"On Nothing", an essay by Ricardo Nirenberg

 

Others have used this title or similar ones before. Hilaire Belloc published one of his many books, On Nothing and Kindred Subjects, in 1908 and Bruno Jasieński’s Polish poem “Nic” (Nothing), of 1921, had not a single word after the title. The minds of these two authors could not have been more divergent: the one a strict, uncompromising Roman Catholic and anti-Jew, the other the son of a lapsed Jewish father, whose real name was Wiktor Zysman and who became an important Bolshevik writer, shot in 1938 on order from Stalin.

About Jasieński’s poem, I’m afraid, I don’t have much to say except to commend it for fidelity to its title, but at the beginning of Belloc’s book we find the following sarcastic panegyric, which was, transparently, a cannon shot against Modernism, the bogeyman of Pope Pius X—Modernism as Nihilism and Science, Modernism as the synthesis of all heresies, Modernism as the Devil:

“There is in Nothing something so majestic and so high that it is a fascination and spell to regard it. Is it not that which Mankind, after the great effort of life, at last attains, and that which alone can satisfy Mankind’s desire? Is it not that which is the end of so many generations of analysis, the final word of Philosophy, and the goal of the search for reality? Is it not the very matter of our modern creed in which the great spirits of our times repose, and is it not, as it were, the culmination of their intelligence? It is indeed the sum and meaning of all around!”

 

In the pages that follow we are told, tongue-in-cheek, that Nothing is the origin of music because there is nothing (sic) in the hollow of a bugle and the inside of a drum; we are also told that a gossamer scarf from Kashmir is “next to nothing” because it floats in the air. Iohannes Ludovicus Vives, considered one of the founders of modern psychology, wrote that the soul is, like light, "next to nothing" —but that was in 1538, long ago. In a dogmatic polemicist like Belloc, such ignorance about well-known matters of fact should perhaps be expected: sharp rhetoric and decent physics seldom cohabit in the same brain. So Belloc’s book is of little use for those trying to learn something about Nothing, and I do not know of any other piece of writing that fills the bill. For this reason I decided to publish the present essay, which will serve, I trust, as a short introduction to the vastest of all subjects, and where I shall endeavor to stay clear from the puns and paradoxes to which the word “Nothing” easily lends itself.

Let us begin with a bit of history. The immediate consequences of the revolutions of 1848 in Europe were not so much political as esthetical: soon after 1848 Nothing replaced Nature as a leading motif and as the prime trigger of the Sublime. The new frissons came no longer from the contemplation of waterfalls or snow-capped peaks (which, after all, can be avoided by staying on dry flat land), but from the awareness that Nothing is always with us, at the turn of any corner so to speak, touching us on the shoulder whether we like it or not. This world-historical event did not happen—no world-historical event ever does—without a long chain of causative or enabling forerunners. Of the many links in this long chain I will refer, briefly, only to a few, before returning to our base-camp, 1848.

Since as far as we know our notion of Nature harks back to the physis of Presocratic philosophy, it is natural to begin there. For the ancient atomists, Nature or physis was an inextricable combination of being (tò ón) and not-being (tò mē ón): the smallest pieces of being were the atoms, and the empty space or void was not-being, i.e. Nothing. Nothing, or the void, was necessary for the atoms to have room to move about and to account for the motions and changes we perceive; in other words, Nothing was necessary to explain becoming. So we can say that for the ancient atomists Nothingness was a full partner in the wondrous enterprise of Nature.

That tolerant attitude was challenged by the Eleatics: according to Parmenides, you cannot pronounce the words “is not,” “not being,” and so on—you shouldn’t even think of them. As a consequence, Nature must be a plenum—all being, whole being and nothing else—rather than the atomists’ mixture of being and not-being. Ancient ontology was peculiar, since there is no compelling reason to identify room or empty space with not-being: we moderns tend to think of empty space (and empty time) as enjoying the advantages of being, as fully as matter, force and energy. Yet Parmenides, Zeno and Melissos did not hesitate to carry their ontology to its limits, and declared that all motion and all change is illusion, that in reality Nature, or the All, is dead-still, full, eternal and spherical. Nothingness was proscribed and erased.

