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1 SYNTHETIC NUMBER: THE STRUCTURALIST CONFRONTATION OF JEAN -PAUL SARTRES CRITIQUE OF DIALECTICAL REASON By BRANDON J. CARR A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF TH E REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS UNIVERSITY OF FLORIDA 2009
2 2009 Brandon J. Carr
3 To my Mom, Grandfather, and Steven
4 ACKNOWLEDGMENTS I would first like to acknowledge the mentorship of my professors at the University of Florida. Philip Wegners introduction to the work of Fredric Jameson and Algirdas Greimas allowed me to generate an optic that I cannot help but take advantage of in the conception of my writing and almost daily in my instruction as a teacher. John Leaveys introduction to the history of the university from the German-model to contemporary considerations of disciplinarity has proven to be an ever expanding incitement to broaden the comparative scope of my investigatio ns. I would also like to acknowledge the continued mentorship from my undergraduate professors at Kent State University. Kevin Floyds introduction to the work of Samuel Delany provided by proxy an introduction to the work of Denise Schmandt Besserat. P amela Takayoshi and Christina Haas have so generously continued to provide a productive forum for considering writing practice. And, the early encouragement from Florence Dore and her introduction to critical theory are no doubt responsible for my choice to pursue graduate study. I must also acknowledge my early exposure to political work at Kent State University. The invitation to agonistic discourse and the patient challenge of my comrades to take responsibility for my positions combined with political work itself are entirely responsible for my search for the Critique before I even knew it existed. Finally, my graduate study would not be possible without the compassion and support of my partner Steven Turner.
5 TABLE OF CONTENTS ACKNOWLEDGMENTS .................................................................................................................... 4 page ABSTRACT .......................................................................................................................................... 6 CHAPTER 1 INTRODUCTION ......................................................................................................................... 7 The Goal of this Work .................................................................................................................. 7 Dialectical Nominalism as Intelligibility ..................................................................................... 8 The Savage Mind and the Critique ............................................................................................. 10 2 INTELLIGIBILITY AS THE NEGATION OF MULTIPLICITY ......................................... 12 The Geometrical Proof ................................................................................................................ 12 S upply and Demand Equalization .............................................................................................. 13 Precious Metal Accumulation in Seventeenth -Century Spain ................................................. 15 3 INTELLIGIBILITY AS THE NEGATION O F NEGATED MULTIPLICITY ..................... 18 The Recalcitrance of Matter ....................................................................................................... 18 The Intelligibility of Cardinality: Neolithic Reckoning Technologies .................................... 21 The Hidden Ordinalism of Cardinals ......................................................................................... 23 4 CONCLUSION ........................................................................................................................... 28 LIST OF R EFERENCES ................................................................................................................... 31 BIOGRAPHICAL SKETCH ............................................................................................................. 32
6 Abstract of Thesis Presented to the Graduate School o f the University of Florida in Partial Fulfi llment of the Requirements for the Degree of Master of Arts SYNTHETIC NUMBER: THE STRUCTURALIST CONFRONTATION OF JEAN -PAUL SARTRES CRITIQUE OF DIALECTICAL REASON By Brandon J. Carr May 2009 Chair: Philip Wegner Major: English This paper will present a reading of the Critique of Dialectical Reason and explicate the role of the structuralist confrontation of the Critique. Specifically I will argue that in presenting a form of dialectical nominalism, the Critique must posit a provisional totalization of structuralism. In doing so, and presenting an alternate example of this totalization, Sartres Critique rediscovers the inversion of its project in the elaboration of synthetic number
7 CHAPTER 1 INTRODUCTION The Goal of this Work Jean -Paul Sartres Cr itique of Dialectical Reason: Volume One, published in 1960 entered into polemic with what it identified as a Marxist scholasticism, namely the closure of dialectical to analytical reason. The Critique ostensibly identified Pierre Naville as the main pr oponent of this trend in France. That many scholars, including Fredric Jameson and Francois Dosse now identify the publication of the Critique as a turning point in the hegemony of Structuralist discourses, however, suggests that Sartres presentation of Lvi -Strausss work conveyed a more fundamental criticism.1 Indeed, in the Critique Sartre specifically addresses the question of numerical structuration in the work of Lvi -Strauss, and Lvi Strausss reply in his 1962 T he Savage Mind initiated a conversation that would be taken up sporadically by both over the decade that followed. In a 1966 interview originally published in lArc Sartre discussed his objections to structuralism at length and, using Foucault as an example, described The Order of Things as an A concise objection to Sartres project appeared in 1954, when Jacques Lacan summarized Sartres position as the belief that if there is a plurality in this world of imaginary inter -relations, t his plurality is not enumerable, insofar as each of the subjects is by definition the unique centre of reference (224). Lacan warned his students that, Sartre does not perceive that the intersubjective field cannot but open on to a numerical structurati on, on to the three, the four, which are our bench-marks in the analytic experience (224). 1 See Fredric Jamesons f oreword to the Critique (xiii) and Francois Dosses The Eclipse of a Star: Jean Paul Sartre in History of Structuralism Volume One (3 9).
