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Paul Valéry's Modernist Aesthetic Object

Author(s): Steven CassedySource: The Journal of Aesthetics and Art Criticism, Vol. 45, No. 1 (Autumn, 1986), pp. 77-86Published by: Wiley on behalf of The American Society for Aesthetics

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STEVEN CASSEDY

a u l

V a l er y s M o d e r n i s t Aestheticb j e c t

IN HIS ESSAY La litt6raturecomme telle,GerardGenette, after analyzing Paul Valery's

theory of literatureand its aesthetic implica-tions, assesses Valery's position in the historyof moder criticism by identifying him as a

precursorto the Russian formalists and theFrenchstructuralists.The autonomous tatus ofart in Valery's conception is what places hisaesthetic theory so distinctly in the modertraditionfor Genette. Valery's ideal of a pure

poetry, his insistence on the accidental, arbi-

traryqualityof the literaryproduct elativeto its

creator, he refusalto sanctioncriticalresponsesthat reason directly from literarywork to au-

thor, the likeningof literature o a form of jeucombinatoire-all this for Genette shows a

quest for an absolutestatus of (literary)art, for

a literatureas such, that places Valery infitting historicalcompany with the formalistsand structuralists.'

Statementsaboutthe ideal autonomyof the

work of art in Val6ry have become almostcanonical in critical writingson Valery's aes-

thetics. Rene Wellek, in a recently publishedseries of lectures on four twentieth-centurycritics, saidthat Valery keeps the threestagesof the aesthetic transaction author,work, and

reader]completelyseparate. 2 In Valery, he

says, we are confrontedwith a

theorythat

assertsthe discontinuitybetweenauthor,work,and reader,emphasizesa most extremeregardfor form and nothingbut form divorced from

emotion, and takes poetry completely out of

history into a realm of the pure and theabsolute. 3

As Wellek points out, however, Valery'sphilosophyof aestheticsmust be gleanedfrom avast andfluid corpusof scatteredwritings,and

STEVENASSEDYs associateprofessorofSlavic and

comparativeliterature at the University of Cali-

fornia, La Jolla.

views expressedin one place are often contra-dicted in another.One important ontradictionconcerns precisely the radical distinctionWellek finds in Valery's aesthetics between

author,work,and reader-the samedistinction,

thatis, that leadsto the received view of Val6ryas a distinctly modern aesthetic thinker. Ifthe main source of Valery's modernism is hisview of the work of art as an absolute andautonomousobject, entirelydivorcedfrom bothits source and its perceiving subject, then

Valeryis at best a confused modernistsince, asI will show, he is not consistent on this point.

No, Valery's modernism in aesthetics lies

elsewhere, I think. It has to do first with themode of investigationinto aesthetic questionsthat is implicit in his treatmentof them. While

Val6ryexamines all three aspects of the aes-thetic transaction, it is his approachto theaesthetic object (and to human products in

general)that is distinctly modern because itis ontological.Because of thishe looks aheadtoa twentieth-centurytradition of aesthetic in-

quiry that will include phenomenologistslikeRomanIngardenandMerleau-Ponty,Americanaestheticians like Pepper, Goodman, Dickie,and Danto, and critics like Rene Wellek him-

self, who introducedthe ontological aesthetictheories of

Ingardento the English-speakingworld in 1942 by writingabout the mode ofexistence of the literaryartwork.4

Valery's solution to the problemof the on-

tology of artworkspoints up a second majorindication of his modernism(while also show-

ing, incidentally,a surprisinglyunifiedpictureof the aesthetic transaction).Val6rywas con-vinced of the objective, indwelling presenceinhumanproductsof a sortof human ntention hedoes not use this term)that expresses itself inthe form of a mathematical ystemof relations.

The inherenceof such systems of relations in

© 1986TheJournalf Aesthetics ndArtCriticism








CASSEDY

humanproductsis what sets them apartfrom

objects encountered n the naturalworld, andthe reasonfor this is that these systemsreflect afundamentalaspect of the human spirit, as

Valerysees this.

Valerywas no truemathematician; e was atbest a talented and enthusiastic amateur.His

quaintproposals(sketchedout at length in his

Notebooks)forapplyingmathematicalonceptsto aestheticsandpsychology frequently ounderindetails, leadingone to suspectthat he himselfdid not takehis ideastoo seriously-at leastnotwhen they were elaborated mplausiblyin the

precise form of algebraic symbols and equa-tions. Still, Valery'smathematicalview of the

Self and the work of art serves an importantfunctionas a conceptualmodel in his theory. In

fact, the key to the unityof the entire aesthetictransaction that is, to the extent thatValeryisinclinedto regard he transactionas unified) is

the processby whichthe artisticSelf, seen as amathematicalstructure, externalizes itself tobecome an artwork.