Aristotle, as is his wont, shows more common sense: he recognizes that there is change and motion in the world, but still denies that there can be a vacuum, or, as he says (Physics, IV, vi, 213a), an extension which contains no body perceptible to the senses. For Aristotle, matter is continuous, with no breaks, empty space is not allowed, and Nothing (still identified with emptiness) is proscribed, just as it was for the Eleatics. But, contrary to Parmenides, Zeno and Melissos, Aristotle maintains (214a) that certain types of motion are perfectly possible in a plenum, namely rotary motion, and vortices (dínai); two-thousand years later, Descartes would adopt the same tricks: Nature is a plenum, and change and motion are explained by vortices—Nothingness is still out. Galileo, too, was of the opinion that “Nature abhors a vacuum.”

Meanwhile, the Church Fathers had adopted, or perhaps invented, the dogma that God created the universe ex nihilo, out of Nothing (except, of course, for Himself). So the question could be restated more Christianly: did God leave rests of the primordial Nothing in His creation, or did He make it as solid as solid can be? Between 1644 and 1654, Torricelli, Pascal, de Roberval, Auzout and von Guericke performed a series of experiments that proved to all except a few entêtés—the Cartesians, some Jesuits, and Thomas Hobbes—that the vacuum exists in Nature. The ingenuity of those experiments, especially of the one called “le vide dans le vide” or the vacuum in a vacuum, is remarkable, but what caught my imagination as a boy was the engraving by Kaspar Schott of the big 1654 show put up by Otto von Guericke, which went by the impressive title of “The Hemispheres of Magdeburg.”

Two half spheres made of copper and about a half meter in diameter were joined, and a vacuum was made inside the resulting sphere by means of an air pump, the first ever, previously designed and built by von Guericke. Two teams of horses are seen pulling in opposite senses, without being able to pull the two hemispheres apart.

A large part of the charm of the picture, to my mind, comes from the striking combination of two entirely different pictorial genres: the landscape with the people, the horses, the town with its cathedral in the distance, the hills, and, as if floating among the clouds, the old technical drawings with their labels: Fig I, Fig II, etc.

But, pictorial charm apart, the deepest appreciation of those experiments and their spiritual significance came from the greatest of those experimenters, Pascal. He put together a new picture of the universe—an infinite space, mostly void; our earth a tiny speck in no special place—and drew the consequences: not just the logical but also the emotional consequences, which are something else. This tremendous miracle, that a speck on a speck, which is what we are, is able to think the whole, and thereby to contain it in a sense; this tragic privilege, that we, the feeblest reed in Nature, know, as Nature does not, that Nature kills us; this middle and precarious place that we occupy between two abysses, Nothing and the All—those are some of Pascal’s logico-emotional conclusions. His fusion of heart and mind and his superb handling of both algebra and metaphor have consistently provoked the animosity of the heartless: to name only a few, I remember reading as a boy E. T. Bell’s Men of Mathematics, a popular set of biographies in which Pascal was excoriated for having wasted his powers as a mathematician in meaningless theological pursuits, and later I found that the French poet Francis Ponge called Pascal “cette planche pourrie”, that is, this man who looks like he might help us but who is actually of no use—he is a fraud.

Pace Ponge, Pascal was of quite some use and he was a prophet rather than a fraud: he anticipated in many ways the philosophical tendencies of the 18th century, most notably the appearance of nihilism. As Professor F. C. Beiser puts it in his The Fate of Reason: German Philosophy From Kant to Fichte, Harvard U. Press, 1987, p. 4:

“As early as the 1780s, nihilism, ‘that most uncanny of guests,’ was knocking at the door. It was F. H. Jacobi who introduced the term ‘nihilism’ (Nihilismus) into modern philosophy. To Jacobi, the paradigm case of the nihilist was someone like Hume at the end of the Treatise. The nihilist was a skeptic whose reason told him that he had to doubt the existence of everything—the external world, other minds, God, and even the permanent reality of his own self; the only reality that he could affirm was nothingness itself.”

 

But even a little earlier, in 1761, in a novel that Kant relished, Rousseau's  La Nouvelle Heloïse, the heroine Julie had this to say: "To such a degree are all human affairs naught, that with the exception of the being which exists by itself [i.e. God], there is no beauty except in that which is not."

