Valéry and the Discourse On His Method

Paul Valéry lived his life as though he had been put on earth to provide the rest of us with a caricature of the French mind. "Ce qui n'est pas clair n'est pas francais," goes the timeworn eighteenth-century expression that our French teachers taught us in high school. But clair in French means both "clear" in the sense of comprehensible and "light" in the sense of bright, and Valéry's poetry is filled with radiant Mediterranean sunshine. The mind strives for the clear and comprehensible because what is comprehensible is radiant. Valéry worshipped the human mind, especially his own. The "hero" of his prose work Monsieur Teste (Mister Head) says something that perfectly describes the author and his characteristic pose:"Je suis étant, et me voyant; me voyant me voir, et ainsi de suite . . ." ("I am [in the process of] being, and seeing myself; seeing myself see myself, and so on . . .").^[12]

Valéry loved admiring the workings of his own mind. Wrapped up

with this fascination for the mind was a fascination for mathematics that went far beyond the numerical fantasies of Mallarmé. Unlike Mallarmé, Valéry actually fancied himself a mathematician, and he devoted an astounding amount of time and energy to studying contemporary mathematical theory and then trying to find applications for it in the most extraordinary fields. His friend Pierre Féline introduced him to a number of areas of mathematical study, among them group theory and transformation group theory. Valéry was apparently fond of using his knowledge of mathematics to dazzle his other friends, people like André Gide, who knew very little about such things.^[13] The twenty-nine-volume set of Valéry's notebooks is a startling record of a mind obsessed with numbers, with itself, with its obsession with itself, with a mathematical expression of its own workings, and so on—a kind of monument to neo-Cartesian narcissism.^[14]

Valéry's notebooks show a curious attitude toward "the original founding genius of all modern philosophy." To begin with, even though he devoted a substantial number of pages to ruminations on philosophers, Valéry was fond of playing the part of someone who is foreign to hard-core philosophy and doesn't quite understand it all. So when it comes to Descartes, he likes to talk about things that fussy, scholarly people would consider trivial. In one fairly long notebook entry he mentions the qualities that have struck him personally in various philosophers—this after saying that philosophers are boring to read and that their language is antipathetic to him. Of Descartes, Valéry can say only that it is the "individual" that "appears" to him, meaning, I assume, that he is attracted by the personal style of Descartes's writing.^[15] He returns over and over again to the subject of Cartesian doubt and the most famous phrase from the Discourse on Method, "I think, therefore I am." And he speaks of the "insignificance" of the principles in the Discourse, saying that the charm of the work is "above its substance" (C, 16:728 [1:673]).

Like Descartes, Valéry sought clarity, certainty, evidence (again in the sense of "state of being evident"), and he sought it in mathematics. "Descartes. No occult qualities—made the greatest effort for Clarity, " Valéry muses at one moment in his notebooks (C, 10:103 [1:595]). "On Descartes: Clear and distinct ideas, " he writes a number of years later (C, 20:508 [1:700]). But the model he used was always the structural one, the one that placed the emphasis on the relation between elements rather than on the elements in and for themselves. Valéry saw the mind as essentially a relational system whose operation he attempted to de-

scribe in the language of group mathematics. "Every act of understanding is based on a group," he says (C, 1:331). "My specialty—reducing everything to the study of a system closed on itself and finite" (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one "group" undergoes a "transformation" and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: "The S[elf] is invariant, origin, locus or field, it's a functional property of consciousness" (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind's momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. "Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind" (O, 1:36). "Psychology is a theory of transformations, we just need to isolate the invariants and the groups" (C, 1:915). "Man is a system that transforms itself" (C, 2:896).

The Notebooks are not the only place where Valéry indulges in this kind of speculation. His mathematical theories turn up in his published writings, too. In an article in Mercure de France in 1899 he wrote about what he called the reversibility of states of consciousness. "The transformations that any given system undergoes are reversible when the system is able to return from a certain state to an earlier state, passing through the same states during the return as it had on its way here, only in reverse order. This definition, though its origin is in physics, is sufficiently general that one can attempt to apply it to the mind and view the mind as a system of transformations" (O, 2:1459). In a piece called "A Few Words about Myself," published in 1944, Valéry describes how he discovered at the age of twenty "that man is a closed system with respect to his cognition and his acts" (O, 2:1518). Later in the same essay he describes the entire credo of his youth:

There was a time when I saw.

I saw or wanted to see the figures of relations between things and not the things.

Things made me smile from pity. Those who paused to consider them were to me sheer idolaters. I knew that the essential thing was figure .
(O, 2:1532)

The term system has at least two important senses for Valéry, and several of his notebook entries show that the elaboration of the idea of systems was associated with Descartes. I mentioned earlier that Mallarmé had a metaphysical crisis in his twenties, which led him to some important philosophical discoveries that were to occupy his mind for the remainder of his life. In 1892 Valéry, who had just met Mallarmé the year before, had a "crisis" of his own. On the face of it, it was a rather trivial matter—a case of unrequited love. It did, however, lead him to a major turning point: he renounced the emotional life in favor of something that he would call the System (with a capital S ). The System was an ideal program of intellectual contemplation whose chief purpose was to submit all important phenomena of mental life to rigorous, dispassionate analysis, the sort of thing we see piecemeal in Valéry's notebooks, which in a significant sense are the result of this program.^[16] But system (with a lowercase s ) also means relational system in the sense I've been using. When Valéry talks about the System he often feels the need to mention systems and to bring up Descartes:

Grosso modo the System has been the quest for a language or a notation that would make it possible to treat de omni re just as analyt[ic] geo [metry] allowed Des Cartes [sic ] to treat all figures.

