There was a time when a learned fellow (literally, a Renaissance man) could read all the major extant works published in the western world. Information overload soon put paid to that. Since there is "no end" to "making many books" – as the Old Testament book Ecclesiastes prophesied, anticipating our digital age – the realm of the unread has spread like a spilt bottle of correction fluid. The librarian in Robert Musil's The Man Without Qualities only scans titles and tables of contents: his library symbolises the impossibility of reading everything today. The proliferation of lists of novels that you must, allegedly, have perused in your lifetime, reflects this problem while compounding it. On a recent visit to a high street bookshop, I ogled a well-stacked display table devoted to "great" novels "you always meant to read". We measure out our lives with unread books, as well as coffee spoons.

The guilt and anxiety surrounding the unread probably plays a part in our current fascination with failed or forgotten writers. Hannah Arendt once wondered if "unappreciated genius" was not simply "the daydream of those who are not geniuses", and I suspect there is indeed a touch of schadenfreude about this phenomenon too. On the book front, we could mention Mark O'Connell's Epic Fail, the brilliantly idiosyncratic Failure, A Writer's Life by Joe Milutis, and Christopher Fowler's Invisible Ink: How 100 Great Authors Disappeared, based on the longstanding column in the Independent on Sunday. Online, there is The New Inquiry's Un(der)known Writers series, as well as entire blogs – (Un)justly (Un)read, The Neglected Books Page, Writers No One Reads – devoted to reclaiming obscure scribes from oblivion. One of my personal favourites is The Biographical Dictionary of Literary Failure, which celebrates the lives of writers who have "achieved some measure of literary failure". The fact that they all turn out to be fictitious (à la Félicien Marboeuf) and that the website will vanish after a year, make it even more delightful. I recommend the tale of Stanhope Sterne who, like TE Lawrence, lost a manuscript on a train – at Reading, of all places: "Is there, I wonder, some association with that dull junction's homonym, that it is a writer's fear of someone actually reading their work that causes these slips?"

When Kenneth Goldsmith published a year's worth of transcribed weather reports, he certainly did not fear anyone would read his book from cover to cover – or even at all. That was not the point. With conceptual writing, the idea takes precedence over the product. This is an extreme example of a trend that began with the advent of modernity. Walter Benjamin famously described the "birthplace of the novel" – and hence that of modern literature – as "the solitary individual": an individual now free from tradition, but also one whose sole legitimacy derived from him or herself, rather than religion or society.

In theory, the novel could thus be anything, everything, the novelist wanted it to be. The problem, as Kierkegaard observed, is that "more and more becomes possible" when "nothing becomes actual". Literature was a blank canvas that increasingly dreamed of remaining blank. "The most beautiful and perfect book in the world," according to Ulises Carrión, "is a book with only blank pages." Such books had featured in eastern legends for centuries (echoed by the blank map in "The Hunting of the Snark" or the blank scroll in Kung Fu Panda), but they only really appeared on bookshelves in the 20th century. They come in the wake of Rimbaud's decision to stop writing, the silence of Lord Chandos; they are contemporaneous with the Dada suicides, Wittgenstein's coda to the Tractatus, the white paintings of Malevich and Rauschenberg, as well as John Cage's 4'33".

Michael Gibbs, who published an anthology of blank books entitled All Or Nothing, points out that going to all the trouble of producing these workless works "testifies to a faith in the ineffable". This very same faith prompts Borges to claim that "for a book to exist, it is sufficient that it be possible" and George Steiner to sense that "A book unwritten is more than a void." For Maurice Blanchot, Joseph Joubert was "one of the first entirely modern writers" because he saw literature as the "locus of a secret that should be preferred to the glory of making books".

If literature cannot be reduced to the production of books, neither can it be reduced to the production of meaning. Unreadability may even be a deliberate compositional strategy. In his influential essay on "The Metaphysical Poets", TS Eliot draws the conclusion that modern poetry must become increasingly "difficult" in order "to force, to dislocate if necessary, language into its meaning". The need to breathe life back into a moribund language corrupted by overuse, chimes with Stéphane Mallarmé's endeavour to "purify the words of the tribe". The French writer was very much influenced by Hegel, according to whom language negates things and beings in their singularity, replacing them with concepts. Words give us the world by taking it away. This is why the young Beckett's ambition was to "drill one hole after another" into language "until that which lurks behind, be it something or nothing, starts seeping through".

Literature (for the likes of Mallarmé and Blanchot) takes linguistic negation one step further, by negating both the real thing and its surrogate concept. As a result, words no longer refer primarily to ideas, but to other words; they become present like the things they negated in the first place. When critics objected that Joyce's Finnegans Wake was unreadable, Beckett responded: "It is not to be read – or rather it is not only to be read. It is to be looked at and listened to. His writing is not about something; it is that something itself." Unlike ordinary language, which is a means of communication, literary language resists easy, and even complete, comprehension. Words become visible; the bloody things keep getting in the way. From this perspective, the literary is what can never be taken as read. In a recent article, David Huntsperger gives an interesting contemporary twist to this debate. He views the opacity of some contemporary novels as a healthy corrective to our "clickthrough culture, where the goal of writing is to get you from one place to another as effortlessly as possible, so that (let's be honest here) you can buy something".