And Pascal anticipated, too, the esthetical revolution of two centuries later; Baudelaire’s sonnet “Le Gouffre” (which means, roughly, the abyss or the groundless — Greek kólpos, English gulf are cognates), from Les Fleurs du mal, 1857, pays explicit homage to the great predecessor and is possessed by his dread, though not by Pascal’s conceptual penetration or his classical taste:

« Pascal avait son gouffre, avec lui se mouvant.
- Hélas ! tout est abîme, - action, désir, rêve,
Parole ! et sur mon poil qui tout droit se relève
Maintes fois de la Peur je sens passer le vent.

En haut, en bas, partout, la profondeur, la grève,
Le silence, l’espace affreux et captivant...
Sur le fond de mes nuits Dieu de son doigt savant
Dessine un cauchemar multiforme et sans trêve.

J’ai peur du sommeil comme on a peur d’un grand trou,
Tout plein de vague horreur, menant on ne sait où ;
Je ne vois qu’infini par toutes les fenêtres,

Et mon esprit, toujours du vertige hanté,
Jalouse du néant l’insensibilité.
Ah ! ne jamais sortir des Nombres et des Êtres ! » [1]

A gulf always accompanied Pascal.
—Alas!  All is abyss—deed, wish, dream,
Our very words! my hair stands on end
As the wind of fear blows by.

In the sky and on earth, everywhere, depth and sand,
Silence, space horrid, hypnotic…
On the walls of my nights God with his finger writes
Protean, unending nightmares.

I fear sleep as if it was a deep hole,
Full of vague terrors and ending in the unknown;
Through all windows I only see infinity,

And my heart constantly seized by vertigo
Envies the apathic Nothingness.
Ah!  To be able to stay within Beings and Numbers!
(My translation.)

 

We have overstepped our boundary of 1848: we must go back, for Pascal and 17th-century European science were not the only influences acting on the vast artistic movement that at a later point would be sarcastically dubbed the Grand Hôtel du Gouffre, a vast movement that includes Modernism: the other influences came from the Orient. To the vacuum or absence of matter demonstrated by Pascal, de Roberval, von Guericke, and others, was later added the Vedantic and Buddhist Śūnyatā, or absence of self. Matter and self are commonly contrasted in modernity, but they are the two sides of the coin called in Latin substantia and in Greek tò hypokeímenon—in both cases literally meaning, “that which lies underneath.” The value of this coin is wholly dependent on whether or not you believe that the concept of relation necessitates a previous concept of what are the things to be related, or in other words, whether you believe that an object can be conceived by itself, independently of the rest of the universe. All we perceive, all we can think of are relations: this was the teaching of the great Buddhist teacher Nāgārjuna (c. 150-250 CE), and there is nothing under those relations, no relata: if you accept this statement, the coin of substance is worthless. And note, most importantly, that the Nothing that results from the subtraction of substance—both matter and self—is also the All, the undifferentiated All.

In 1804, a Persian version of the Upanishads (the Oupnekhat) was rendered into Latin by the French Orientalist A. H. Anquetil-Duperron: there Arthur Schopenhauer learned the Vedantic doctrines which, supplemented by his own artistic bent, were offered to the European public in 1819 under the title, Die Welt als Wille und Vorstellung, The World as Will and Representation. Schopenhauer and his book remained obscure until the revolutions of 1848 and their aftermath of bitter disillusion. Hegel’s philosophy guided, and would guide for quite some time, the thought of political revolutionaries; Schopenhauer’s provided the artists with a refuge from politics and the world [2]. The revolutionaries accused the refugee artists of being “escapists,” to which the latter replied that, on the contrary, they were the only ones who faced the ultimate reality, that is, death and nothingness, from which the din of politics and the world distracts the mindless mob. A permanent polemic was thus renewed, and was renewed again in my lifetime by the dropout hippy movement and the Vietnam-War Era rebels of the 1960s and 70s. It is essential to note, however, that both the revolutionaries and the navel-gazers, the militants and the anchorites, were joined in viewing Nothing as identical with the All. For here Hegel (Wissenschaft der Logik, 1812) is agreed with Nāgārjuna and Schopenhauer.

And now we can return, with better intellectual conscience, to the aftermath of the European revolutions of 1848. Says Karl Marx in The Eighteenth Brumaire of Louis Bonaparte, first published in New York in 1852:

“The social revolution of the nineteenth century cannot draw its poetry from the past, but only from the future. It cannot begin with itself before it has stripped off all superstition in regard to the past.”

