Contradiction, Political Agency and the Formalized Subject by Brendan Rome

THE BROTHERWISE DISPATCH, VOL.3, ISSUE#7, JUNE-AUGUST/2019

“Politics is war without bloodshed. War is politics with bloodshed”-Huey P. Newton “Functional Definition of Politics” [1]

“From San Diego up to Maine/In every mine and mill/Where working men defend their rights/It’s there you’ll find Joe Hill.” -Earl Robinson, “Joe Hill.” [2]

The place of the subjective in relation to the objective has long been an enigma in historical and dialectical materialism. In his 18th Brumaire of Louis Bonaparte, Marx recognizes and highlights this fundamental antimony. He writes, “Men make their own history, but they do not make it as they please; they do not make it under circumstances chosen by themselves, but under circumstances, encountered, given from the past.” [3] As authors of history, humans are at once determined by and determining of history. In order to properly account for historical change and the possibility of revolution in the future, we must recognize this problem, and not take for granted this subject as an author of history. To account for a determined, yet history-determining subject, we can express it as a formalized subject that does not take on the assumptions of the liberal, atomic subject of modernity, but is rather emergent of yet irreducible to its historical conditions. That is to say, the subject is not natural and transhistorical, but rather emerges within antagonistic political conditions to exceed these determinations. The minimal structural or formal characterization of a subject emergent of antagonism can help us to recognize when revolutionary politics is possible and can help us to sidestep the considerable intellectual labor of nominating a particular revolutionary subject (e.g. unions, party, masses).

The wild contingency of historical conditions has led to a critical reworking of Marx’s original formulation of historical materialism (see Gramsci’s emphasis on superstructure or Lenin and Mao’s emphasis on the less industrialized periphery of capital/empire) at best, or at worst an outright and premature denial of Marx’s historical materialist methodology because capital persisted far beyond the publication of 1848’s Communist Manifesto. This denunciation of historical materialism from poor readers of Marx comes from their ascribing predictive powers to Marx that Marx himself denied. If we are to maintain the relevance of historical materialism today, we should turn to Georg Lukacs’ characterization of orthodox Marxism in his landmark History and Class Consciousness. He writes, “on the contrary, orthodoxy refers exclusively to method. It is the scientific conviction that dialectical materialism is the road to truth and that its methods can be developed, expanded, and deepened only along the lines laid down by its founders.” [4] In other words, an orthodox “Marxism,” is nearly entirely flexible in terms of content, but not form: so long as it maintains a dialectical methodology fixed on the class struggle, the particularities of the class struggle can be accounted for.

By recognizing the orthodoxy in method rather than content, we can avoid three major missteps in historical materialism and the Marxist tradition. The first is the aforementioned outright dismissal, a “throwing of the baby,” of the method with the “bathwater,” of historical contingencies. The second is the quasi-theodicy of a communist historical determinism, which reduced outlooks as varied as Austrian Second International economism, Stalinist “Diamat,” and the recent fad of “Fully Automated Luxury Communism’s” faith in an inevitable technological utopia to an impoverished secular messianism. The third and final misstep is an uncritical voluntarism following Louis Auguste Blanqui’s Romantic figure of the “professional revolutionary,” and its unlikely successor in the mid-20th century “Marxist humanism,” popularized by the Existentialists and Marcuse. An orthodox Marxist viewpoint on subjectivity and political agency is to recognize that we are neither radically free, unconditioned agents nor mere determined effects of historical inevitability, but are “authors of history,” that are at once determined and exceed socio-historical determination. To find the possibility of a revolutionary politics, one should find the conditions wherein one’s determination is “exceeded,” and a fairly straightforward way to understand this is through formalizations of subjectivity.