8 eclectic synthesis in which Robbe Grillet, structuralism[,] linguistics, Lacan and Tel Quel are systematically utilized to demonstrate the impossibility of historical knowledge ( Replies 110). This paper will pre sent a reading of the Critique of Dialectical Reason and explicate the role of what might generally be understood as the structuralist confrontation with the Critique An operating definition of the structuralist project, implied by Sartre, closely approx imates the inverse formulation of Sartres position, described by Lacan above. Structuralism presents the numeric structuration and unity of the social milieu. Just as the project of the Critique reserves the verification of historical knowledge to its s econd volume, the following paper will restrict its analysis to the synthetic totality implied by Sartres investigation of analytical reason. I will argue that the Critique in presenting a counter example of structuralism (negating structuralism) reenco unters the inertia adopted in its own investigation. Specifically, the Critique in attempting to forward a nominalism that represents the social milieu as a multiplicity of totalising individualities (37), produces the inversion of this project by pres enting the structural unity of seriality within the social milieu. The unity of seriality emerges as a numerical structuration and the inversion of Sartres act of negating structuralism. Since Sartre identifies these moments of an investigations invers ion as an investigations intelligibility, the structuralist confrontation of the Critique, I will argue, establishes an intelligibility of the Critique itself. Dialectical Nominalism as Intelligibility The investigation that was to comprise the two vol umes of the Critique of Dialectical Reason relied on two separate forms of narration outlined in a prefatory work as the regressive progressive method.2 2 Sartres regressive progressive method is described in detail in the prefatory work Search for a Method included i n the French edition of the Critique The distinction between the regressive and progressive moments corresponds to The only completed example of the regressive method is offered in the
9 first volume of the Critique published in 1960. The presupposition that "the dialectic, if it exists, can only be the totalisation of concrete totalisations effected by a multiplicity of totalising individualities" (37) begins Sartre's Critique and provides a preliminary definition for what he refers to as dialectical nominalism. In his criticism of the Critique in The Savage Mind, Lvi -Strauss argues that the sociological knowledge Sartre claims to discover is itself a part of an analytical investigation, and that what Sartre call s dialectical reason is only a reconstruction, by what he calls analytical reason, of hypothetical moves about which it is impossible to know (254). However, Sartre does not object to the use of analytical reason in a dialectical investigation. Instead, the Critique suggests that the explanatory power of an analytical investigation fails only in those moments when the analyst presents, as a unity, the external numeric relation of objects without simultaneously reconstructing the manifold reexteriorizatio n of the investigation's adopted structure within his results. Such a reconstruction would attempt to validate the necessary accompanying presupposition that the dialectic "always appears as necessity in the investigation which reveals it, nor is it vali d unless we apprehend it as the intelligibility of the process in question" (Critique 37). Intelligibility is therefore the rediscovery of an investigations adopted inertia in the material field and the apodictic fact that this inertia can be redis covered precisely because it has been effected materially within the field by the investigation itself. Intelligibility corresponds to what Sartre also refers to as the new the trace left by a totalising temporalisation on the absolute, inert dispe rsal which represents space ( Critique 63). In other words intelligibility is discovered as the trace effected by the negation of the negation. the evaluation, in the former, of the intelligibility of abstract categories of sociological knowledge. The progressive moment evaluates t he intelligibility of concrete historical knowledge.
10 Sartre includes historiographic narration (the deforestation by Chinese peasants, the accumulation of precio us medals in medieval Spain, and the French Revolution) to examine the intelligibility of the inert structure adopted and the terms extended. None of these narratives represent concrete analogs for the local historical movement in question. Instead, Sart re evaluates the intelligibility of inflation in seventeenth -century Spain insofar as inflation can be reconstructed through the accumulation of gold in Spain, and he evaluates the intelligibility of supply and demand equalization insofar as this equalizat ion can be reconstructed through considering the choices of presentation made by the economist. In each of these examples, Sartres investigation in the first volume of the Critique attempts to establish "the basis of the intelligibility of sociological K nowledge" (69). "The intelligibility of historical Knowledge" is reserved for a different type of reconstruction in the second volume of the Critique (69) The Savage Mind and the Critique Since the Critique solicits a specific rejoinder in the form of Th e Savage Mind, and this polemic with Lvi -Strauss continued for over a decade I will appeal to The Savage Mind for examples against which might be understood the type of investigation Sartre contrasts with a dialectical investigation in the Critique Alt hough Sartres understanding of structuralism as a unified project carried out in the discourse of his time may be glimpsed in hi s interviews, a complete totalization3 3 The term totalization is used throughout Sartres text to refer to practical, synthetic, and inert forms of unification and dispersal and the necessary copresence of each of these movements at each lev el of praxis. Specifically, Sartre explains that totalization attempts the most rigorous synthesis of the most differentiated multiplicity. Thus, by a double movement, multiplicity is multiplied to infinity [and] on this basis, it is easy to estab lish the intelligibility of dialectical Reason; it is the very movement of totalisation (46). of structuralism is never presented in the Critique It will therefore be the task of t his investigation as it attempts to understand the influence of this synthetic totality (structuralism) on Sartres initial project, to comparatively reconstruct the synthetic totalization of structuralism operating within the Critique And, just as the Critique takes up many
11 anthropological terms to enter into dialogue with a synthetic totalization of structuralism, Claude Lvi -Strauss in formulating his own response to the Critique allowed himself not without ulterior motive, to borrow a certain amou nt of Sartre's vocabulary" (245). While we will examine some specific examples of this later, it will suffice to say that we appeal to The Savage Mind not for a definitive example of analytical reason at work, but because Lvi -Strauss establishes an inte ntional dialogue with the Critique Lvi -Strauss s presentation of classification although presented after the publication of the Critique provides a depiction of totalization starkly in contrast with the operation of synthetic number described by Sartr e as seriality Additionally, the syntagmatic and associative attributes described by Lvi Strauss address the formal process of naming considered in my own reconstruction of an analytical investigation in the work of Sartres geometer and economist.