Valery's ormalism, then, is not to be soughtin his isolationof the aestheticobject.Myclaimis thatValerydoes not ontologicallyisolate theaestheticobjectfromits authoras absolutelyor

as consistently as is usually maintained.The

only consistent isolationof the aestheticobjectin Valeryis simply its isolation as an object ofphilosophical-aestheticspeculation. The truesource of Valery's formalismis his attempttoreduce the aestheticobjectand artistic ntentionto a condition of purealgebraicrelationalism.And the true source of his modernism,beyondthis formalism, is the distinctly ontologicalapproachhe takes in his investigationof aes-theticobjects in particular nd humanproducts

in general.I. Posing the OntologicalAestheticProblem

One of Valery's most penetrating nquiriesinto the natureof objects, aesthetic and ordi-

nary, is an odd little passagein his Socratic

dialogue, Eupalinos.5Valery's decidedly mod-ern Socratesdescribesa baffling encounter he

has had at the seashore with a smooth, white

objectthat defies characterization reciselybe-

cause it gives no clue to its origin. Had it been

madeby humanhands,by another ortof livingcreature,or by the chance agitationof the sea?

Nothing will tell. Socrates realizes that his

experience has brought him to a completeimpasse, so he throwsthe object back into thewater(0, 2:120).

The problem s clearlyone that has occupiedthe attentionof the twentieth-century rtist andaesthetician. Both have been obsessively inter-ested in preciselysuchlimitingcases as the onethat Valery's Socratesstumblesupon. What if

Socrates had seen theverysameobject, say,in the market place or, to pursue Valery'splayful anachronism,in ancient Athens's an-swer to the Museumof Moder Art? Wouldthishave changed its essence? What happens, themodem aestheticianhas asked time and again,to the status of the seemingly non- or anti-

aestheticobject-the Brillobox, the latrine,anindifferentobjectfoundin the street-once it is

placed in a museum, where spectatorswill becalled upon to behave towards it as if it be-

longedto the same class of objectsas the Pietdor the Night Watch?6Does it undergo a true

change of essence? If it were to be removedfrom the museum and placedon the seashore,would a precivilizedman, unfamiliarwith la-trines and Brillo boxes, respond to it as

Socrates does to the bafflingwhite thing in

Eupalinos?Socratesclearly does not come up with an

answer to this question. But he has certainlyposed it, and Valery knows this even if hisSocratesdoesn't. For the termsof his descrip-tion indicate the necessity he sees of discover-

ing an intention, or somethinglike it, in an

object: some sign, in other words, that willcommunicate to the spectatorthat the objectbefore him is a humanproduct.Discoveringthe

distinctive, indwellingqualityof humanprod-ucts, then, is one aspect of the ontological

problemfor Valery.The other aspect is suggested in the manystatementsValerymakesasserting he indepen-dent, at times phenomenalstatus of all human

objects, even those as insubstantialas liter-

ary texts. Valery speaks of his effort tophenomenalize the whole psychic mechan-

ism through writing,7 to find a purely phe-nomenal value for things of the 'inwardlife '

(C, 19:649),and defineswritingas wishing to

give a certainexistence, a continuedduration o

phenomenaof the moment (C, 4:912 [2:998]).Thus the ontological problem ncludes a kind

of where in addition to the what sug-

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Paul Valery'sModernistAestheticObject

gestedby theconcernwithindwelling qualities.And the where problemis not confined to

Valery'swritingson literaryobjects. Itemergesin discussions of humanproductsof all kinds:

those as literally substantialas sculpturesandcathedrals as well as those as abstract and

intangible as poems, dances, and geometric

figures.I will discuss this problemfirst, then turnto

the problemof indwelling qualities, and con-clude with the issue of genesis.

II. Ontic Place: Where HumanObjectsAre

Thelogicalpointof departureor anontologi-

cal investigationof aesthetic, or just human,objects, is to considersuch objects thatpresentthe greatest confusion with natural objects.What, for instance, distinguishes a concrete,humanobject like a work of architecture rom a

concrete, natural object like a stone? For

Valery, posing the question what an object is

entails at the same time posing the questionwhere it is, identifyingand defining, that is, amanifold peculiarto humanobjects in such a

way that we can distinguish the place or

space of even an object like a cathedral,which appears quite simply to exist in the

space-timemanifoldof the phenomenalworld.In anotherpartof Eupalinos Socrates and his

pupil Phaedrusagree that architecture s themost completeof arts, because, as Socrates

explains, the bodyobliges us to desire whatisuseful . . ; the soul requiresbeautyfrom us;but the rest of the world, both its laws and its

contingencies, obliges us to consider in everywork [of spirit] the question of solidity (0,2:130). Architectures thus the most complete

of artsbecause,while satisfyingthe needs of thesoul, it also dwells in the world.

