Alain Badiou’s oeuvre sits uneasily astride a bewildering paradox. Badiou repeatedly asserts that the single most imposing impediment to our subjective access to truths, to our finite, yet substantial and materialist participation in the infinite, is the tyrannical domination of global social relations and subjectivity by the economic rationality of capitalism. In Number and Numbers, he writes: ‘Number governs the economy; and there, without a doubt, we find … the “determination in the last instance” of its supremacy’.1 Similarly, in one of his most recent books, Happiness, he tells us that the good and real life, ‘la vraie vie absente’ as Rimbaud writes in Une saison en enfer, is systematically reduced in the world of global capitalism to the specious freedom of consumerist choice: ‘Freedom is coded or precoded in the infinite shimmer of commodity production and in what monetary abstraction institutes on that basis’.2 In the face of this overdetermined and seemingly universal untruth, the name Badiou has steadfastly maintained to indicate the political dimension of the true life, is, of course, the ‘Idea of Communism’.
And yet, for all that, one could assert with little exaggeration that Badiou’s engagement with Marx’s critique of political economy is a veritable empty set. Badiou’s repeated, sustained, admiring and attentive engagement with this great thinker is, in other words, addressed almost univocally to the political Marx, the Marx of the Communist Manifesto and The Civil War in France. But if capitalism constitutes the dominant logic of our untrue world, and not merely a passing epiphenomenon, how can a reader hope to formalise the logic of the true life, life subtracted from the reign of commodity fetishism, without a systematic, formal construction of the categories and logic of the world of capitalism?
Like Adorno’s superficial comments in Negative Dialectics on capitalism as universal fungibility, Badiou’s explicit pronouncements on capitalism are not false, but remain manifestly inadequate to the real complexity of their object, betraying only the vaguest sense of the complexity of the logic governing the valorisation of value, the many laws of the tendencies determining production, circulation, exchange, and accumulation that Marx painstakingly develops. We know as much as Badiou tells us about the logic of capitalism from even the first sentence of Capital volume one: that the form of appearance of social relations in which the capitalist form of production predominates is that of universal commodification and exchange.3
This disinterest is of course odd coming from Badiou, who devotes meticulous care precisely to the formalisation of his primary objects of inquiry in systematic, philosophical and mathematical-logical terms. But while this is the case, for example in Logics of Worlds, it is nonetheless striking that the worlds in question there, along with the events that break free from them remain either entirely generic, worlds as such, events as such, or else constitute decidedly minor, even ‘baroque’ subsets of what Marx called the general social forms (gesellschaftliche Formen) that govern social existence in any specific historical domain and period:
a country landscape in autumn, Paul Dukas’s opera Ariadne and Bluebeard, a mass demonstration at Place de la République, Hubert Robert’s painting The Bathing Pool, the history of Quebec, the structure of a galaxy … Rousseau’s novel The New Heloise … Sartre’s theatre, Julien Gracq’s novel The Opposing Shore and the architectural form of Brasilia [or] a poem of Valéry.4
To take two other examples of events named in Logics of Worlds, it is certainly the case that Toussaint Louverture and Schoenberg name world-historical events in the political and musical domains respectively. But in both these cases, there is no substantial demonstration of the structures either from which these events break free nor the worlds into which they subsequently open. Only the briefest presentation of the Haitian Revolution, and nothing of the essence of slavery and capitalism in the Caribbean, arguably the logics governing these two worlds, before and after Toussaint Louverture. Similarly, in Badiou’s ‘Scholium’ to Book I of Logics, one finds no substantial demonstration of the logic of traditional western harmony and the various points and sites where Schoenberg ruptures this logic to implement two entirely novel operational procedures, free atonalism and dodecaphonic composition.