The human body (viewed as a syst[em] of variables) must be able to reveal this secret.
(C, 9:82 [1:812])

In another long entry, written about fifteen years after this one, Valéry's subject is once again the System: "It used to be, would have been, is, was, and would be a kind of method à la Descartes—I mean Geometry—because it would have to do with a sort of systematic translation of the diversity of objects and the transformations of consciousness or the mind into elements and modes of functioning (observable or probable) of this mind." And a little later in the same entry he brings up once again the notion of system:"In short, it seemed ever more strongly to me that what appears almost always and necessarily, like things, world, ideas, cognition, was somewhere else, the product of a functioning—that is, a bounded, closed system, forced to return to itself" (C, 20:290–292 [1:846]).

Perhaps the most intriguing of the notebook statements on the System

and its Cartesian analogy is the one in which Valéry writes in adjacent columns about Descartes and himself. On the left side of the page are four brief phrases having to do with Descartes: "Discours de ma méthode" (instead of "Discours de la méthode"), "Story 1892" (the year of his crisis), "The finite—reduction to my system," and, in a reference to the Latin version of Descartes's famous sentence, "Instead of Cogito and Sum, my formula." On the right side of the page he writes this: "The System—is not a 'philosophical system'——instead, it's the system of me —my potential —my coming and going—my way of seeing and returning" (C, 18:55 [1:841]). As this entry and many others show, Valéry regarded Descartes's method not precisely as being similar to his own but as being a kind of analogical model, much as Kant invoked the name of Copernicus to call attention not to the content of his own new philosophy but to its revolutionary character.

The last entry I quoted is especially valuable because it hints at the reason for the difference between Descartes and Valéry. Descartes, too, founded a "system." In fact, his philosophy is often referred to as systemlike because of the coherence of its parts and its "closed" nature. But for Valéry, it is still just a philosophical system, that is, a corpus of writings on "philosophical" subjects. Valéry's System is different because its very logic is different. In Valéry we see the logic of relational systems, the "system of me." And what could be more systematic than a system of thought whose primary characteristic is that it is systemlike?

Valéry was consistent, and we find the system concept everywhere. In a world where the mind is a system, it is natural that the things the mind makes should look like systems, too. "I have eternally sought to define or construct a system of variables (that is, a systé[em] of notations)—and of the relations of the conditions among them that would make it possible to represent tangible life," reads an entry in the Notebooks (C, 18:608). One important category of things the mind makes is of course artworks, and not surprisingly, these behave like the systems (the minds) that created them. There's a reason for this, but it has to do with the subject of Part IV of this book, so I will put off talking about it until then. For now, let's just observe how the system concept works in Valéry's vision of artworks.

To a certain extent Valéry's remarks on artworks are historical. That is, he sees the relational quality of art partly as a phenomenon peculiar to the modern age. In an early article called "On Literary Technique" Valéry writes about the modern conception of the poet: "He's no longer the disheveled, delirious man, someone who writes an entire poem in a

night of fever; now he's a cold scientist [savant ], almost an algebraist, in the service of a refined dreamer" (O, 1:1809). Mallarmé is partly to be credited with the modern spirit in poetry, as Valéry says in another place: he was "the first writer who dared to envisage the literary problem in its full universality . . . He conceived as algebra what all the others have thought about only in the particularity of arithmetic."^[17] But certain types of artwork for Valéry are intrinsically structural, regardless of the historical period during which they were created. Valéry was a firm believer in the poetry-prose distinction. In "Poetry and Abstract Thought" the emphasis is on the difference between poetic language and the language of prose. Valéry felt that the distinction extended to the entire work of an, which is to say that a poem as a whole is different from, say, a novel as a whole. The distinguishing factor is the relational quality of poems, as he explains in his "Homage to Marcel Proust": "And while the world of the poem is essentially closed and complete unto itself, being the pure system of the ornaments and possibilities [chances ] of language, the universe of the novel, even of the fantasy novel, is connected with the real world." (O, 1:770). One of Valéry's favorite art forms was dance, because it so clearly embodied the relational principles he wanted to see in everything. In an essay originally given as a lecture in 1936, "Philosophy of the Dance," he says: "No exteriority! The dancer has no outside . . . Nothing exists beyond the system that she forms through her acts" (O, 1:1398). And a paragraph later he describes dance as "a group of sensations that makes an abode for itself, . . . that emits from the depths of itself this beautiful series of transformations in space" (O, 1:1398). Valéry's personal dream was to create the perfect, mathematically determined work of art, something he mused about in his notebook the year before he died:

To arrive at the completion of a work by means of formal conditions accumulated like functional equations——

in such a way that the possible contents are more and more circumscribed —

Subject, characters, situations result from a structure of abstract restrictions—
(C, 28:468 [1:314–15])

If ever there was a prestructuralist thinker, it was Valéry. I say pre structuralist not only because Valéry's thought looks like structuralism even before there was any such field as structural linguistics, anthropology, or criticism but also because it shows the logical foundations of struc-

turalism in all their naked, unabashed glory. Few structuralists later in the twentieth century felt the need to expose the mathematical foundations of their thought or repeat the by then timeworn credo about how the importance is in the relations and not in the elements themselves. They had gone beyond this credo, had taken it all for granted as something that didn't need to be said in their elaborate discussions of structures and systems. But Valéry did feel the need to say it—over and over and over again. For him, the real truth—the real essence, to be more accurate—always had to be anchored firmly in the neo-Cartesian logic of relationalism. And the credo was always worth repeating, as if that would keep the relational essence from suddenly slipping away, leaving behind the most dreaded monster of all: things themselves .