12 CH APTER 2 INTELLIGIBILITY AS T HE NEGATION OF MULTI PLICITY The Geometrical Proof The presentation of intelligibility to which Sartre will directly refer throughout the Critique appears in an extended footnote describing the establishment of a geometrical pro of (Critique 614). Sartre argues that a child intuitively understands that a line, entering the image of a circle on a blackboard, will emerge at another point on the circle. However, the analytical investigation of a geometer in establishing a mathemat ical proof destroys the sensible and qualitative unity of the circle -gestalt in favour of the inert divisibility of geometrical loci (Critique 62). In the act of presenting the circle and the line that bisects it, the geometer hypostatizes an ensemble of points necessary for the proof to be established. Sartre explains that if we take a point and baptise it centre; it is connected to a given line by a line segment baptised radius. Then one can prove that there is another point on the line which can be connected to the centre by a segment equal to the first ( Critique 62). Such a baptism, however, occludes the synthetic movement of the childs eye as it traces the line, establishes the enclosure of the form, and projects the infinite extension of the line so as to mark the points where the line enters and exits the form. The movement of enclosure and the movement of flight1 1 Sartre refers to the process, whereby an investigation discovers the insufficiency of its adopted inertia and the inversion of its goal, as an investigations line of flight (282, 650) and all future references to this process should therefore not be confused with the popularization of this phrase by Deleuze and Guattari two decades later. represented by the line that bisects the circle are both lost in the geometrical proof. More importantly, the point where the line exits the circle can only appear as the movement of the line itself ( Critique 62). In other words, if the search for a geometrical proof occludes the synthetic movement of enclosure and the synchronous projection of the line, the line of flight can not appear as anything but the
13 circles self -motivation, a motivation of the baptized center. Therefore, in representing enclosure as an extension of geometrical loci the intelligibility of the geometers investigation (its inverted praxis) is rediscovered as the baptism of center, the trace left by a totalising temporalisation on the absolute, inert dispersal which represents space ( Critique 63). The center is therefore revealed as a unification of multiplicity,2Supply and Demand Equalization and the investigation of intelligib ility carried out in the first volume of the Critique not only looks for the line of flight (the literal inversion of the investigations goal) but the accompanying trace that marks the synthetic act of enclosure (the negation of multiplicity). To extend Sartres brief allusion to the palisade, we might rephrase this process in anthropological terms and say that from the perspective of a group in danger, the possibility of an attack appears to an ensemble that has enclosed itself in a palisade as the quant itative measure of the space between its banisters and not from the very fact that the spatial definition of defeat has been materialized by the palisades construction ( Critique 63). In a discussion of the calculation of supply and demand, Sartre argues that the analytical investigation of the economist must present the equalization effected on the market as either the synthetic action of the market itself or the action of a population of individuals participating as either sellers or buyers ( Critique 28085). In defining the equalization of supply and demand the economist might simply say that the price of a commodity, given the competition of x number of sellers for y number of buyers, is the highest possible price a buyer is willing to pay for a commodity without the supply exceeding the demand or the lowest possible price a buyer is willing to pay for a commodity without the demand exceeding supply. However, the 2 The unification of multiplicity refers generally to the process of pr esenting as unified an ensemble of people or things. Within Sartres discussion of dialectical nominalism this multiplicity refers specifically to the ensemble of totalising individualities (37), the individual people participating individually in the s ocial milieu.