 

We must first go back to 0 or back to nothing. To advance we must retreat; in other words, we must advance toward forgetfulness. Although Hegel’s 1812 preface to the Logik has great philosophical relevance here, what comes to my mind instead, and with great force, is an image from a German newsreel of 1944 showing the retreat of the Wehrmacht from the Russian steppe. With the sophistical skill of which Goebbels was master, defeat was presented as victory, retreat as advance. The Germans had a policy of scorched earth, and the image I mentioned is that of a steam locomotive with a large metal hook in the back; as the engine advanced, the hook caught the ties, lifted them up and removed them, and the rails withal—German technology. When I read Hegel or Marx I cannot help having that image somewhere in the back of my mind.

Richard Wagner, who had been a revolutionary and had to flee into exile in 1849, discovered Schopenhauer five years later, a discovery that he later described as the most momentous in his life. The artistic result was Tristan und Isolde, 1857-9, which closes with these words, sung by the dying Isolde:

In dem wogenden Schwall, in dem tönenden Schall, in des Weltatems wehendem All, ertrinken, versinken, unbewusst, höchste Lust!

(In the heaving swell, in the resounding echoes, in the universal stream of the world-breath, to drown, to founder, unconscious, utmost rapture!)

 

And Baudelaire, at about the same time:

Que nos rideaux fermés nous séparent du monde,
Et que la lassitude amène le repos !
Je veux m’anéantir dans ta gorge profonde,
Et trouver sur ton sein la fraîcheur des tombeaux !

(“Les Femmes damnées”, Les Fleurs du mal, 1857. My translation: Let tight curtains protect us from the world,/ And let weariness bring rest!/ I want to vanish in the depths of your throat,/ And find on your bosom the coolness of the grave!)

 

Nothingness has replaced Nature. “Tristan und Isolde marked the end of all romanticism. Here the yearning of the entire 19th century is gathered in one focal point,” said Richard Strauss. “The end of all romanticism” means the end of Nature as locus of the sublime, and its replacement by Nothingness. Baudelaire’s gouffre and gorge profonde and Wagner’s Schwall are avatars of the Nothing that is also the All, the last refuge for the artist eager to escape the world, and to blow it up as he makes his escape. Les Fleurs du mal and Tristan und Isolde were meant both as works of art and as incendiary devices to be hurled into the ignoble crowd of the bourgeoisie and their accomplices, the scientists and engineers, who had become masters of the world. Both works are pillars on which twentieth-century Modernism was built, and that is why T.S. Eliot incorporated into his Wasteland fragments from them, and only from them.

 

 

By 1880, the year of the death of Flaubert (who, when working on Madame Bovary, had told his friends he prepared a novel about nothing), the central place of Nothing in the human heart was widely acknowledged. In Massachusetts, around 1883, Emily Dickinson composed this enigmatic, ambiguous poem (number 1563 in the Harvard edition of 1955):

By homely gift and hindered Words
The human heart is told
of Nothing—
“Nothing” is the force
That renovates the World—

 

Is the poet seriously saying that Nothing is the force of renovation? Isn’t it rather the force of meaninglessness? Or is she merely reporting on what “the human heart is told” by the likes of Hegel and Marx? But are Hegel’s and Marx’s words hindered, or their gifts homely? And in any case, can it be “By homely gift and hindered Words” our heart is told about Nothing? Isn’t it rather by anxiety and terror, as we can read on the eyes of these two figures in Piero Della Francesca's famous fresco in the church of San Francesco, in Arezzo?

 

The Russian Leo Tolstoy had much to say about meaninglessness, which tormented him through life. Being the author of War and Peace and Anna Karenina, a writer celebrated throughout Europe, hailed as a genius, was not nearly enough to give a meaning to Tolstoy’s life; having achieved what among us is called “professional success” and “international acclaim” did not help; nor did his being the scion of old Russian nobility, with lots of serfs, a young wife, and many children. He constantly thought of the prince Siddhartha Gautama, who left his house and became an ascetic upon discovering that men get old and sick and die, and of Francis of Assisi, who renounced a life of honors and pleasures for his beautiful bride, la povertà. Tolstoy was a man of the world, very well educated, not a stranger to science and math, and in his My Confession of 1880 (roughly when Dickinson was writing her poem) he wrote about his search for meaning:

“And then I began to build up on rational foundations, out of what I knew, an explanation which would give a meaning to life; but nothing could I build. Together with the best human intellects I reached the result that ø equals ø, and was much astonished at that conclusion, though nothing else could have resulted.”