Alain Badiou and Jacques-Alain Miller’s articulations of a formalized illustration of a subject in the Cahiers pour analyse build upon Althusser and Lacan’s inversion of conventional philosophical thought on the subject and its formation. In spite of their differences (Lacan finds the subjective to be an enunciative function over a lacuna of one’s psychological topography while Althusser finds the subject to be an effect of discourses, primarily ideological), both push back against a naturalized, transcendental subject in favor of one that is a socio-linguistic effect that is entangled with interpersonal phenomena, whether familial or ideological. This pushback is instrumental against the atomic, ostensibly autonomous subject that characterized modern philosophy and political thought, such as the Cartesian cogito, the Kantian cosmopolitan-rational subject, and the “Robinsonade” of Smith’s and Ricardo’s economics.

The consequence of this “turning a philosophical subject on its head,” is that the subject is not the inalienable, always-already there “kernel” of ourselves, is rendered an effect of socio-linguistic discourse, and is thus produced and always-already intersubjective. In his letter to his students, including Badiou, “Three Notes on the Theory of Discourses,” Althusser describes subjectivity as a discursive effect. He writes:

If we compare the different existing forms of discourse – that is, the forms of unconscious discourse, ideological discourse, aesthetic discourse and scientific discourse – we can demonstrate the existence of a common effect: every discourse produces a subjectivity-effect. Every discourse has, as its necessary correlate, a subject, which is one of its effects, if not the major effect, of its functioning. [5]

The subject Althusser outlines here is not the natural, unified subject-individual that characterized modernity and liberal political philosophy, but is rather a disunity and effect. There is a subject produced by ideological discourse, a subject produced by aesthetic discourse, a subject produced by the discourse of the unconscious, and so on. From this, one can infer that the subject is not the constant that exemplifies a self, but rather arises out of particular contexts and discourses. A subject is a particular effect of the function of ideology, aesthetics and the like. Thus, if we are to think of a political subject, it is not the invariable atom, but rather arises in particular conditions, most importantly antagonistic contradiction, which I will examine further.

Lacan’s “Science and Truth,” shares Althusser’s anti-essentialist view of the subject and also recognizes the antimony between science and a humanist or liberal subject-atom. He writes, “if the subject is truly there, at the nexus of that difference [between psychoanalysis and other sciences], all humanist references become superfluous in science, the subject cutting them short.” [6] For Althusser and Lacan, psychoanalysis is a science of the unconscious, which is at odds with the humanist reference of the “liberal subject.” The discovery of the unconscious was akin to a “splitting of the atom,” of the subject, for it was rendered a bundle of drives, repressions, and intersubjective formations alien to itself, rather than the rational, self-transparent agent that was assumed.

In order to better account for the antinomy between the subject “superfluous to science,” and psychoanalysis, Lacan turns to structural linguistics and logic. If a subject is to be found, it is to be found in the indeterminacy, the incompleteness of science. Lacan writes of logic, “It is indisputably the strictly determined consequence of an attempt to suture the subject of science, and Gödel’s last theorem shows that the attempt fails there, meaning that the subject in question remains the correlate of science, but an antinomic correlate since science turns out to be defined by the deadlocked endeavor to suture the subject.” [7] If we consider science to be an endeavor that produces determinate knowledge of a specific object, then, our curious object of inquiry, the subject, remains the stubborn remainder to science. Here, Lacan describes the subject as an “antinomic correlate,” of science, a correlate that science situates itself in relation to, but a correlate that remains at odds with science and its determination. This antinomy between science and the subject may be approached two ways. The first is Miller’s embrace of Lacan’s term “suture,” taken from the sewing over an open wound, over this subjective “gap” in his essay of the same name, or Badiou’s denial of a subject of science, in his response, “Mark and Lack.”

Lacan’s overtures to mathematics in examining the place of the subjective are made more explicit by Miller and Badiou as they examine the formal sense of “zero” as they debate the possibility of a subject of science.

Miller’s “Suture,” borrows from Frege’s Foundations of Arithmetic to find the place of the subjective formally. Fregean arithmetic expresses a number as a signifier for both an individual and set. Miller identifies the subject as a paradoxical appearing of number in a formal system. He writes, “the subject…Frege [sets] himself from the start against the empiricist foundation of arithmetic, excludes from the field in which the concept of number is to appear.” Miller’s formalization of the subject is a formalization where the subject appears as a number, but is nevertheless irreducible to number. Enter “zero,” which, for Frege and Miller, is “the number assigned to the concept ‘not identical with itself.’” [9] The zero here is a placeholding concept of a paradoxical non-identical identity, and when related to the subject, this becomes a mark of indeterminacy and irreducibility, which is nevertheless referred to in discourse.