14 economists investigation, in attempting to define the equa lization of supply and demand by the interindividual determination of the price, without falling into the passive voice, would necessarily need to choose its subject. And, although Sartre suggests that the "apparent structure of the [social] milieu makes sociologists take it for a Gestalt which performs a synthetic action on its structures" ( Critique 279), the choice that must be made in naming the subject is equally precarious if the economist chooses to identify, in place of the gestalt market, an indistinct population of buyers or sellers. In the example Sartre provides, supply and demand equal each other, with 11,000 consumers equaling 11,000 sellers at the price of 6 francs. Only 8,500 sellers would be able to sell their product for the price of 5 francs, and the corresponding demand for the product at this price would increase to 12,250 buyers. This price point may therefore appear to be rendered untenable by the inability of 2,500 sellers to sell their commodity for 5 francs. If the econom ist chooses to identify this ensemble of 2,500 sellers as the subject of supply and demand equalization, this small ensemble, only a fraction of the total number of individuals (buyers and sellers) involved, appears as a group whose collective action has determined the relations between the other individuals involved. Sartre explains that these individuals are united by the fact that the juxtaposition of men is not that of sardines in a tin: sellers who carry out the same operation determine a social fi eld, simply because every operation, in addressing itself to the indistinct mass of buyers, projects a human future ( Critique 285). This unity is in fact a spatial and intentional disunity. The abstract sellers do not cooperate nor do they unite t o pursue a common project. Instead, each seller attempts to benefit from the buyers or sellers profit ( Critique 284). The multiplicity is in fact bound by alterity, and the future that each seller projects is a future profit obtained at the
15 expense of every other seller. However, the unity of the ensemble of 2,500 buyers presents itself as a material unity. The profit of these sellers is secured, not by their competition, but by their very inability to reduce their price to 5 francs. Sartre explai ns that, just as in the geometrical proof, the mathematical rigour of the object demonstrates precisely that it is the objective representation of a line of flight ( Critique 282). This means that the economist is able to name the subject of equalizatio n of supply and demand because such an identity has already been effected materially within the social milieu. The economist rediscovers his identification, as an apodictic fact of the phenomenon itself. This identification is made possible precisely b ecause the synthetic inertia of the investigation adopted is reexteriorized objectively as a part of the investigation itself. In other words, the investigation is only able to name the subject of the equalization of supply and demand because such an iden tity has already been produced within the social milieu by a multiplicity of individuals carrying out the same totalization in light of their projected future. The economists fate is therefore the fate of the seller who is not able to lower his price to 6 francs and the geometers fate in hypostatizing geometrical loci. The results of his investigation can only condemn him to live his investigation in passivity, as the inalterable inertia of the phenomenon in question. Precious Metal Accumulation in Seve nteenth-Century Spain In an extensive engagement with Fernand Braudels The Mediterranean and the Mediterranean World in the Age of Philip I Sartre explicates precious metal accumulation in the economy of sixteenthand seventeenth -century Spain ( Critique 16582). An economic investigation contemporary with the inflation that took place,3 3 This abstract economist is therefore not Braudel but the medieval economist, perhaps an official of the royal court, living within the phenomenon itself. after increased gold mining in
16 Peru and the introduction of new amalgamation processes, would necessarily attempt to extrapolate a natural law or function from the incre ase in gold production, imperial conquest, the direction of money exchange, and inflation. Such an investigation would therefore need to identify the object of the function, the gold itself. Some natural qualities of the gold play a role in the choice of this substance over others. Quantity is itself a quality of matter. However, a standardization of the measure of quantity and gold is necessary before quantity brings its form to bear as an inert quality of gold ( Critique 1689). Adopting a metaphor extended in Braudels work, Sartre argues that in order for a quantity to become an inert motive force in the exchange of gold, a vessel, a synthetic unity, is necessary for conceiving the outflow of gold ( Critique 168). At a given point it is possible, Sartre argues, to consider that this vessel is either matter in the form of boats and the material dimensions of the Spanish galleon transporting the gold from the Americas ( Critique 168). It is also possible to consider that this vessel is praxis in the form of social and labor organization, administrators, policemen, customs officials ( Critique 168). However, in reality, it is completely impossible to separate the first interpretation from the second ( Critique 168). Let us return to the previous example of supply and demand. The economists investigation of supply and demand equalization discovers the inertia adopted (the identification of the social milieu as a unity) within the material fact of being able to calculate supply and demand and pr edict the equalization taking place. This means two things. First, the identification of the social milieu as a unity carried out by the economist takes place after the same identification is made by the majority of individuals within the social milieu. Second, the calculation of supply and demand and the identification of the ensembles involved is only possible because these divisions and unifications have already been produced within the practical
17 field of the investigation. Sartre explains that In f act, in the collective, exigency really is in the object, because some men have put it there and others maintain it there on the basis of the entire historical process; and it really is inhuman, because inorganic matter, as the conducting medium, necessari ly inverts the structures of praxis. ( Critique 305) Returning to the concrete example of gold accumulation in Spain, Sartre explains that, in the importation process, the idea is gold revealing itself as a precious metal; but at the same time, it is ine rt; it is not an invention of the mind, but a petrification of action ( Critique 171). The accumulation of gold within a nation state had therefore designated Spain as a vessel within which gold could be measured and by means of which the measured gold be came a measure of Spains wealth as a whole ( Critique 173). Sartre explains that, what had to be stopped was the outflow of gold. This outflow through the Other became a spontaneous movement of matter as Other ( Critique 172). In other words, just as t he hypostatization of geometrical loci appears to the geometer as the self -motivation of the baptized center, the official adoption of a single quantitative measure of Spains wealth condemns each individual participating in the economy to live a function that inverts the goal of his praxis.4 4 This official adoption of a single quantitative measure acts as a negation of a mult iplicity of buyers and sellers. To negate multiplicity here refers simply to the process of representing as one unified body individuals participating individually within the social milieu. For indeed, if for him every new quantity increases his wealth, in the national community it devalues the unit; and thus individual wealth constantly deteriorates in the hands of the merchant or the industrialist, and his own increasing prosperity is partially responsible ( Critique 173). The outflow of gold, therefore, appears as the line of flight resulting from the simultaneous synthetic enclosure carried out by the measure of quantity.