Now, no one can know or say everything, and it may be fine to leave the details to others, given the suggestive nature of Badiou’s propositions. But my point is rather that while Logics of Worlds casts its remit explicitly as the apodictic exposition of the ‘logic of appearance’ (la logique de l’apparaître) governing any world (and thus the plural of its title), none of the examples in Logics of Worlds in fact addresses the general logic and laws governing the forms of appearance of any specific object in capitalism. Perhaps Badiou simply is not interested in developing in his own terms the structural categories and logic of capital that Marx initiated. Indeed, Badiou often appears more interested in the novelty of events than the mundane regularity of the dominant logic of the world: ‘Philosophy is asked to be capable of welcoming or thinking the event itself, not so much the structure of the world, the principle of its laws or the principle of its closure, but how the event, surprise, requisition, and precariousness can be thinkable in a still-rational configuration’.5
I wish to argue in this final chapter that Badiou has, in the three monumental volumes of Being and Event, in fact produced the materials for precisely such a logic, but in the form of an arsenal of concepts that remain to be precisely measured against Marx’s critical and formal reproduction of capitalism, confronted with what Marx called his Gedankenkonkretum, a materialist, scientific ‘thought-concrete’, the systematic exposition of which consumes the three volumes of Capital. In what follows, I will proceed in two moments, the first critical, the second comparative. While Badiou’s disinterest in the logic of capitalism and Marx’s Capital specifically constitutes a silence that traverses his entire oeuvre, this absence takes on a strongly symptomatic, spectral presence in the 1994–95 seminar recently translated to English as Lacan: Anti-philosophy 3.6
Secondly, while the previous chapter indicated certain general aspects in which Badiou’s ontology reproduces the fundamental gestures of Marx’s materialist critique, here I wish to push this claim further and more strongly: while it is true that Logics of Worlds never discusses the logic of appearance that governs all capitalist things (i.e., commodities), we should nonetheless read Logics in a quite specific sense as the (objective, likely unintentional) abstract displacement (Verschiebung) and formalisation of Marx’s Capital. In this view, Capital should quite simply be read as the systematic demonstration of the logic of what Marx calls the capitalist social form, which is to say in Badiou’s jargon, as the logic of the appearance of things in the capitalist world.
This will then entail two subsidiary claims: 1) that the notion of a materialist logic bears the same meaning for Marx and Badiou, and 2) that the domain Badiou calls a ‘world’ encompasses what Marx calls social form. In a sense, then, this means nothing more, though nothing less, than subjecting Logics of Worlds to a Marxian torsion: what Badiou has neglected, Marx has in fact already accomplished (with his own specific formal, conceptual, and discursive means): the systematic, synthetic demonstration of the necessary forms of appearance of commodities in the capitalist social form.
1 Badiou’s Lacan, Badiou’s (Marx)
While Badiou fully grasps the essential nature of formal demonstration for Lacan, his 1994–95 seminars circle around, and yet nonetheless betray a symptomatic repression or blindness regarding Marx’s critique of political economy. In these lectures, Badiou explicitly names Marx alongside Lacan as occupying a very particular status in the pantheon of anti-philosophy, insofar as both Marx and Lacan mount a critique of philosophy and truth in the name of science, rather than Nietzsche’s poetic utterances or Wittgenstein’s language games. Despite this crucial insight, Badiou nonetheless remains symptomatically deaf in these lectures, as elsewhere, to Marx’s scientific discourse – to Capital, that is to say.
This repression results in a highly problematic suturing in Badiou’s discourse, a suturing of the ideological imaginary to a politics of the real. In suppressing any consideration of scientific discourse – whether of Marx’s Capital or even Lacan’s systematic demonstration in the 1950s of the structure of the unconscious, a demonstration that Badiou suggestively names a ‘hyperstructural axiomatic’7 – Badiou enacts a short-circuiting of analytical critique. The result of this suture as theoretical short-circuit is that politics in Badiou’s Lacan seminar lacks any consequential formalisation of the categorial structure of capitalism understood as social form, as the value-forms of abstract labour, that is to say. In its absence, politics can take the form not of a true act, but only and ever the mere acting-out of ideological fantasy.
This becomes eminently clear in what is for me the key passage in the entire seminar. Here is Badiou’s citation from Lacan’s Radiophonie:
What Marxism has shown by its actual revolution: that there’s no progress to be expected from truth, nor any well-being, but only the shift from imaginary impotence to the impossible, which proves to be the real by being grounded only in logic: in other words, where I claim the unconscious is located, but not so as to say that the logic of this shift shouldn’t hasten the act.8
Badiou’s commentary of this passage is revealing, both in what it says and does not say:
In short, in Lacan’s view, Marx showed that, instead of philosophical fantasies about the good state or the good society, it was the logic of Capital that had to be identified at the point of the real. Marx’s actual revolution is a liquidation of philosophy. Should we say that Marx substituted a science or knowledge for the philosophical imaginary? No, says Lacan, because we must maintain that the ‘logic of this shift’ must ‘hasten the act’.9
The first point to note in Lacan’s original statement is his indication of Marx’s refusal of ‘truth’ and ‘well-being’. This formulation reiterates Lacan’s post-May ’68 rejection of traditional, Leninist Marxism, as both a moralism of the proletariat as the universal class, and Bolshevism as a mere programmatic redistributionism of wealth. It is Lacan’s rejection of the Leninist misreading of Marx’s critique, the reduction of the critique of political economy to an ideological moralism of the working class in the form of a politicised redistribution of the wealth of production, in short, Left Ricardianism.10 Leninist Left Ricardianism ignores Marx’s systematic demonstration of the laws of the tendencies of capitalism as a structure and social form, while the mere superficial forms of appearance of modes of market exchange become the target of political redistributionism.