Miller expresses the indeterminacy of the subject as an empty set, which carries with it the possibility of adding signifiers (this however ignores Frege’s caveat of non-addition to the zero as a “non-identical” placeholder). In other words, the subject is “n,” but keeps the door open for “n+1,” “n+2,” and so on. For Miller, this is what a formalized subject is. He writes, “the definition of the subject comes down to the possibility of one signifier more.” [10] Thus, Miller’s formalized subject is a mark of a lack in actuality, but this mark of lack brings with it an open-ended possibility of additional signification. Miller thus finds the subject to be indeterminate itself, but is nevertheless a wellspring of signification in potential.

The young Badiou of “Mark and Lack,” on the other hand, explicitly denies the limitless determining potential of an itself indeterminate zero-subject. His response to Miller employs Gödel’s, rather than Frege’s arithmetic framework. In this essay, Badiou employs a triple articulation of logical processes. In the category of “expression,” there are either ill-formed or well-formed expressions, and the well-formed expressions are divided from the ill-formed by the mechanism of formation. Put more simply, this is a division between gibberish and expressions that signify. Well-formed expressions are themselves divided between decidable and undecidable propositions. Decidable propositions are the only domain of science, and Badiou argues against placing the subjective here.

Given Badiou’s insistence on decidability for scientific discourse, the question remains: is there a place for a formalized subject in scientific discourse? In short, no. Badiou denies the mark of a lack that Miller associates with the subject. He writes of the zero, “neither thing nor object have the slightest chance here of acceding to any existence beyond their exclusion without trace.” [11] Rather than positing the zero as a mark of lack with seemingly limitless potential for determination or signification, the zero is a mere lack. Badiou finds the zero to be a lack of a mark in particular as well as a lack in general.

Since, for Badiou, a lack in science is a mere lack, the zero-subject cannot be expressed in science. He writes, “there is no subject of science. Infinitely stratified, regulating its passages, science is pure space, without inverse or mark or place of what it excludes.” [12] Here Badiou denies the very possibility of the existence of a subject of science. The indeterminate lack is denied by science, as science excludes indeterminate propositions entirely, even the mark of them in absentia. In “Mark and Lack,” Badiou relegates the subject’s place to ideology, echoing Althusser’s description of subjectivity as an “effect” in “Three Notes on the Theory of Discourses” and anticipating his 1970 essay, “Ideology and Ideological State Apparatuses.” Here, Althusser describes the subject as, “the category of the subject is only constitutive of all ideology insofar as all ideology has the function (which defines it) of ‘constituting’ concrete individuals as subjects.” [13] Thus, ideology functions in a manner that produces subjects as its effect. Ideology takes individual organisms (which can be expressed as decidable propositions), and makes subjects (which are undecidable) of them. Though the subject is refused by science, it is constituted by ideology.

If we take subjects constituted by ideology in the political, then we can employ another logical abstraction, that of the logic of contradiction in dialectics, to find the place of the subjective and reconstitute subjects as political agents and authors of history. Dialectical contradiction is the motor of history. Badiou writes, “Not only is this type of [internal] contradiction not an abnormal phenomenon, but it is ‘the very moving principle of the world’…wherever there is contradiction, there is movement and development.” [14] The contradiction in dialectical logic allows for movement and development in a way refused by Badiou’s decidable propositions in “Mark and Lack.”

Badiou’s dialectical logic during his post-68 turn during the années rouges draw heavily on Mao Zedong’s 1937 “On Contradiction,” which privileges the antagonistic role of contradiction to development from the “unity of opposites” in a dialectical system. Mao describes the relation between internal contradiction and development, “the fundamental cause of the development of a thing is not external but internal; it lies within the contradictoriness within the thing. There is internal contradiction in every single thing, hence its motion and development.” [15] By imbuing any thing with internal contradiction, Mao is able to account for development and avoid the fixed determination of Badiou’s decidable propositions. While a decidable proposition would have one determination (t), a dialectical thing is divided into two and has an unstable divided determination of opposites (t, ~t).