18 CHAPTER 3 INTELLIGIBILITY AS THE NEGATION OF NEGATED MULTIPLICITY The Recalcitrance of Matter In the process of negating multiplicity in the investigations of the geometer and economist, the unity created occludes the fact that the synthetic process of enclosure and the process of projecting a specific future appear simultaneously. Having examined this process, we may begin to examine the intelligibility of Sartres own project of dialectical nominalism. Instead of presenting the unity of multiplicity as a hypostatization of cent er, Sartre has attempted to establish the intelligibility of analytical reason as the negation of multiplicity. In the investigations of the geometer and the economist discussed above Sartre has presented this negation of multiplicity as a process that pr esents the line of flight (the inversion of an investigations goal) as a self -motivated anti -praxis.1 In The Savage Mind Claude Lvi -Strauss argues against Sartres depiction of anti -praxis as In other words, the line of flight appears as the self -motivated activity of hypostatized objects or qualities. Sartre has suggested that the line of flight is actually the projection of a future coterminous with the synthetic movement of enclosure. However, in acknowledging that matter does indeed invert the structure of praxis Sartre must, as we will see, reintegrate this discovery into a larger exp lanation of the process of inversion. This reintegration appears as seriality or what I will refer to as the operation of synthetic number and its qualities. Insofar as analytical reason at all points appears as an implicit analog for structuralist disco urses, the following chapter will also examine Sartres own counter project of dialectical nominalism as a necessary negation of negated multiplicity. 1 I have chosen to use the term anti praxis to refer to the mom ent of praxis in which an investigation rediscovers its adopted inertia as the passive inertia of its object and in doing so perceives the resulting unintelligibility as a constant force preventing the success of the investigation. The Critique attempts to reveal that permanent anti praxis is a new and necessary moment of praxis (125).
19 a result of the hypostatization of an analytical investigation. Lvi Strauss explains that each system, in totemic classification is "defined with reference to two axes, one horizontal and one vertical, which correspond up to a point with Saussure's distinction bet ween syntagmatic and associative relations" (149). Although Lvi Strauss points out that these qualities interpenetrate, they nonetheless represent the types of definitions involved at one level of classification. It is through this process that an analytical investigation disassembles and reassembles different representations. The hypostatization of the social milieu as a collective is therefore only a temporary process, and Claude Lvi -Strauss explains that within a system of representation "the whole set thus constitutes a sort of conceptual apparatus which filters unity through multiplicity, multiplicity through unity, diversity through identity and identity through diversity" (153). However, even through this syntagmatic and associative assembly, di sassembly, and reassembly, the inertia involved does not limit a classificatory systems explanatory power but is explained as a positive function of the system itself. Instead of discovering a self -motivated anti -praxis, "the structure intelligible at th e start, in branching out reaches a sort of inertia or logical indifference it can thereafter undergo the effect of multiple and varied incidents which occur too late to prevent an attentive observer from identifying it and classing it in a genus" (1 60). For Sartre, on the other hand, inertia is precisely the closure of intelligibility insofar as this closure appears as the self -motivation of the discourse itself. Sartres analysis of the inversion of praxis as it becomes invested in matter extend s to discourse. In a general explication of the instrumentality of language and its limits Sartre explains that "these verbal structurations (practical schemata for constructing an indeterminate series of sentences) are characterized by an absolute refusa l to make a distinction at any level between the agent (or agents) as member of a series and the object as producing men as its products ( Critique 305). Sartre here makes a
20 distinction between encountering anti praxis in a social organization and encount ering anti praxis within matter itself. This distinction attempts to consider the dual quality of language as both instrumentalized and instrumental in praxis. Such a distinction necessarily represents both the negation of negated multiplicity (it negate s a structuralist unity) and the reexteriorization of the synthetic negativity (structuralism) interiorized. If it were not the goal of our investigation to examine this process within the dialectical nominalism of the Critique itself we might simply say that, in countering structuralism, Sartre must posit his own unity. In contrast to the syntagmatic and associative representations in which, according to Lvi Strauss, the savage mind recognizes physical and semantic properties simultaneously (268) an d a system of concepts [are] embedded in images (264), Sartre argues that if one wanted to incorporate this set of indications into a general theory for signs, one would have to say that the tool is a signifier and the man here is a signified ( Critique 161). For Sartre, signification is therefore not the combination of semantic and physiological properties in an abstract sign but the endowment of a function directly in matter and the compulsion for that function to be carried out. Lvi -Strauss, howeve r, identifies material signification differently. Specifically, Lvi Strauss addresses the argument made by A. H. Gardiner, that "the ultimate diversity of individual and collective beings [was] named only because they could not be signified" (172). Lvi Strauss questions Gardiner's analysis asking how could this quantified thought, to which, on the practical plane, we attributed the great discoveries of the neolithic revolution, have been both theoretically satisfying and effectively applied to th e concrete if the latter contained a residue of unintelligibility to which, in the last analysis, concreteness itself is reducible which is essentially recalcitrant to signification? (172) Although, both Lvi -Strauss and Sartre suggest that matter manifest s a direct signification, for Sartre the recalcitrance of matter is the appearance of anti -praxis by synthetic number