Taken as a whole, the above paragraph shows l’air du temps: a well-educated man who didn’t go to church was bound to consider any problem, be it the nature of the universe or the meaning of life, in the light of reason, and that meant, and still means for us, scientific reason, which is built on mathematical foundations. The remarkable detail, however, is the result Tolstoy says he obtained and which astonished him: “ø equals ø”, that is, zero equals zero, or else, the empty set is equal to itself. It is remarkable, among other reasons, because most authors of Tolstoy’s time and place who wished to give an instance of indubitable truth, chose “2 + 2 = 4” instead. So did, to mention only Russians, Dostoevsky and Bakunin. And Turgenev, in Fathers and Sons (1861) has Bazarov, the nihilist, say, “What is important is that two and two make four, and the rest is trivial!” But Tolstoy chose instead “ø equals ø”, a more significant truth, both rhetorically and philosophically.

Zero and the empty set are signposts on the road to Nothing, and Nothing and meaninglessness are related. Meaninglessness means complete indifference: nothing points to any distinction in pattern or level; in common parlance, “everything’s the same,” “nothing makes any difference,” “nothing matters.” No object in the world or thought in my mind is able to elicit in me the will either to abide in it or to keep going in any particular direction. Whence the cohabitation of ennui and nothingness in Baudelaire, in Mallarmé and elsewhere, and whence, too, Heidegger’s selection of nihilism and boredom as the twin hallmarks of our epoch.

Mark, however, the above characterization of boredom: “No object in the world or thought in my mind is able to elicit in me the will either to abide in it or to keep going in any particular direction.” Here only one side of the coin of substance is devalued, the side of the objects of my representation; the other side of the coin—me, my self—keeps or tries to keep its value and its self-regard—unhappy, noble me, unable to abide or to keep going, because of this supremely boring world!—by pathos and a radical detachment from things. But can only one side of a coin be worthless? It is at this point that, if you have just an ounce of metaphysical sense, you seize on the only thing—if indeed it may be called “a thing”—you can possibly seize on, the only thing where you are able, or rather forced, to abide: No-thing itself. Having seized on Nothing, you endeavor to stay in it, to perch on it, to abandon yourself to it; and then, by diverse and secret ways, to leap from Nothing to the All, from meaninglessness to the fullness of meaning, from ennui to joy. No-thing turns out to be identical with the All, as Hegel taught, and meaninglessness is fullness of meaning.

Tolstoy, a reader of Schopenhauer, was very much aware of this new status of Nothing, and he suggests it by writing that the only result of his rational quest for meaning turned out to be “ø equals ø”, where ø may stand either for zero or for the empty set. Neither of which is the same as Nothing, but both definitely point to Nothing.

 

 

The following generations, especially those who experienced the Great War, saw a formidable expansion of the artistic predominance of Nothing. Here is the Dadaist Francis Picabia, in his Manifeste Cannibale of 1920, in which he drums his « rien » into us, nothings:

« DADA lui ne sent rien, il n’est rien, rien, rien.
Il est comme vos espoirs: rien
comme vos paradis: rien
comme vos idoles: rien
comme vos hommes politiques: rien
comme vos héros: rien
comme vos artistes: rien
comme vos religions: rien. »

 

And here is Eugenio Montale, another great reader of Schopenhauer, circa 1925:

“Forse un mattino andando in un’aria di vetro,
arida, rivolgendomi, vedrò compirsi il miracolo:
il nulla alle mie spalle, il vuoto dietro
di me, con un terrore di ubriaco.

Poi come s’uno schermo, s’accamperanno di gitto
alberi case colli per l’inganno consueto.
Ma sarà troppo tardi; ed io me n’andrò zitto
tra gli uomini che non si voltano, col mio segreto.”

My translation: Perhaps on a morning while walking in a glassy air, / arid, I’ll turn around and see the miracle accomplished: / Nothingness behind me, the void / to my back, with a drunken terror. // Then, as if on a screen, they’ll all rush into place / trees, houses, hills, for the habitual deception. / But it will be too late; and I’ll go silently / among those who never turn, holding to my secret.