The “thing” Mao refers to here is not a single determination, a singular “one” that characterizes the decidable proposition (t) in “Mark and Lack,” but is rather divided in two. In “Theory of Contradiction,” Badiou describes the role of division in constituting a dialectical “thing.” He writes, “Mao Zedong has accomplished in the program fixed by Lenin: develop the ‘kernel of the dialectic,’ that is to say the axiom: ‘one divides into two.’” [16] The axiom “one divides into two” distinguishes the object of dialectical logic from the simple, singular object of a determinate proposition. The “division of two,” is the very “kernel” of the dialectical logic at work here. From this “division into two,” both the possibility of an internal contradiction and thus of movement and development arise. The fundamental process of division from one to two makes the subject possible for Badiou. While there is no subject of science, which according to Badiou is expressible only through determinate propositions, a political subject can arise in antagonism that follows the logic of contradiction.

Badiou’s emphasis on antagonism as a motor for historical change, and the possibility of a politics at all likewise takes its cues from Mao’s “On Contradiction.” Mao distinguishes between three forms of contradiction, non-antagonistic, latently antagonistic, and actively antagonistic. Non-antagonistic contradictions can coexist without resolution, particularly violent resolution, and thus don’t bring about change. For example, my preferring chocolate ice cream and my friend preferring Neapolitan ice cream is contradictory, but not antagonistic. We can each choose our flavors of preference and move on without coming to blows. On the other hand, some contradictions, like that between proletariat and bourgeoisie are antagonistic. [17] Radical change can occur when these contradictions cease to be latently antagonistic and become actively antagonistic. Mao describes this phenomenon,

Before it explodes, a bomb is a single entity in which opposites coexist under given conditions. The explosion takes place only when a new condition, ignition is present. An analogous situation arises in all those natural phenomena which finally assume the form of open conflict to resolve old contradictions and produce new things. [18]

Non-antagonistic contradiction aside, the qualitative transformation between a latently and actively antagonistic contradiction lies in the introduction of a new condition, in this case ignition. Ignition here is analogous to the more universal dialectical phenomenon of a qualitative change in the old oppositions that beget “open conflict” that resolves existent contradiction. Historically speaking, this new condition is a moment of weakness of the exploiting classes and the state apparatuses that hold them up, such as Louis Bonapartes capitulation to Prussia preceding the Paris Commune, Tsarist’s Russia’s collapse and Kerensky’s provisional government preceding the October Revolution, or France’s post-WWII exhaustion preceding the Algerian and Indochinese wars of independence. All these instances are contingent upon fruitful historical conditions but are nonetheless irreducible to the historical conditions.

This irreducibility of the qualitative transformation of antagonism to historical conditions distinguishes dialectical materialism from a crude historicism and necessitates some sort of active, voluntarist agent in the transformation of antagonisms. It is in this enigma of revolutionary change that Badiou finds his form of the subjective. He writes, “it is a dialectical mediation centralized between objective processes of the class struggle and subjective practice guided by the terms of the project of proletarian revolution.” [19] As we have seen with an analysis of the historic transformations between latent and active antagonisms in revolutionary ruptures, great historical change is possible precisely when objective processes in the class struggle beget a weakness in the exploiting classes, but a passive approach of historical determinism squanders the objective conditions. This is why a dialectical mediation between the objective historical terms and appealing to the subjective in the form of a project of “proletarian revolution” is necessary for Badiou.