Butthe locus of architecture s notabsolutelythe same as that of objectsdwelling in the restof the world. Worksof architecture exist inthe middle of this world, like monuments ofanotherworld;or else like examples, scatteredhere and there, of a structureand a form of

duration hat are not those of beings but rather

those of forms and laws (0, 2:105). Thus it

appears hat,at least in the case of architecture,a human, and specifically an aesthetic object,has its own special space-time manifold: onethat resembles the space-timemanifold of na-

ture, indeedin some cases maybe conceivedofas superimposeduponit, butone thatis closedon its objectsandparticularo them, one whose

objectsare determinedby theforms andlaws ofa humanspiritinsteadof by the causal laws ofnature.

These characteristicswill be found to definethe place of aestheticobjectsof all sorts, infact of any product of the human spirit for

Valery,froma dance, which exists in a sortof

space-timethat is no longerentirelythe same asthatof practical ife (0, 1:1391), to geometricfigures, beings half-concrete and half-abstract (0, 2:111), to works of music, which

Valery's Socrates surprises his disciples by

likeningin this respectto works of architecture.The most important category of human

oeuvre for Valery is, of course, the literaryaesthetic object, which shows the same onticattributes as other human products-quasi-phenomenalqualitiesand existence in a closedworldpartlyresemblingour own. For instance,in the 1927 lecture, Propos sur la poesie,Valery describes what he calls the poeticstate like this: the poetic state, or emotion,seems to me to consist in an emergingpercep-tion, in a tendency to perceive a world, or

complete system of relations, in which beings,things, events, andacts, even if they resemble,one for one, those that populateand make upthe sensible world, the immediate world fromwhich they are borrowed, find themselvesnonetheless in an indefinable,but marvelouslytrue juste]relation o themodes and laws of ourown generalsensibility (0, 1:1363).

Humanobjectsall occupy, at least in part,anexistential locus that looks very much like theworldof nature,and thus they mimic the ontic

status of concrete objects in that world. Thenatureof the artistic space varies with eachof the artforms, butValeryis always emphaticabout distinguishingthe two spaces. And theelement that serves to set the quasi-phenomenalspace of human objects apart from that ofnaturalobjects is that humanobjects conformnot to the laws of causalitybut to the modesand laws of our generalsensibility. Thus the

where of humanobjects is a consequenceofthe what, as we will see in a moment, sincethe inneressence of such

objectsis

exactlythe

thing that determines the existential locus inwhich they dwell.

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CASSEDY

III. What AestheticObjectsAre:Mathemat-ical GroupsandCreativeIntention

The factor that Valery always mentions as

distinguishingbetween humanobjectsand natu-ral objects is the lawful qualityof the human:the geometricfigurethatexists in obedience tothe relational ntentionof its creator,the dancethat exists as an expression of the dancer's

figuralimagination, he intelligible spaceofmusic that is filled with forms and laws of the

composer'sdesigning. It is not surprising hat

Valery'sinterest n mathematicsed him, often

with results that cast doubt on his own serious-

ness, to seek parallelsbetween the relationalandlawfulqualitiesof humanartistic ntentions

anda varietyof principles romalgebra hathad

caughthis fancy.Val6ry's obsession with mathematics and

specificallywithalgebra s well knownand well

documented,as a glance at almostany page ofhis Cahierswill show. Mathematicalprinciplesfind their way into the most diverse fields of

investigationfor Valery. Among these is art,

particularly oetry.Writing,forexample, is a

sort of calculation (0, 2:1515), and Valerydreamsof arriving at the executionof a work

by means of formal conditionsthat have been

accumulated like functional equations (C,28:468 [1:314]).

Valerycomes to envision thecompositionof

any artworkas consisting in a process where acollection of objects or elements is assignedafunctionalrule that defines the orientationofthose elements relative to one another. Butwhen Valery speaks of collections of objectsunited by a relationalprinciplehe has some-

thing specific in mind. His interestin contem-porarymathematicshad early led him to the

concept of the mathematicalgroup, a conceptthat at least one authorityhas called the most

prominent n nineteenth-century ighermathe-matics.8

The vocabularyof group mathematicsap-pears n the Cahiers andValery'sothertheoreti-

cal writings with amazing frequency, and for

this reason it is worthwhileto define some of

the termshe uses. A group, inthemathematical

sense, is any set of elements subject to a

combinatoryoperationsuch that the productof any two elements, that is the result of

combininganytwo elements of thesetunder he

operationin question, will always be anothermemberof the group.Threeadditionalproper-ties must hold: 1) there must be an identityelement which, when combinedwith any ele-ment in the groupunder the operation n ques-tion, leaves that element unchanged;2) theremust be an inverse which, when combinedwith

anyelement,yields the identityelement;and3)there must be an associative principle, in ac-cordance with which the productof three ormore elements is the same regardlessof theorderin which they arecombined.

