We are sceptical about literary prizes. And yet – come on, confess – we like literary prizes as well.

I'm not talking about the winning, though winning them can – and probably should – produce a potent, mingled sense of scepticism and pleasure. I'm talking about the divide we may feel upon hearing that a certain book has won an award.

On one hand, there's the prize's obvious absurdity – its inevitable subjectivity, not to mention the plain silliness of deeming one book better than another. (Quick, off the top of your head: is Middlemarch better than Bleak House?) On the other, there is our rightful devotion to the whole "ta-da" business: the pronouncement, the trumpet blare, the laying of the laurel wreath on the most gifted head in the arena. It's human.

There is, however, a certain question that tends to arise among juries whenever prizes are being contemplated. Is it the fundamental purpose of the prize to acknowledge the writer who has veered closest to greatness that year (or decade, or century), regardless of the boxcar-loads of accolades that may already have been delivered; or is it to draw attention to an extremely good and possibly significant writer who seems to be passing more or less unnoticed?

I don't think such bifurcation is called for where a contemporary prize is concerned – after all, history's verdict is still out on newer books. But I feel torn between naming one of the most obvious 50 or so best books, and naming a less-than-deified book. The list of undeniable greats is predictable, and so a little dull. However, if I were to name a book that has been (in my estimation) under-recognised, I'd be implying that some lesser-known book leaves Middlemarch and Bleak House in the dust.

And so, at the risk of disappointing those who like a savage singularity, and if we're talking about every book ever written in English, I have to suggest two Folio prizes. One for the greatest, and one for the wrongfully under-appreciated.

The greatest

I'm afraid there's more equivocation to come. I'd award the greatness prize to two books: James Joyce's Ulysses and Virginia Woolf's To the Lighthouse.

I'm not talking about a tie. I'm talking about two seminal works of literature that should be considered in tandem.

Let's pause to remember that the novel, in English, is less than 300 years old. Given its youth, its track record is remarkable. We've had, in relatively short order, Pride and Prejudice, Wuthering Heights, The House of the Seven Gables, Moby-Dick, The Golden Bowl, The Sound and the Fury, and The Great Gatsby – just to name a few (Middlemarch and Bleak House have probably been sufficiently acknowledged already).

For me, however, it was the modernists who engendered the most significant literary revolution. Suddenly, in the early 20th century, novels had as much to do with language as they did with events. They were about outwardly ordinary lives, and thereby established that there's no such thing as an "ordinary" life; there is only inadequate appreciation of humanity. And a novel was no longer meant as moral instruction for readers who were, perhaps, ever-so-slightly in need of it.

Ulysses is, of course, Godzilla, and we are the citizens of Tokyo. Joyce's book changed everything. It's the novel most likely to inspire in a writer the question: "Oh, well, now that's been done, why bother any more?"

To the Lighthouse doesn't slay and pillage in the same way, yet it is every bit as revolutionary as Ulysses, and for some of the same reasons. Like Joyce, Woolf knew the entire world could be seen by looking not only at the big picture, but also the small one, in more or less the way a physicist who studies subatomic particles is witness to miracles every bit as astonishing as those observed by an astronomer.

Unlike Joyce, Woolf didn't wish to devastate her readers. Nor did she need her readers to comprehend how brilliant she was. And, of course, she cared more than Joyce did about the lives of women. If Joyce, in Ulysses, is the vengeful god – if he's the father who gives his children the occasional, all-too-clear sense of their own limitations – Woolf, in To the Lighthouse, is Winnicott's good-enough mother, the one who's able to love her children while simultaneously urging them towards lives of their own, beyond her reach or influence.

For all their genius, both authors arrived with limitations, as humans always do. Woolf was a snob, and could not, would not, write about sex. Joyce was something of a bully on the page: he cared, at times (or so it seems to me), a bit more about his readers' apprehension of his immense talent than he did about the readers themselves – or, for that matter, about the characters in his book.

Mom is adoring and nurturing and ever-so-slightly out of touch. Dad is potent and challenging and ever-so-slightly uncaring.

And so, I nominate Ulysses and To the Lighthouse, not by way of a draw, but as a pair – a marriage, if you will. A partnership in which each member is enhanced by the other, which creates a two-part entity more influential, and more important, than either individual.

The under-appreciated

As I've said, if there's an unknown or neglected book on the same level as Ulysses or To the Lighthouse, it's unknown to me. It's also neglected by me, along with everybody else.

There are, however, a number of books which (in my opinion) should be read by everyone, and haven't been.

In alphabetical order, the prize(s) go to:

The House in Paris by Elizabeth Bowen

White Noise by Don DeLillo

Train Dreams by Denis Johnson

Blood Meridian by Cormac McCarthy

The Little Disturbances of Man by Grace Paley

Light Years by James Salter

And that, surely, is more than enough out of me.

• Michael Cunningham is an Academy member of the Folio prize, which is running daily blogs on the books academicians wish to see retrospectively awarded the prize.