This subject for Badiou isn’t the individual atom of a singular subject, but is rather an interpersonal subject of a class in struggle. Badiou finds the subject par excellence of history to be the class-in-struggle. He writes, “(the combative class) becomes the subject of historical processes by mastery of these laws [of contradiction] and its goal.” [20] This subject of history is not a stable subject of identity but is rather a subject through processes (dialectical processes governed by contradiction). It is defined not by simple determination but is rather determined through antagonism and the objectives of its struggle. This process is not then without a subject but is a subjectivizing process. Thus, in a reversal of his foreclosure of subjectivity in “Mark and Lack,” Badiou not only admits the possibility, but also highlights the political necessity of the subject. The subject is not the subject we departed from however, this ontological reference point of a singular, individual “I,” that is transhistorical. Rather it is the historical, transindividual combative class that becomes a subject in its active relation with the processes of contradiction and its goal of overturning the exploiting classes.

How does this illustration of the subject as emergent in a dialectical process appear in a formalized manner akin to Miller and Badiou’s earlier attempts in the Cahiers? The zero-place of a mark of lack Miller proposes does not account for Badiou’s proposal for a new subjectivity. The “possibility of one signifier more,” [21] Miller presents is a logic of addition ex nihlo and forms a chain of signification that is an open-ended set beginning from an empty set. This formalization is inadequate in two respects: first it begins from an empty set and doesn’t account for the conditions that Badiou identifies as necessary for subjectivity, the antagonism and contradiction present in a one that divides into two. Second, it is an addition from a zero point, and the subjectivity at hand here arises from existent conditions that have a determinant element and an excess of that determinism.

Likewise, in “Mark and Lack,” the Badiou of 1968 is unable to account for this subjectivity because he refuses the subjective in a rigorous historical materialism. He writes, “when Historical Materialism claims to elucidate subjective enslavement to ideologies on its own, or when psychoanalysis effaces the specificity of its place where it must uncover the mark of lack in the generality of a logic of the signifier, then these disciplines are collapsed and reduced to one another. They become stratified: un-scientific.” [22] Here, Badiou, thinking of himself as a faithful Althusserian opposes ideology starkly from truth, and its handmaiden, science. The historical materialism that Badiou opposes to ideology here is one he later recants and denounces as a dialectical myopia. He writes, “but Althusser here only generously lends to Lenin his own dialectical myopia.” [23] In reducing historical materialism to processes without subjects, a reduction Althusser actively advocates (this advocacy is complicated by his work in 1970’s “Ideology and Ideological State Apparatuses” and his work on “aleatory materialism” late in life) and Badiou at first defends in “Mark and Lack” is a myopia that desubjectifies and thus strips history of a motor for change, the antagonism of an exploited class-subject. This “myopia,” is the root of the impasse of Althusser’s thought: he is both an excellent structural and descriptive thinker, but his opposition to dialectical thought prevents prescriptive thought in his philosophy or a robust account of radical historical change. Thus, the lack of mark is as unsatisfactory a formalization of (non-)subjectivity as Miller’s mark of a lack.

In Badiou’s analysis of Mao’s theory of contradiction and antagonism, we find conditions that complicate the subjectivity-effects Althusser, Lacan, Miller, and early Badiou theorize to turn the ostensibly naturalized, liberal subject on its head. They find the subject to be an illusory effect of ideology, or a chain of enunciation that emerges from a zero-point. A dialectical analysis of contradiction and antagonism find the subject too to be emergent, not from a mark of lack, but from a specific latent antagonism, that the subject emerges from and is self-productive in the class struggle. In order to account for past historical change, and discover and foster conditions for future revolutions, Dialectical Materialism demands an emergent subjectivity-effect. This subject emerges from the contradiction and dialectically synthesizes the objective historical determinations and subjective voluntarism of a struggling exploited class. Badiou’s titan lectures, Theory of the Subject attempts to formalize this sort of subject, a refreshing revitalization of the “algebra of revolution” that Lenin famously praised Hegel’s Logic to be. Because the contingencies of history make the particularities of a “revolutionary subject” difficult to articulate and predict, finding the formal conditions where a revolutionary political subject can emerge is indispensable for both a historical materialist theory and socialist practice. This article has been a preliminary sketch teasing out features of a revolutionary subject through mathematical and linguistic formalism. Though oft ignored, discovering an “algebra of revolution,” through dialectics, critiques of political economy, and set theory can produce a breakthrough in dialectical materialism while maintaining Lukacs’ “Marxist orthodoxy,” a project which I hope to dive into much more in-depth.