One exampleof a mathematical roupis the

(infinite)set of all integerswith multiplication

as the combinatoryoperation.It is easy to seethat this set satisfies all the requirementsof a

group: heproductof anytwo integers s alwaysanother integer; there is an identity element,

namely1, since foranyintegera, I x a = a; theinverse is the process of division, since anyinteger divided by itself yields the identityelement, 1;and the associativeprincipleholds,since any numberof integerscan be multipliedin any order and still yield the same result.

The specifics of this technical definition areless important han its underlying conceptionand its possible ramifications.The four funda-mental propertiesof the group-the inverse,

identity, and associative properties, and the

requirementhat the combinatoryoperational-

ways yield a memberof the set-give thegroupclosure, that is, they make it a set of elementsthat is entirely self-sufficient and, one mightalmost say, self-referential.Thus the underly-ing conceptionis of a closed, boundedcollec-tionof elements, where it is not the elements inand forthemselves thatareimportant,but rather

thefunctionalprincipledefiningtheirrelation oone another. This is essentiallythe notion of a

system,butwith therequirementhatthesystembe self-contained, closed on itself. The ele-ments that constitute a group may be almost

anything,as can the relationaloperation:a setof objects whose relative spatial positions are

subjectto variousdeterminedpermutations,he

pieces in a chess game, a set of algebraicequations,and so on.

Group theorywas discoveredby the FrenchmathematicianEvaristeGalois (1811-1832) in

1829.9 Valerywas introduced o the subjectin1893 by his friend Pierre Feline.10 He learned

80









thetechnicalspecificsof grouptheoryprimarilyfrom the writings of Felix Klein, one of themostrenownedmathematicians f the latenine-teenth and

earlytwentieth centuries. One

shouldby no meanspresumethat, in followingthis branch of algebra, Valery was merelydabblingin a capriciouslychosen, arcanefieldof knowledge. Even if Valerylacked the exper-tise of a truemathematician ndoftenappears obe little more than an enthusiasticdilettante nhis mathematical peculations,he did have thesense to recognize the real implicationsof his

pet subject. For group theory was only onemanifestationof a trend n moder thinking hat

arguablypenetratesto the very foundationsof

early twentieth-centuryphilosophy of scienceand mathematics.It also anticipates,even pre-pares, such fields as modem structuralism nd

systems theory.Groups, sets, structures, systems of rela-

tions, closed systems, closed worlds are all

concepts and images that arise in this trend.

Valeryadopted he principlesof this trendearlyin his adult life, complete with the specializedterminologyof group theory,andbuilt a world-view on it that shows all the unguardedconfi-dence and extravaganceof true fanaticism. A

passagethatValerywrotelater(presumablyat amore skeptical age) describesthe credo of the

young relationalist:

Therewas a time when I saw.

I saw, or wished to see, figures of relationsbetween

things, and not things themselves.

Thingsmade me smile frompity. Those who preoccu-

piedthemselves with them were for me

nothingmore

than idolaters. I knew that the essential thing was

figure.

( Propos me concernant, O, 2:1532)

Truth, in this conception, is to be sought in

figures, systems of relations between ele-ments, which are without significance in andfor themselves. But if the systems view is the

key to truth n general, it is also the factorthat

distinguishesbetweenaestheticobjectsandnat-ural objects. The vocabulary of groups andclosed relationalsystems arises with insistent

frequency in Valery's discussions of artworksof all types. Inone placehe writesaboutpoetry,

saying that the world of the poem is essen-

tiallyclosed andcompleteuntoitself, being the

pure system of the ornamentsand the possibil-ities of

language (0, 1:770). Dance,he writes

elsewhere, is thesystemformedby thedancer'sacts (0, 1:1398, 1:1330). And at one point heconceives a project for an ideal book (verymuch like the semi-mystical Livre Mallarmehaddreamedof making)thatwould be defined

puzzlinglyas an infinitelytransformablemathe-matical set subject to combinatory operations(O, 2:1483).12

What,then, is thedifferencebetweennatural

objectsandaestheticobjects?Ina marginalnoteto the Introduction o the Methodof Leonardo

da Vinci, Valeryhad spokenof the capacityofgreat men to discover relations among thingsthattherestof us don't knowhow to transposeor translate nto the system of the complete setof ouracts (O, 1:1160), implyingthatif, as hehad suggested elsewhere, truth in nature con-sists in systems of relations, it is not becausesuch systems objectively exist in nature. It isratherbecause truth s imposedby a larger-than-life intelligencelike Leonardo's.Thussystems,strictlyspeaking,are not inherent n natureor innaturalobjects. But in aesthetic

objectsthe

system is objectively inherent, and for the

simple reason that the artist, and not just a

spectatorendowed with a Leonardian ntelli-

gence, puts it there. The system is the sign ofthe humanintention n aestheticobjects. If the

universe of poetry is experienced as a

tendency to perceive a world, or completesystemof relations (O, 1:1363)in a poem, thisis differentfrom the complete system of rela-tions that a Leonardosees in the naturalworld

(by imposing it on that world), because the

objects in the poetic world are alreadyalignedwith the modes and laws of our own generalsensibility (ibid.).

