard; because of this trust, he could never reveal their secrets. Likewise, we—the listeners to Prufrock's monologue—experience his revelation uniquely among humankind. The speaker can only tell us about the deep confusion of his inner life because he knows that, for whatever reason, we will never be able to repeat it to anyone else.

Throughout much of the poem, the settings and places the speaker describes are fairly mundane, such as streets and drawing rooms. Towards the end of the poem, however, a sense of the dreamlike re-emerges in the idea of "mermaids," and the suggestion that voices might "wake us, and we drown." Looking at this section in conjunction with the epigraph, it is almost as if we are speaking to Prufrock in some purgatorial dream state, and when we emerge from it, we will metaphorically "drown" and forget everything we have been told about this lonely, solitary man.