[1] Newton, Huey P., “Functional Definition of Politics,” The Black Panthers Speak, (Chicago, IL: Haymarket Books, 2014), pp. 45.

[2] Lyrics: “Joe Hill,” https://www.marxists.org/subject/art/music/lyrics/en/joe-hill.htm.

[3] Marx, Karl, The 18th Brumaire of Louis Bonaparte, (New York, NY: International Publishers Co, Inc., 1972), pp. 15.

[4] Georg Lukacs, History and Class Consciousness: Studies in Marxist Dialectics, (Cambridge: MA, MIT Press, 1971), pp. 1.

[5] Althusser, Louis, “Three Notes on the Theory of Discourses, The Humanist Controversy and Other Writings, (London, UK: Verso Books, 2003), pp. 48.

[6] Lacan, Jacques, “Science and Truth,” Ecrits, (New York, NY: W.W. Norton & Company, Inc, 2006), pp. 728.

[7] Ibid, pp. 731.

[8] Miller, Jacques-Alain, “Suture,” Concept and Form Vol. I, (London, UK: Verso Books, 2012), pp. 94.

[9] Ibid, pp. 97.

Ibid, pp. 100.

[11] Badiou, Alain, “Mark and Lack,” Concept and Form, Vol I., (London, UK: Verso Books, 2012), pp. 166.

[12] Ibid, pp. 171.

[13] Althusser, Louis, “Ideology and Ideological State Apparatuses,“On the Reproduction of Capitalism, (London, UK: Verso Books, 2014), pp. 262.

[14[ Badiou, Alain, The Rational Kernel of the Hegelian Dialectic, (Melbourne, Australia: Re:Press, 2011), pp. 28-29.

[15] Zedong, Mao, “On Contradiction,” Mao: On Practice and Contradiction, (London, UK: Verso Books, 2017), pp. 69.

[16] Badiou, Alain, “Theorie sur la contradiction,” Les Annees Rouges, (Paris, FR: Les Pariries Ordinaires, 2012), pp. 37. Translation mine. Original text reads, “Mao Tsé-Tsong accomplit donc la programme fixé par Lénine: développer le ‘noyau de la dialetique,’ c’est-à-dire l’axiome: ‘un se divise en deux.”

[17] In “On the Correct Handling of Contradictions,” Mao outlines the fundamental difference between antagonistic and non-antagonistic contradictions in politics, “the contradictions between ourselves and the enemy are antagonistic contradictions. Within the ranks of the people, the contradictions among the working people are non-antagonistic, while those between the exploited and exploiting classes have a non-antagonistic as well as an antagonistic aspect.” (Zedong, Mao, “On the Correct Handling of Contradictions,” Mao: On Contradiction and Practice, pp. 131).

[18] Zedong, Mao, “On Contradiction,” Mao: On Practice and Contradiction, (London, UK: Verso Books, 2017), pp. 99.

[19] Badiou, Alain, “Theorie sur la contradiction,” Les Annees Rouges, (Paris, FR: Les Pariries Ordinaires, 2012), pp. 46, translation mine. Original text reads, “C’est une médiation dialectique centralisée entre le processus objectif de la lutte des classes et la pratique subjective, dirigée en termes de projet de la revolution prolétarienne.”

[20] Ibid, pp. 47, translation mine. Original text reads “(la classe combatante) devient sujet du processus historique par la maîtrise des ses lois et de son but.”

[21] Miller, Jacques-Alain, “Suture,” Concept and Form Vol. I, (London, UK: Verso Books, 2012), pp. 100.

[22] Badiou, Alain, “Mark and Lack,” Concept and Form, Vol I., (London, UK: Verso Books, 2012), pp. 172.

[23] Badiou, Alain, “Theorie sur la contradiction,” Les Annees Rouges, (Paris, FR: Les Pariries Ordinaires, 2012), pp. 44, translation mine. Original text reads, “Mais Althusser ne fait ici que prêter généreusement à Lénine sa proper myopie dialectic.”