Book of the week: The Infinity of Lists

This strange concoction, hodgepodge, mishmash, ragbag, potpourri, jumble, confusion, melange, gallimaufry, hash, assortment, miscellany, profusion, mixture, riot, conglomeration or medley of words and pictures is itself a list, record, directory, archive, inventory, catalogue or enumeration of other lists. While many of these mention things that are not themselves words, such a meta-list itself serves as a museum, treasury, collection, set, display and exhibition of members of the very genre of which it is itself an instance. It is the latest jeu d'esprit, enterprise, undertaking, endeavour, venture, exercise, activity, operation, task, proceeding, project, scheme or plan of the eminent semiotician, medievalist, novelist, storyteller, philosopher, magus, authority, joker, comedian, intellectual, sorcerer, scholar, rhetorician and Italian, Umberto Eco. And if you think the previous sentences were a little clogged, repetitive, extravagant, wasteful, prodigal, lavish or over-egged, then it is just possible that this is not the book for you. To anyone, however, who takes pleasure, delight, joy, gladness, glee, satisfaction, gratification, contentment, enjoyment or amusement in contemplating excess, it may be just the ticket, pass, authorisation, permit, token, coupon or voucher.

Eco explains in the introduction that when the Louvre asked him to organise a series of happenings for this November - "conferences, exhibitions, public readings, concerts, film projections and the like" - he did not "hesitate for a second" but proposed the list as the topic. So what he has done is to trawl literature and painting for examples in which authors and artists have decided that they needed to enumerate vast sets of things, and it is perhaps surprising how many authors have felt that need, from Homer to James Joyce.

The results may be merely whimsical, and done simply for the pleasure of doodling, or serious, done to make a point about the activities of classification themselves. The most famous and most often quoted list with this last intention is from Jorge Luis Borges' imagined encyclopaedia, the Celestial Emporium of Benevolent Knowledge, in which it is written that animals are divided into: those that belong to the Emperor, embalmed ones, those that are trained, suckling pigs, mermaids, fabulous ones, stray dogs, those included in the present classification, those that tremble as if they were mad, innumerable ones, those drawn with a very fine camel-hair brush, others, those that have just broken a flower vase, and those that from a long way off look like flies.

Borges' brilliance encompasses several logical tangles, including suggesting that the word "innumerable" could characterise an animal in the same way that, for instance, being a suckling pig might, presenting "fabulous" or non-existent as a kind of property, and allowing what a logician would call an impredicativity, when the classification is partly made on the basis of being included in the present classification. Borges must have known his history of mathematical logic, since the development of that subject was largely the product of the problems posed by venturing in these directions. Including in his list "others", or things not included in the list, is trivial by comparison, although it would disadvantage a shopping list, for example, if alongside humdrum meat and potatoes one added "everything else".

Perhaps surprisingly, Eco says little about the logic of lists. He does not explore, for instance, the question of whether you have the same list or a different one if you list the same ingredients in a different order. A shopping list with "pork, carrots, shampoo, raisins" on it is not much different from one listing them the other way around. Yet presumably a menu ought to read "hors d'oeuvres, soup, fish, chicken, dessert, coffee" rather than "coffee, fish, dessert, chicken, soup, hors d'oeuvres", since it is regularly assumed that the order on the menu will correspond to the temporal order both of appearance of the items listed and of their consumption. But is this assumption a good enough reason to deny that the two menus are, in themselves, identical?

Eco wisely remains silent, and he also does not tell us which infinity the infinity of lists requires: are there merely as many lists as there are ordinary natural numbers? Or do we have to follow the mathematician Cantor into the higher infinities needed to count the points on the real line? Is a list of all lists possible, or would it fall victim to the same paradox that besets the set of all sets? The Italian title of this book was not The Infinity of Lists but La Vertigine della Lista, which perhaps better suggests the labyrinths into which the subject leads.

Eco clearly had a lot of fun compiling his anthology, and his collaborators on the paintings must have done so as well. The book is beautifully produced. It would, obviously, be wearisome to read it from beginning to end, more so even than ploughing through a dictionary of quotations, since the latter would have been chosen for their pith and wit, whereas the excesses of Ezekiel, Rabelais, Cervantes, Burton, Perec and the many others collected here - I refrain from adding to the list - are in themselves pretty tedious. The lists are the bits one skips, even in Homer.

Rather innocently, or at least so it seems, Eco quotes Paul Valery on just this problem: "I don't like museums much. There are some admirable ones, but none is delightful ... a strange organised disorder spreads out before me. I am seized by a holy dread. My gait becomes religious. Soon I no longer know what I came to do in this waxen solitude, redolent of the temple and the salon, the cemetery and school ... all this is inhuman. It is not pure. This onset of independent and inimical marvels, and the more inimical the more they resemble one another, is paradoxical ... the ear would not bear ten orchestras playing at once."

Valery's comparison is surely apt, as is his summary that a museum may be impoverished by the excess of its own riches. Eco admits that the voraciousness of museums, deriving from the voraciousness of private collectors, remains a problem, and even the most avid curators have learnt to highlight their star items rather than throw a jumble into the public's face.

Collectors often aim to complete their collections, and then whether they are train-spotters or twitchers (as opposed to birdwatchers) they are rightly regarded as obsessive: nerdy, anoraked, fanatical, neurotic, excessive, pathological or myopic. But many of the lists that appear in literature are made with the opposite passion: love of the very fact of incompleteness. When Kant rhapsodised over the starry heavens above, it is the fact that the stars resist enumeration that enthused him. The sublime is whatever dwarfs our efforts to tame or encompass it, even with words. And even as they set about describing things, writers know that their words will almost inevitably fall short of their ambitions.

There is never going to be the last word, the whole truth, the final history, the book of the recording angel, the word, as Joseph Conrad put it, "whose ring, if it could only be pronounced, would shake both heaven and earth". But Conrad was lamenting the difficulty of lassoing a psychology and a character, rather than that of the less rewarding drudgery of a minute, pre-Raphaelite, pixel-by-pixel depiction of the human scene.

THE AUTHOR

Umberto Eco, president of the Scuola Superiore di Studi Umanistici, University of Bologna and an honorary fellow of Kellogg College, Oxford, is perhaps best known for his 1980 novel The Name of the Rose.

Born in Piedmont in 1932, Eco was urged to take up law by his father, but opted to study philosophy and literature at the University of Turin instead. His career has seen him lecture at many universities, including Harvard University, the University of Firenze and the Ecole Normale Superieure.

More recently, parallels have been drawn between Eco's novel Foucault's Pendulum and Dan Brown's The Da Vinci Code. While some have accused Brown of plagiarising Eco's work, Eco has been relaxed, answering questions about Brown by saying: "Dan Brown is one of the characters in my novel Foucault's Pendulum."