Oursensibility.This is important,because itshows once againthatthe lawfulnessof human

products,this indwellingessence or value that

Valery speaks of as distinguishingart objectsfromordinaryobjects, has its ultimatesource inthe humansensibility. Thus the ontic place ofhumanandaestheticobjectsdiffers fromthat ofnaturalobjects as the determinantsof the twoclasses of

objectsdiffer. Natural

objectsare

ultimately determinedby the causal laws ofnature. So are certain human objects, like

81








CASSEDY

works of sculpture and architecture. But allhumanobjectsare also determinedby laws and

relationsbornin the spiritof theircreator,andthe sign of this is the relationalsystem.

IV. The Sourceof the AestheticObject:SystemandGeometricTransformation

The inherence in art objects of a kind of

intention in the formof a systemof relations

born in the modes and laws of our general

sensibility also suggests that there is a conti-

nuitybetween artobjects and the creativesen-

sibility, thatartobjects may be conceived of as

extensions, or projections, of the systematic

(human) organization that produced them.Valeryexplicitly proposesthis view in a num-ber of placeswherehe treats he aestheticobjectas an act or as identicalto the creative act

thatbrought t intobeing. A workof the spiritexists only in act (0, 1:349), he says in one

place. Works of the spirit, poems or others,relateonly to whatengenderswhatengenderedthese worksthemselves,and to absolutelynoth-

ing else (0, 1:1350).If there is continuitybetweenhumanobjects

and theirsource in creativeacts of the mindor

self, then it is not surprisingto find that thissource sharesthe relationalcharacteristicshat

inhere n its products.Partof Valery's youthfulfascinationwith algebrawas his either naive or

disingenuous faith in the possibilities of the

group and system model for psychology. The

Cahiers contain literallyhundredsof passageswhere Valery proposes the analogy between

grouptheoryand the workingsof the mind or

self:'3 Man is a systemthattransformstself

(C, 2:896); every act of comprehensionis

based on a group (C, 1:331);any given ideais most certainlyderived from a system that

comprisesalso thesubsequentdeas,rather han

being the originor cause of them (C, 7:365).The mindor self is repeatedly eenas a bounded

relational set of constituent elements, where

these elements are understoodvaguely as the

factorsmakingup an individual'spersonality.

Valery, in his momentsof mathematical er-

vor, rarelyappears o be botheredby the obvi-

ous limitations of a model that simplisticallyreduces the psychic life to a finite set of

elements bound togetherby a functionalrule.One limitationdid bother him, however, and

this he addressedby sophisticating he mathe-matics an additionalstep. Groupsandsystems,taken by themselves, are static concepts, ade-

quateperhaps o describing he mindat a singleinstant,but incapableof conveying the notionof the progressof the mind throughtime. The

problem was to find a dynamic mathematicalmodelthat would bothrepresent he humanegoas a relationalsystem in time and contain aelement of constancyor continuityin order to

representthe integrityof personalitythroughtime.

Valeryfoundjust what he was looking for inan offshoot of group mathematics,the projec-tive geometryof Felix Klein. The key concepts

are transformationgroups and invariants. Atransformations a one-to-one mapping ofthe elements of one set ontoanother hrough he

application of a functional rule. It can bedescribedmathematicallyike this:take a givenset S and call the transformation of that setS'. If we designate any elementof the originalset S as x, and any elementof the transformedset S' asy, then foreveryelementy thereis oneandonlyone elementx suchthaty = f (x), where

f is the functiondefining he transformation.Now a transformationroupis a boundedset

of elements where those elements, instead ofbeing numbersor objects, are transformationsof the type just described,and where the same

principlesof closure hold as for an ordinarygroup.A commonapplicationof transformation

group theory, and the one that seems to havebeen most familiar to Valery, is to be found in

projectivegeometry. Projectivegeometryin its

simplestsense is the branchof mathematicshat

investigatesthe transformations line or planefigure undergoes when it is projected or

mapped onto a new planeor line, as if froma point of illuminationnot lying in either the

originalfigureor theprojected igure.Transfor-

mations, however, need not be conceivable

literally as projections. They are simply anyalterationbrought about by a change in theorientationof the original figure relative to a

second plane. One of the tasks of projective

geometryis thus to discover the mathematical

functions thatdescribesuch transformations.A

set of transformationsn this field is referred o

as a space, andaninvariant s defined as any

property or functional relation that is notchanged by the transformation.