 

Attila József (1905-1937) was an attentive reader of Hegel and Marx; here is his “Perched on Nothing’s Branch”, translated from the Hungarian by Peter Hargitai:

I finally arrive
at the sand’s wet edge,
look around, shrug

that I am where I am,
looking at the end. A
silver ax strokes
summer leaves. Playfully.

I am perched solidly
On nothing’s branch.
The small body shivers
To receive heaven.

Iron-colored.

Coolshiny dynamos revolve
In the quiet revolution of stars.
Words barely spark from clenched teeth.

The past tumbles
Stonelike through space,
Blue time floating off
Without a sound. A blade
Flashes, my hair—

My mustache is a full
Caterpillar drooping
Down my numb mouth,
My heart aches, words are cold.
There’s no one out here
To hear—

 

In conclusion, I offer two quotations from the essay by Lionel Trilling, “James Joyce In His Letters” (1967), collected in The Moral Obligation To Be Intelligent, New York, 2000. First, from a 1935 letter James Joyce wrote in Italian to his son George:

“Here I conclude. My eyes are tired. For over half a century they have gazed into nullity (nulla), where they have found a lovely nothing (un bellissimo niente).”

 

Next, a few pages later, a remark by Trilling himself, which sums up the literary situation better than anything I could concoct:

“More and more the contemporary reader requires of literature that it have a metaphysical rather than a moral aspect. Having come to take nullity for granted, he wants to be enlightened and entertained by statements about the nature of nothing, what its size is, how it is furnished, what services the management provides, what sort of conversation and amusements can go on in it.”

 

 

 

 

By now you should be convinced that Nothing occupies a pre-eminent position in our cultured collective imagination, but you may still be under the impression that this is so only in literature, in the arts, and in the sorts of philosophy known as existential and existentialist. Although you have read here about Pascal and the void and you should have gazed at von Guericke’s spectacular experiment, you may think that the natural sciences have long since overgrown that infantile disorder or obsession with Nothing. Nothing could be farther from the truth, as we will see.

The 1920s, so rich in expressions of Nothing as the sublime (like Montale’s and József’s poems above, but see also JR Solonche's poem "For a friend who wants to hear the music better" in this issue of Offcourse), closed with the Great Depression and with Heidegger’s notorious statement, „Das Nichts nichtet“, occurring in his inaugural lecture of 1929 at Freiburg, „Was ist Metaphysik?“ This statement, which can be roughly translated as “Nothingness is where negation originates,” was subsequently much ridiculed by other philosophers of the strictly logical tribe. Rudolf Carnap, the German logical-positivist philosopher, called Heidegger’s phrase a Scheinsatz, a pseudo-statement—a polite German way of saying “bullshit.” This is perfectly logical and not to be wondered at, for one of the tenets logicians hold on most to is that “no” and “not” are primitive notions, or symbols, or operations, not to be derived from anywhere, least of all from psychology.

I think we can safely say that when Heidegger delivered his 1929 lecture, and went so far as to assure his audience that all the sciences taught at university are based on Nothing (without, however, persuading any scientist, then or later), he was not aware that five or six years earlier a great mathematician had provided a logical proof of that same fact. John von Neumann died in 1957 at Walter Reed Hospital in Washington, D.C., surrounded by military officers hanging on every one of his last, agonizing mutterings in case they expressed a new and brilliant strategic insight that might give the US a decisive advantage over the USSR. Indeed, Johnny (as he was called) had been prominent among the inventors of nuclear weapons, and had been, too, an inventor of Game Theory as well as of the modern computer: those inventions together made him the father of MAD, the strategy of mutually assured destruction that ruled international policies throughout the Cold War. On that basis alone we may say that Johnny deserves a privileged place in the Nothing Hall of Fame, but this type of Nothing, the Armageddon-Nothing, is a local one, restricted to this planet, a Nothing that would not affect the sun and the other stars.