21 operating within what Lvi -Strauss refers to as quantified thought. Indeed we might even consider this process by examining a neolithic revolution that, while not contained within the Critique provides a particularly apt illustration, like the geometrical proof and Spanish inflation, of one aspect of synthetic number (cardinality) in signification. The Intelligibility of Cardinality: Neo lithic Reckoning Technologies That the archeological work of Denise Schmandt -Besserat and its implications for a Marxist basis for Derridas work in Of Grammatology are explored explicitly in the fictional appendix to Samuel Delanys The Tales of Neveryon (253) and implicitly throughout the text suggests the productivity of an illustration derived from her work. Her work not only provides a concrete example of the process of enclosure,2 Our investigation will restrict itself to Schmandt-Besserats argument that the different types of technologies used to count commodities (reckoning technologies) were each determined by a particular mode of counting (111). Her analysis presents three different modes of counting one -to -one correspondence, concrete counting, and abstract counting (111). Schmandt -Besserat suggests that one to one correspondence (a form of counting in which an object is added to a collec tion of objects representing the sum) and concrete counting (in which a specific inscription or object represents each individual number, including different bases for each type of commodity counted) both coexisted in the ancient near east before the but if a reconstruction of the historical knowledge she presents ever becomes possible (the recent devastation of the Iraq war suggests this will not be the case) her work would provide a historical example of the reexteriorization of scarcity in the simultaneous reification of commodity exchange and the invention of protocuneiform writing systems. 2 I here continue to use the term enclosure to refer to the unifying aspect of synthetic and practical totalization and as a means of separating in these instances any sim ultaneous connotation of dispersal.
22 devel opment of abstract counting, the use of a standard numeration system able to count different types of commodities without modification (112). Schmandt Besserat argues that a set of archeological data seems to confirm that one to -one correspondence and co ncrete counting preceded the use of abstract counting in Southwest Asia (114), and that between the periods of Uruk VI 3500 BCE, Uruk IVa 3100 BCE, and Uruk III 3000 BCE we see a transition between three forms of inscription (Schmandt -Besserat 121). In Uruk VI, simple one to -one correspondence appears with each token representing one specific commodity. At this stage the accountants of Uruk use clay envelopes to enclose the individual tokens into a sealed vessel and some of these envelopes contain impr essions or incisions of the tokens contained on the exterior of the envelope. The existence of this form of counting extends to 2600 BCE (Schmandt Besserat 125). However, in Uruk IVa a new form of inscription appears alongside the old form. In this form of inscription both an incision representing the commodity token and an impression of a token representing a numeral appear on the surface of the envelope. Envelopes containing the actual tokens also begin to disappear at this time and are replaced with clay tablets bearing only the incisions and impressions. In Uruk III an additional inscription appears on the tablets representing the abstract measure of vesselled commodities. In the example of oil that Schmandt Besserat provides, each of the three ins criptions stand for one, sila, of oil respectively (121). Schmandt -Besserat concludes from this final extension that once dissociated from any notion of number, the pictographs could evolve their own separate way (121). Schmandt Besserat sugges ts that because the simple one to one correspondence of Uruk VI implied object specificity in which each ideogram fused together the concepts of nature/quantity (i.e., measure of oil) and the number I (117), the extrication of number in the final extensi on of Uruk III
23 necessarily meant the progressive liberation of signification from number. However, from the Sartrean explication elaborated above we can only be troubled by this final extension. The appearance of sila as the quantitative measure of oil should at no point be confused with a concept of nature. The third inscription can be none other than the clay envelope itself, the synthetic movement of enclosure formerly a part of the physical envelopment of the counting tokens in clay as it is reexteriorized in the analytical procedure of the Uruk accountant. The synthetic consolidation of quantity (cardinality) in the act of writing omits the envelope all together, favoring the passivity of the clay tablets surface. We return to our discussion of the Critiques intelligibility by way, therefore, of affirming Lvi -Strausss question. Quantified thought is indeed productive. Its productivity is not unintelligible, nor does its material signification express recalcitrance. However, quantitative thought develops not through syntagmatic and associative extensions in discourse, but by thought taking on a specific inertia of the technology used. Far from recalcitrant, the inertia adopted is inextricable with the mode of production and contains all of its accompanying motive forces. The Hidden Ordinalism of Cardinals Sartres negation of negated multiplicity concerns this initial aspect of synthetic number (the unit of quantity or in other words cardinality) and the changes it undergoes in given inv estigations.3 3My investigation of seriality separates this phenomenon as a more complex process of the interiorization of number (synthetic number) and considers separately moments of cardinality and ordinality. The hypostatization of the unit of quantity, the baptism of sila, is partially the result of the transition, in daily exchange and production, from concrete counting to one -to -one correspondence or in other words the place of counting in t he mode of production. However, within the logic of the Critique this relationship between the unit of quantity and the mode of