82









The obvious analogy for Valeryconsists in

viewing the life of the mindas a progressionof

groupsof elements that merge into each other

through the application of a transformationfunctionand where the principleof constancybindingall the groups together(which, to pur-sue the psychological analogy, would corre-

spondto the identityof the self through ime) isa sort of invariant. As early as 1900 an

enrapturedValeryexclaimsthat psychology isa theory of transformations,where one mustdiscover the invariantsand the groups, that is,figures and distances, in order to establishthe

psychologicalspace (C, 1:915).All thetermi-

nology of groupmathematics s here, including

the word space, which is used in a dualsense: as the geometric applicationof the math-ematical notion of set and, in the moreabstractsense, as the locus of consciousness.

Valery'sCahiers, especially the early ones,are full of similarmathematicalormulationsofthe dynamicprocessof consciousness. Psycho-logical life, he says, is the transformation fdata or their mapping [substitution] (C,10:517). The Self is invariant,origin, locus or

field, it is a functional property of con-sciousness (C, 15:170[2:315]). The element

of existence-consciousness is invariant withrespect to all the transformations C, 11:243

[2:307]).14

How does the aesthetic object come into

being from this source?The obvious responsewould be to envision the act of genesis as a

geometrictransformation f the ego, a projec-tive mappingof the system of the mind ontoanother space, namelythat of art, wherethe

ego, orwhatValerycalls the Moi pur, wouldbe the invariant, ust as it is in the mind itself.

Manystatementsby Valery eadto the possibil-ity of such a view. In a numberof cases where

Valerydescribestheprocessof coming-to-beofhumanoeuvres the vocabularyof transforma-tionandgrouptheorycropsup. Forinstance,ina passage on writing as calculation, Valeryspeaksof the domain of literature as consist-

ing in a certain mode of combinatoryworkand goes on to say that this work consists oftransformations 0, 2:1515). Nothing in the

passage explicitly indicatesthat Valeryunder-stands transformation n a specialized mathe-

maticalsense. But the context is clearly math-ematical (he is speaking of problems,

operations,combinatorywork),and, moreover,Valeryuses the word in the plural, suggestingseparateacts or operationsof transformation.

Geometry,a field ofactivity

whoseproductsare analogous to those of artistic creation, is

the machine of the spirit made visible, the

very architecture of the intelligence fullysketchedout-the temple erected to Space bythe word (0, 1:1013). How does the machineof the spiritbecome externalized?The geome-triciangenerateshis geometricfiguresin such a

way that nothingis left of thoughtbut its pureacts, by which, beforeits veryeyes, it changesand transformsitself into itself. In short, itextracts rom its own shadowsthewhole pattern

[jeu] of its own operations (0, 2:111). Themindthusappears o be performing ransforma-tion operations,butwith results(products) hatare actuallyexternalto it.

Music, too, suggestsa transformationmodel:in a passage on music in Eupalinos, Valeryincludes all the standard erms, from substitu-tion(orprojectivemapping),to space (orthe setof transformationsn geometry),to transforma-tion itself: Did it not seem to you that an

intelligibleandchanging space was being sub-stitutedfor the originalspace . . . ? Did younot find yourself living in a mobileedifice thatis continuallyrenewedandreconstructednsideitself, dedicatedentirelyto the transformationsof a soul thatcould be seen as the soul of spatialextension? (0, 2:102; my emphasis). And

poetryis describedat one point in the Cahiersas the study(moreconscious)of verbaltrans-

[formations] that conserve their initial

impulses (C, 9:924 [2:1015]), a passage thatshows at once the notion of creationas trans-formation and the notion of constancy (or

invariance) hroughtransformation.Even where Valery is not explicit on thetechnical aspects of transformation heory as

applied o thecreativeact, the important ointisunmistakable:namely, that, just as the humanmind is continuouswith itself (andhereValeryrepeatedly nsists on the transformationmodel),it is also continuouswith, but not identicalto,its own works, and this includesthings like

geometric iguresas well as aestheticobjects. Infact, this subject raises what might at first

appearto be a problemfor Valery'stheory

ofthe aestheticobject and its ontic status, for his

writingsshow two apparently ontradictorypo-

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sitions: one that asserts the autonomyof theartworkwith respectto the moi of its creator,and one that asserts a limited degree of conti-

nuitybetween the artworkand the moi.

