It would be natural to assume from the title of Terry Eagleton's new book that it might, in some way, be applying to literature Alain Badiou's idea of the event – the rupture in the nature of being and seeming that allows, momentarily, the omnipresent, unchanging and therefore invisible truth to become evident. Eagleton's argument for literature may be less revolutionary, but he wishes to retain a degree of radicalism in the inter-related endeavours of creating, reading and criticising literature. He contends that it is possible to define "literature". This may come as a surprise to readers familiar with his 1983 book Literary Theory: An Introduction, where he argued firmly that there was no quality or set of qualities which were evident in all works of literature.

Though not repudiating that argument, he now finesses it, suggesting, via Wittgenstein's theory of family resemblance, a way back to a "common sense" notion. Eagleton has not reneged on scepticism: he is just sceptical about it. That aspect of "common sense" is of key importance: although academics can doubt the existence of a specific thing called literature, or argue for its socially constructed nature, or give up and write cultural studies of Pokémon instead, readers, for the most part, believe in literature. So do the funding bodies that run literature faculties, Arts Councils, librarians, booksellers and even newspaper reviewers.

Eagleton's solution is elegant in that it is inherently fuzzy. "My own sense", he writes, "is that when people at the moment call a piece of writing literary, they generally have one of five things in mind, or some combination of them. They mean by 'literary' a work which is fictional, or which yields significant insight into human experience as opposed to reporting empirical truths, or which uses language in a peculiarly heightened, figurative or self-conscious way, or which is not practical in the sense that shopping lists are, or which is highly valued as a piece of writing." These categories he calls the fictional, moral, linguistic, non-pragmatic and normative. The virtue of this admittedly porous definition is in providing a rationale for why – to take some Penguin Classics at random from my shelf – Hume's Dialogues Concerning Natural Religion, the Molesworth stories, Bataille's Story of the Eye, Cicero's Murder Trials and Chekhov's The Cherry Orchard can all be considered literature.

Subsequent chapters give more detail on these categories, with the section on fiction being perhaps the most intellectually sprightly. An avowed aim of this study is to straddle (continental) literary theory and (Anglo-Saxon) philosophy of literature. Assessing the truth-status of fictions – that is, deciding on the truthfulness or not of a statement such as "all unicorns have two horns", with the intellectual battle line being drawn between those who say that unicorns aren't real and therefore have no horns and those who say that the fiction is such that it is necessary for it to have only one horn – is not just a parlour game. Throughout the book, Eagleton writes with his customary felicity (his aphorism, for example, on significant affinities in Wittgenstein's theory of family resemblances, "a tortoise resembles orthopaedic surgery in that neither can ride a bicycle", is a delight). He never writes better than when he is gleefully demolishing rival theorists, and sometimes their theories. His favoured tactic throughout is the counter-example.

There are, however, shortcomings. Eagleton sometimes throws off by-the-way speculations which prove, on reflection, less evident than he appears to think. "It is hard to think of a major work of literary art from Propertius to Pamuk that sings the praises of torture or genocide, or which dismisses mercy, courage and loving-kindness as so much high-sounding cant", he says. The "major" is a get-out-clause, and in terms of dismissal one might cite Celine, Bernhard, or Cioran. As for genocide – well, the Book of Judges might still be considered a work of literature (although it predates Propertius, conveniently enough).

Eagleton's theory – thanks to his "normative" category, which as a set of assumptions might better be termed "inherited" – allows some literature to be bad literature (he rather off-handedly suggests Southey and Beddoes in this respect). But it cannot explain how things become literature. He approvingly refers to Leavis's championing of TS Eliot when other dons were apoplectic with confusion, but this is to fall into the circularity for which he condemns Lamarque and Olsen: that literature is what academic institutions decide is capable of undergoing literary criticism. The value question is suspended by allowing that even though, say, Melville's Pierre is a terrible literary novel it is unquestionably a literary novel. Likewise, Eagleton's linguistic category needs further thought. It is not a question of style – he cites Hemingway's stylish artlessness alongside more baroque varieties. But this occludes the question of subordinated or merely efficient prose; the sort associated with, say, Jeffrey Archer. Again, a value judgment or a theoretical proposition is evaded.

Eagleton's "event" is only part of the story: "One of the paradoxes of the literary work is that it is 'structure' in the sense of being unalterable and self-complete, yet 'event' in the sense that this self-completion is perpetually in motion, realised as it is only in the act of reading. Not a word of the work can be changed, yet in the vicissitudes of its reception not a word stays dutifully in place." This is neatly phrased, but leaves the distinct impression of a spinning wheel that never becomes a gear.

When, as a critic, I call something literature, I mean that it expands the field of what literature can be. David Foster Wallace is literature. Jonathan Franzen just tried to write a literary novel.

• Stuart Kelly's The Book of Lost Books is published by Polygon.