24 production is only a prior conditioning and not an anti -praxis. This conditioning is important for reasons we will examine lat er, but before synthetic number can become self motivated within matter, it must first encounter a second praxis. It must encounter counting again. Sartre explains that although marginalism claims that the marginal unit that with the lowest use -valu e determines the value of all the others it is through the decomposition due to Gossens law, [that marginalism] impregnates the sum of marginal units with its unitary project ( Critique 177). Although Sartre does not specify which of Gossens laws he is referring to, from his previous discussion of the geometrical proof we can understand that the primary function of a proof makes this link of interiority [between commodities] commutative (Critique 177). This equalization facilitates a hidden ord inalism of cardinals ( Critique 177). In other words, insofar as the cardinalized unit, the sila of oil, is counted by an investigation that seeks to satisfy a need, or in this case to maximize a unit of labour time, the unit of quantity becomes a measure of the success or failure of production itself. Any sila of oil may be the last sila of oil produced in a given day. Therefore the quantitative unit must undergo another form of counting before becoming an anti -praxis. This form of counting is repres ented here abstractly by an economic investigation with the immediate goal of determining feasibility. The very determination of the proof reexteriorizes not only the measure of feasibility, but the possible measure of unfeasibility. Here the synthetic p rocess of enclosure represented by the ordinalism of cardinals is accompanied by the projection of a line of flight, the possible loss of profit. More importantly, although Sartre initially described his investigation as a dialectical nominalism that maintains the irreducibility of totalization as a multiplicity of totalising individualities ( Critique 37) he here presents a unity with the potential to bind each of these
25 individualities. The ordinalism of cardinals represents the final form of what I hav e referred to as synthetic number and what Sartre refers to as seriality. Transcending the Baptism of Centers Although the unity of scarcity depends on the interiorization of seriality, the use of analytical reason as a tool toward specific ends (the nega tion of scarcity) represents the reinvestment of anti praxis in an object. Sartre explains that under fire, the unit replaces dispersal with practical organization; it encloses its multiplicity in itself. But first the unity is counted; and before long it will count its wounded and its dead ( Critique 555). What Sartre describes as the serial numerical statute ( Critique 555) of this synthetic action represents the transition from the cardinal to the ordinal or in other words the way in which the observation of the quantity of wounded members of a regiment disclose to each member of the group their ordinal or ranked possibility for defending themselves against other known ensembles with which they may enter into conflict. This synthetic disclosure, inso far as it is taken as analytic disclosure, represents at the moment of its active negation the reexteriorization of a nonsynthetic numeric relation of failure, or the praxis of counting. Within these disclosures, the prior conditioning of cardinality by t he mode of production reappears within moments of danger as a Manichean ethic binding the group to the future of the material field. Insofar as the group begins to manifest a seriality similar to that of the collective from which it emerged, its very ling uistic incarnation may disclose the numerical statue of the group, the number and relation of its members. The Critique recognizes this inversion of the groups praxis as the inversion of its own project (dialectical nominalism). Sartre explains that bo th the dialectical structures and the synthetic movement which produces the opposition proceed from organic praxis and that multiplicity is a factor of dialectical intelligibility only insofar as it manifests itself as untranscendable inertia, that is to s ay, as the explosive exteriority of the interiorisation of number. ( Critique 555)
26 If we consider that the identification of the grammatical subject may be the incarnation of synthetic number, the group in -fusion avoids the interiorization of scarcity by a voiding the enunciation of the grammatical subject. The group -in -fusion avoids this enunciation by creating a multiplicity of centers that do not circulate like the coin, but are incarnated in the other in the very movement of the groups directives ( Crit ique 391). The imperative form to the Bastille, omits the pronoun or the we -subject as it moves throughout the ensemble. Unlike the declarative statement the imperative form marks the absolute limit in non -null subject languages in which a grammatica lly correct expression may not include a subject form. Therefore, if reciprocity replaces external bonds of alterity within a serial collective, within the group the bond of reciprocity is marked not by a transition from the IThey relationship to the We They, but by the refusal to interiorize the grammatical subject into the collective. Therefore, while the grammatical subject is the linguistic incarnation of number, the group itself insofar as it acts not out of fear or through a form of counting manife sted by that fear, will remain irreducible to the incarnation of number represented by the grammatical subject. Indeed this seems to be precisely the point Sartre makes just before his death in the controversial conversation with Benny Levy where he expli citly suggests the political power of a politic resembling Jewish messianism. Sartre explains that For the Jew the essential thing is that for several thousand years he has had a relationship with a single God. What is new is the kind of relationship this God entered into with men. It was an immediate relationship that the Jews had with what they used to call the Name, that is to say God. God speaks to the Jew, the Jew hears his word, and the reality to emerge from all this was a first metaphysical l ink of the Jew with the infinite. ( Hope Now, 104) Sartre argues that what is important is not the name itself, but the metaphysical character (Hope Now 105) engendered by the Jewish relationship to a single God. This relationship
27 necessitates the pro jection of a goal onto an anticipated future, a project maintained by the very injunction of the subjects linguistic enunciation or in other words the enunciation of the name of God.