Ned Bastet has writtenaboutthis dual statusof the Valeryanoeuvre in an article entitled

Oeuvre ouverte et oeuvre fermee chez

Valery. '15 astet sees twodivergent endenciesin Valery's thinkingon this subjectat variousmomentsof his career.The first is to regard he

oeuvre as an open-ended, accidental, unfin-ished structure,the productof an act of the

esprit, where the esprit is seen in a closed stateof perfection and all its productsare merelycontinuous with it. The second is to follow

Mallarm6 n regarding he oeuvre as a closed,autotelic structurethat has primacy over the

esprit.It is certainlytrue, as Bastetpointsout, that

in passageswhereValeryassertsthe continuityof the work with the creative source he often

emphasizestheunfinished,accidentalqualityof

the product, claiming that the product is not

nearly so importantas the system of acts that

produced t. The book-the writtenwork-isfor me an accident-the factitious limit of a

process of mental development (C, 14:704

[1:269]). The practice of writing arduouspoetry has accustomedme to considerall dis-

course and all writingas a state in a labor that

can almost always be resumed and modified*.... A work [oeuvre] is never necessarily

finished, since he who made it has never

fulfilled himself (C, 8:7733 [2:1011]).But the divergence is not necessarily so

markedas Bastet makes it out to be. For one

thing, it should be pointed out (and Bastet

certainly says nothing to contradictthis) that

when Valery asserts the autonomyof the art-work with respectto its creator,his concernis

usuallyto separate he oeuvre from the histori-cal person who creates it andnot from the moiof thatperson. WhatValeryreallyhas in mind

is to take a stanceagainstan expressivepoeticsthatallows thereader o reasonfromthework to

the social personalityof its creator. One must

never draw from the work [oeuvre] inferences

about a man-but ratherreasonfrom the work

to a mask-and fromthe maskto the machine

(C, 4:405 [2:1155]), Valery says, using his

favorite metaphor( machine ) for a system.The point here is not so much to make an

absoluteclaim for the autonomyof the aesthetic

object as to separatethe poet's creative mindfrom the poet seen as an individual in his

entirety.There are other passagesthat do not fit into

either of Bastet's categories. These passagesshow the aestheticobject in a dual status: bothcontinuous with the moi and havingundergonea change of state. For a work [oeuvre] is nomore than a sort of relation between us andourself establishedby means of the apparatuscreatedor utilizedby a thirdparty.It is no morethan an order mposedon elementsof ourself,a

machineryfor transporting ourself from onestate to another (C, 11:712[2:1203]). .

I always feel between the book and me,-between the work and true time, a 'change of

state,' (C, 15:511 [1:272]).The point is that both of Bastet's conditions

are presentin Valery's conceptionof the aes-theticobject. But this is preciselythe reason forthe unity in the aesthetic transaction. Thesourceof the aestheticobject must, of course,be understood not as the poet, but as thecreative mind, or machine, as Valery callsit. This creativemind must be envisioned as a

self-transformingrelationalgroup that shows

constancythrough imein aninvariantunction.As this source is continuous,or invariant,with

respectto itself, so it is invariantwithrespecttoits product, the aesthetic object, because this

product, like its source, is a relationalgroupthatappearsas a projectionof its source. It isthus continuouswith that source but not identi-cal to it.

It is clearlydifficult to take Valery'smathe-matical fantasies seriously in and for them-selves. But even if we do notaccept literallythe

mathematicalheoryof the self and mental lifewe muststill recognizeits value as a model fortheaesthetic transaction and forthe status ofthe aesthetic object. The aesthetic object for

Valery is not somethingthat at times appearsindependent rom its sourceand at other times

appearscontinuouswith its source. It simplyhas a dual status in general, because both

conditions are present.The notion of transfor-

mation or geometricprojectionillustratesthis

perfectly.Justas theprojected mageof a given

geometric figure on a new space is an object

distinctfromitsoriginalbutstilldependenton itand continuouswith it, so for Valerythe aes-

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theticobject bears the imprintof its source (inthe form of a relational system) while still

existing as an independentthing. And if, to

pursuethe analogy, the source is a relational

system, thentheproductwill also be a relational

system or group. This, too, suits Valery'spurpose,since the primarydistinctionbetweenhumanproductsandnaturalobjects is the pres-ence in the former of a lawful intentionandsince the clearestsymbol of such an intention,the one, that is, that appearsto present itselfmost readily to Valery's mind, is a relational

system.The dual status of the artwork,that strange

hesitation it shows between self-referentiality

on the one hand and continuitywith its sourceon the other, is what ultimatelysaves Valery'saestheticsfrom the status of pureformalismtowhich Wellek and others relegate it. At the

beginning of this essay I mentioned GerardGenette's claim that Valery's aesthetic theoryshows importantaffinities with bothformalismand structuralism. do not mean to refutethisclaim absolutely.The idea of system, the movetowardsobjectivity,the underlying cientificityare all therein Valeryas they are in formalismand structuralism.But an

importantdifference

remainsfor Valery, and that is the surviving,projectedpresenceof thehumancreativesourcein theaestheticobject.Nordo I mean to suggestthat formalism and structuralismabsolutelydeny the presence of such an element. It is

largelya questionof emphasis. But for Valerythe sourceof anaestheticobject is decidedlyan

integralpartof its ontic status. It haseverythingto do with its essence andthuseverything o dowith its very state of being. Humanthings are

always products,and

theyare

always productsof something.This is why the space of human

things-whether we are speaking of a cathe-

dral,a dance, a polygon, or a poem-is alwaysdifferentfrom that of natural hings.