When he was barely twenty—that is, about 1923—Johnny made a logical discovery that allowed him to put Cantor’s set theory, and therefore all of math, upon the solid foundation of the empty set. Perhaps this calls for a brief explanation. Set theory, the foundation of the great edifice of math, is a game with symbols, and the two most basic are { } and ∈. Let us say that we have: you and I, a table T, and an etherized patient EP. We use the brackets { } as follows: {you, I} is called “the set consisting of you and I,” {you, T, EP} stands for “the set consisting of you, the table, and the etherized patient.” And so on; you get the idea. We read ∈ as “belongs to,” so for example, I belong to the first set {you, I}, but not to the second set; you belong to both, and we write that: “you ∈ {you, I} and you ∈ {you, T, EP}.” We say that two sets are equal when anything that belongs to one also belongs to the other; note that the two sets above are not equal. Now we define the empty set ø as the set (the only one) to which nothing belongs: for any thing, any x you might conceive, we have that x ∈ ø is false, which is written x ∉ ø, meaning x does not belong to ø.

If you have a skeptical turn of mind, like those in antiquity who denied that there exist in the world such things as the points and lines and planes with which Euclid begins, you might object that the empty set ø has no real existence. But remember, set theory is a game, a game with rules that are called axioms, and one of the axioms happens to be that the empty set exists, i.e., that we can go ahead and play with it. The fact that the game of set theory serves as a basis for math, which is the basis of the natural and social sciences, of our world picture and of the actual world we have constructed and where we live, is something with which we cannot be concerned right now—perhaps on some other opportunity.

Anyway, Johnny von Neumann discovered that set theory and therefore all of math can be played with a restricted kind of sets, namely: ø (the empty set), {ø} (the set containing only the empty set), {ø, {ø}} (the set containing two things: the empty set and the set containing only the empty set), and so on non-stop, ad infinitum. Those sets, and combinations of those, are enough to build the vast empire of math and science. What’s marvelous about those special sets is that neither you nor I, nor any table or patient, nor anything in this vale of tears, has any role in them. Only the empty set and brackets, repeated ad nauseam. There are no “external elements,” no things of this world, only sets and sets of sets, and sets of sets of sets…

Thus Johnny based our sciences on the empty set. If you believe that science is not only ours but is also universal, then Johnny’s Nothing is a lot vaster than our planet. Let us not get carried away, though. From a strictly logical viewpoint, Heidegger’s Nichts and the empty set are not the same. Heidegger in his lecture defines his Nichts as follows: for any conceivable thing x, “x is Nichts” is not true. But the empty set ø is defined: for any conceivable thing x, “x ∈ ø” is not true. The two symbols, is and ∈, are not the same, and any logician will tell you that Heidegger’s definition of Nichts violates the identity principle according to which any conceivable thing must be itself, or identical with itself, while the empty set does not violate any logical rules. Heidegger’s point was that, regardless of logic and its rules, our anxiety (or if not ours, then at least Kierkegaard’s, or Pascal’s) reveals Nothing as a fact.

Again, from a strictly logical point of view, Pascal’s and von Guericke’s void is not the same as the empty set: we can have many voids, in separate containers, but because of our definition of equality of sets, there is only one ø. So we are left with three notions: the void, the Nichts, and the empty set, and whether you take them to be all different, or take them to be humanly—I mean psychologically—the same, will depend on your heart, which is to say, on your metaphysics. But whatever your choice, I hope I have convinced you that our scientific as well as our artistic view of the world is, at the present time, based on Nothing.

 

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Notes:

[1] Antoine Compagnon, in his book Baudelaire devant l’innombrable, Paris, 2003, pages 96-9, based on considerations of horizontality versus verticality concludes that Baudelaire’s gouffre is not the same as Pascal’s. The last, enigmatic line of the sonnet, Compagnon declares forever ambiguous (à jamais ambigüe): is it injunctive or optative? Does it say, “Never get out of Numbers and of Beings!” or, “Oh how good it would be, never to get out of Numbers and of Beings!”? The first point about the difference between Pascal’s and Baudelaire’s gouffre is silly—there are no horizontals or verticals in the void. As for the last line of the sonnet, I think the second, optative interpretation is more likely on many counts, and expresses a Pythagorean-Platonic nostalgia for a world, an ideal world, devoid of void but blessed with certainty, the sort of absolute certainty that our civilization has attributed to verities such as 2 + 2 = 4.

[2] On Schopenhauer and his influence on literature and art, you may want to consult for further illumination: Schopenhauer, Philosophy and the Arts, edited by Dale Jacquette, Cambridge University Press, 1996.