It is a critical commonplace to begin an essay about essays with etymology. Essay: noun, from the French essayer, verb, to try. Next is the requisite hat-tip to Michel de Montaigne, Renaissance philosopher and one-time mayor of Bordeaux, who is considered to have been the first great essayist; his Essais, published in 1580, includes disquisitions on, among other things, idleness, liars, imagination, pedantry, the custom of wearing clothes, sleep, names, drunkenness and smells. “I know too well how that particular essay on essays gets written,” Brian Dillon writes in his new book, Essayism, refusing to rehearse these familiar ideas, even as he mentions them.

Over the course of this meditation on that most elegant and slippery of forms, he identifies some “combination of exactitude and evasion” at the heart of it, an inner “conflict”, whereby it “aspires to express the quintessence or crux of its matter … to a sort of polish and integrity”, while also insisting “that its purview is partial, that being incomplete is a value in itself for it better reflects the brave and curious but faltering nature of the writing mind”. The essay has to convey mastery while admitting partiality. This is very hard to do well.

Dillon suggests that we cannot define the essay, but that we might more productively gesture at some quality of essayism: a certain texture, a style, a voice, an “experiment in attention”. The essay will – and by its nature must – always resist attempts to pin it down. It refuses to be contained by any neat summary; it is “diverse and several – it teems”.

Dillon himself is a superbly varied essayist; the author of a range of books about photography, hypochondriacs, the great explosion at a munitions factory in Faversham, Kent, in 1916, and another written in 24 hours called I Am Sitting in a Room, his lines of inquiry are the body and its afflictions, contemporary art and literature, the history of place and ruins. He has a natural affinity for the essay “as a kind of conglomerate: an aggregate either of diverse materials or disparate ways of saying the same or similar things”. Lists are a wonderful tactic of essayism – consider Georges Perec’s astonishing lists in Species of Spaces, from the food and drink he consumed in 1974 to the objects on his desk. Dillon helps us see, via Joan Didion in The White Album, the list as incomplete, the very act of making a list a gesture at what cannot be listed or will always be left out: “the list, if it’s doing its job, always leaves something to be invented or recalled, something forgotten in the moment of its making”.

Then there are aphorisms, the intellectual acrobatics that go into establishing some apparently immutable, essential truth. The aphorist declares that x is y; “Or better, according to the writer’s need to surprise the reader: x is actually y. Still more effectively: x is, after all, only y.” Dillon argues earnestly for aphorists to turn away from this fetish for essence or assertion and to instead fill that space with “desire” and urgency. He quotes Emil Cioran: “No need to elaborate works – merely say something that can be murmured in the ear of a drunkard or a dying man.”

One of the marks of a great essayist is to be able to see connections

The essays that he most admires, Dillon writes, are those “that pay the minutest or most sustained attention to one thing, one time or place, one strain or strand of existence. An essay that performs its mode of attention …” He offers by way of example the art critic TJ Clark writing in his book The Sight of Death about looking repeatedly at two paintings by Poussin, paying “too much attention to these works”, recording the failures in what can be seen at any one moment. Dillon then moves on to Perec’s An Attempt at Exhausting a Place in Paris, which similarly records the impossibility of noting everything happening in the Place Saint-Sulpice on a series of afternoons in 1974; it is a testament to Dillon’s sharp critical eye that he can move from Clark to Perec in this way. One of the marks of a great essayist is to be able to see connections.

Where his earlier essay collection, Objects in This Mirror, took on myriad subjects – from the art of Robert Smithson to Victorian rhetoric manuals, from cravat-tying manuals to what it means to be ill – this one is a collection of essays on essays, part literary critical appreciation of writers such as William Gass and Elizabeth Hardwick, part belle lettristic exploration of the essence of a genre. But Dillon does not shy away from letting us in, obliquely but unmistakably, to his own personal struggles with depression and anxiety. In these more personal passages, he resembles a critic, wary of “overstating”his case. He needn’t worry: written in lucid, exacting and unsentimental prose, Essayism is a vital book for people who turn to art – and especially writing – for consolation.

As the book draws to its conclusion, it must confront another habit of the merely competent essay: the way such a piece of writing returns, too neatly, to an initial premise or image. This, too, raises Dillon’s critical hackles. “I like circles and lines and symmetry too, more than is good for me as a writer and as a human.” But that kind of circularity is the opposite of genuine essayistic thought, he maintains. And so Essayism ends with an unglossed quote from William Carlos Williams: an appropriate stopping point for a book about a form that, at its best, refuses to conclude, but above all invites in, opens up, opens out.

• Essayism is published by Fitzcarraldo. To order a copy for £9.34 (RRP £10.99) go to bookshop.theguardian.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.

• Lauren Elkin’s Flaneuse is published by Vintage.