Perhapsthe true reason for the differencebetween Valery's aesthetics and any kind ofstrict ormalism sjust thisconcernwithessenceand space. The underlying question for

Valery is and remainsontological, and this isa majorreason for his modernityas a thinker:a modernity,that is, that takes a slightly dif-ferent direction from that of formalism andstructuralism.

GerardGenette, La litteraturecomme telle, inFigures (Paris, 1966), p. 253-65.

2 Rene Wellek, Four Critics: Croce, Valery,Lukacs,and Ingarden(Universityof WashingtonPress, 1981), p.vii.

3 Wellek, p. 19.4 Wellek, The Mode of Existence of a Literary

Work, SouthernReview7 (1942): 735-54, later incorpo-rated in almost identical form as a chapterin Wellek andWarren,Theoryof Literature New York, 1949).

5 PaulValery, Oeuvres(Paris, 1957-1960), 2:115-20.This edition will be cited in the text as O. All translationsare mine.

6 The examples of Warhol's Brillo boxes andDuchamp'surinalare favoritesin the institutionalor con-textual theories of American aestheticians like GeorgeDickie andArthurC. Danto. See, forexample, Dickie, Artand the Aesthetic:An InstitutionalAnalysis (Cornell Uni-

versity Press, 1974), Chapter1,What is Art?:

An Insti-tutionalAnalysis ; and Danto, The Transfiguration f the

Commonplace:A Philosophy of Art (HarvardUniversityPress, 1981),Chapter , AestheticsandtheWorkof Art.

7 Paul Valery, Cahiers in 29 volumes (Paris,1957-1961),20:383. Thiseditionwill be cited in the text asC. Where passages occur in both this edition and thetwo-volume Cahiers edited by Judith Robinson (Paris,1973-1974), the C.N.R.S. edition will be cited first, fol-lowed by the Robinsoneditionin squarebrackets,thus:(C,9:924 [2:10151).

8 See HermannWeyl, Philosophyof MathematicsandNaturalScience (PrincetonUniversityPress, 1949), p. 28.

9 For a fascinatingaccountof the discovery of grouptheoryand an

equally fascinatingannihilationof the 150-

year old accepted account of that discovery, see TonyRothman, The ShortLife of EvaristeGalois, ScientificAmerican246 no. 4 (April, 1982): 136-49.

'0 See Reino Virtanen, Paul Valery'sScientific Edu-cation, Symposium27 (1973): 362-78.

' Fortheconnectionwithstructuralism,ee Piaget,LeStructuralisme Paris, 1968), Chapter2: Les structures

math6matiqueset logiques. Ernst Cassirer has arguedpersuasivelyin a numberof places that the moder scien-tific outlook is dominatedby the same principlesthat arefundamentalo grouptheory,namelythe conceptionof thebounded system and the location of objective truth inrelationsrather hanthings. See, forexample, ThePhiloso-phy of SymbolicForms, Volume3: The

PhenomenologyofKnowledge,trans.RalphManheim(Yale UniversityPress,1957), Part3, Chapter4, The Objectof Mathematics,pp. 357-405; The Problemof Formand the Problem of

Causality, in TheLogicof theHumanities,trans.ClarenceSmithHowe (YaleUniversityPress, 1960), pp.159-81;and

The Concept of Groupand the Theory of Perception,Philosophy and Phenomenological Research 5 no. 1(1944): 1-36.

12 Citedin JeannineJallat, Valeryet le m6canisme-la notionde modele et la theoriede la construction, Saggie Ricerchedi LetteraturaFrancese 8 (1967): 226-27.

13 The applicationof the notion of groupto the ego in

Valeryhas been amplydocumentedby JudithRobinsonin

L'Analvse, Chapter 3, Vers une mathematique de1'esprit ;andby Nicole Celeyrette-Pietri,Valervet le moi:des Cahiers a l'oeuvre (Paris, 1979), Chapter1, section 2,

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Les images mathematiques u moi. these andrelatedconcepts.14 See Celeyrette-Pietri,pp. 10-26, La theorie de '1 Annales de la Faculte des Lettres et Sciences

soi-meme et l'algebre du moi, for a full discussion of Humainesde Nice 2 (1967): 103-19.

art - paul valery, modernist aesthetic object

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