28 CHAPTER 4 CONCLUSION In the preceding investigation I have examined t he Critiques implicit totalization of structuralism as an analytic process of negating multiplicity. The Critique exposes the intelligibility of the geometrical proof by examining the way in which the hypostatization of center occludes the synthetic move ment of enclosure and the projection of a future. The intelligibility of supply and demand equalization reveals anti -praxis as the recognition that an investigation has already been effected materially in the social milieu. The intelligibility of preciou s metal accumulation returns the process of synthetic enclosure to a historical analog and rediscovers the line of flight as an anti -praxis. Having established a provisional reconstruction of Sartres totalization of structuralism, I have attempted to sho w that the anti -praxis of an investigations adopted inertia is not a transhistorical recalcitrance of matter but a contingent process of synthetic number. This process of synthetic number, like the analyses of the geometer and the economist includes mome nts of synthetic enclosure. However, unlike these abstract analytical investigations the line of flight presented necessarily reflects a project that negates a synthetic negativity (scarcity). In examining the work of Denise Schmandt Besserat we revealed that cardinality is the product of the praxis of counting and intrinsic to both signification and the development of the mode of production. Finally, I have concluded by suggesting that it is this very connection with the mode of production that allows t he negation of scarcity to ordinalize cardinals, or in other words to constitute a seriality that connects group praxis to material antipraxis. In the process of negating the unification of multiplicity Sartres Critique has therefore manifested an inver sion of its stated goal (dialectical nominalism). However, the Critique
29 recognizes this inversion and suggests the prescriptive antidote, in the form of the groups possibility to hold up its refusal to name itself as the very mark of its engagement. Wh en the analytical investigation presents associative relationships scarcity insinuates itself as the contingent possibility that any enunciation may be last, or in other words that the last word spoken might be the verdict for the project as a whole. In t hese instances a discourse is endowed with the limits of its explanatory power, converts the positive potential for being rearticulated in a moment of praxis and is instead converted into the inert function of a discourse that extends its own possibilities This extension is not the resultant of narration itself. The closure of a discourse is the operation of synthetic number insofar as it appears contingently in moments of articulation as a quantitative measure occluding the movement of enclosure and an anti -praxis concealing the projects own future projection. Attempts to rupture these closures occur at the level of synthetic number, insofar as synthetic number is itself expressed in moments of narration and are conceived within a logic that while cons istent with the possibilities contained within, is not immanent in any specific way to the discourse as an objectified structure itself. It is perhaps only now in the wake of the continuing devastation of the invasion of Iraq, the looting of the Iraq mus eum, and the complete desolation in so short a time of the archeological sites of ancient Uruk that the techniques of synthetic reconstruction offered by the Critique and carried out in the science fiction of Samuel Delany offer the only coherent access to the simultaneous emergence of written language and the money-form. Indeed this loss is two -fold. Not only is the possibility of such an investigation harmed by the loss of material artifacts, but insofar as the archeologist maintains his commitment to a n empirical methodology, such a loss must appear as the complete loss of his investigation. For like the geometer, economist, and the
30 neolithic accountant he studies, the evidence that forms the archeologists proof may well condemn him to live his invest igation in passivity, his assertions never reaching the speculative power of Schmandt Besserat, Sartre or Lvi Strauss but producing their own dwindling line of flight, like the newly exposed clay tablets themselves, disappearing to unknown collectors, dis solving in the rain.
31 LIST OF REFERENCES Delany, Samuel R. Tales of Neveryon. Hanover: Wesleyan UP, 1993. Dosse, Francois. History of Structuralism Volume One: The Rising Sign, 1945-1966. Trans. Deborah Glassman. Minneapolis: U Minnesota P, 1997. Jameso n, Fredric. Foreword. Critique of Dialectical Reason Volume One. By Jean -Paul Sartre. Trans. Alan Sheridan -Smith. London: Verso, 2004. Lacan, Jacques. The Seminar of Jacques Lacan Book One: Freuds Papers on Technique 19531954. Trans. John Forrester. Ed. Jacques -Alain Miller. New York: Norton, 1991. Lvi -Strauss, Claude. The Savage Mind. Trans. Weidenfeld, George. Chicago: U Chicago P, 1967. Sartre, Jean -Paul. Critique of Dialectical Reason Volume One. Trans. Alan Sheridan -Smith. London: Verso, 2004. ---. Interview. Replies to Structuralism: An Interview with Jean Paul Sartre. Trans. Robert DAmico. Telos 9 (1971): 11016. Print. ---. and Benny Levy. Interview. Hope Now: The 1980 Interviews Trans. Adrian Van Den Hoven. Chicago: U Chicago P, 2007. Schman dt -Besserat, Denise. How Writing Came About. Austin: U Texas P, 1996.
32 BIOGRAPHICAL SKETCH Brandon J. Ca rr received a Bachelor of Arts d egree in English and Russian from Kent State University in 2007 This work represents the culmination of his work tow ard the Master of Arts d egree in English at the University of Florida His research examines relationships between twentieth -century Russian philosophies of language, Marxism and Jean-Paul Sartres Critique of Dialectical Reaso n.