It is clear from his many disparaging comments on the proletariat and proletarian politics after May ’68, a number of which Badiou cites in the course of the seminar, that Lacan discounted all mythification of the proletariat as ideological, as what he calls here the ‘impotent imaginary’. Virtually no attention, including Badiou’s presentation, however, has been devoted to a number of brief but incisive comments Lacan makes on the formal logical structure of Marx’s analysis in Capital in the seminars from the 1950s, precisely the period when Lacan was elaborating his own systematic formalisation of the symbolic structure of the unconscious. That said, Badiou rightly reads Lacan as here, in the wake of May ’68, affirming in place of all utopian ‘philosophical reveries on the good state and good society’ the systematic analysis of the structure of capitalism. The point though is that this work, both Lacan reading Capital and Lacan articulating his own structural demonstration of the nature of the unconscious, had occurred long before, in the 1950s seminars, a period of his thought Badiou studiously ignores in these seminars.
In this passage, Badiou reads in Lacan’s assertion a rejection of philosophy (‘no clamor of being or nothingness’), revealingly identifying Marx as an anti-philosopher of the same stripe as Lacan himself. In this vein, in order to analyse Lacan’s assertion that philosophy merely plugs the hole of politics, Badiou had reminded his listeners of Marx’s famous taking leave of philosophy in the eleventh thesis on Feuerbach: ‘Philosophers have only interpreted the world; the point is to change it’. While this disparagement of philosophy and truth casts both Lacan and Marx as anti-philosophers, they are, as Badiou points out regarding Lacan, different from all others in that for both, the rejection of philosophies of truth is enacted in the name of the rigour of scientific, apodictic demonstration; for Lacan, the demonstration of the structure of the unconscious, for Marx, the demonstration of the structure of capitalism.11
Badiou cites Lacan in a further development of what I would call Lacan’s scientific anti-philosophy: ‘Thus the real differs from reality. This is not to say that it’s unknowable, but that there’s no question of knowing about it, only of demonstrating it’.12 Here, and although his name is never mentioned in the whole of Badiou’s seminar, we are resolutely on the terrain of Spinoza. Not the Nietzschean misreading of Spinoza as an invocation of the mere affect of beatitude as a joyful wisdom or Gay Science, but the precise categories of adequate knowledge that Spinoza terms the general and the intuitive (the imaginary remaining a necessary, but wholly inadequate form of knowledge, as we first learn in the famous Appendix to Book I and more fully in Book II of the Ethics). If Lacan is an anti-philosopher, Spinoza nonetheless remained the crucial formative philosophical reference for Lacan, prior to Hegel and Kojève, most explicitly in the 1932 dissertation, where the entire presentation is framed by citations and analyses of key propositions from the Ethics.13 No less is Spinoza the crucial reference, as I have argued throughout this book, to grasp Marx’s epistemology of the substantial unity of the real and the synthetic production of analytic thought, as Althusser and Macherey famously argued in their analysis of the 1857 Introduction in Reading Capital.
It was Spinoza whose demonstrations already put Hegelian negative dialectics in its proper place: things (such as the unconscious or capital) adequately grasped in their singular essences, know no contradiction or negation. Here is Badiou:
The real is the remainder of the disjunction between the knowable and the unknowable. Here we take the measure of the anti-dialectical dimension of every anti-philosophy: the point of access to the real cannot be reached negatively. As compared with knowable reality, no negation procedure provides any access to the real.14
Contradiction adequately understood is a figure of experience, of the forms of appearance of things. While this has been well-understood of the unconscious since Freud’s Traumdeutung, in Marx’s case, I have argued (in Chapter 3 above) that we witness across the development of his critique in the wake of the dialectical Hegelianism of the Grundrisse a series of theoretical revolutions in the notes and manuscripts of the 1860s and 70s: there, what Jacques Bidet has called various Hegelian theoretical impediments (the identity and non-identity of production and consumption, for example, or the merely apparent contradiction between the exchange of equivalents and the realisation of surplus value) are removed and in their place Marx develops, or tends increasingly to develop in his unfinished masterpiece, the full relational complexity of the laws of the tendencies and counter-tendencies as they determine the increase in the organic composition of capital: not the mere falsity, but the absolute necessity governing the phenomenal, fetishistic forms of appearance of capital (profit, rent, finance, for example).
Adequate knowledge, knowledge of both the general laws governing the unconscious as well as the essence of any singular case, governs Lacan’s understanding of analysis. While in the Écrits and seminars Lacan develops a systematic exposition of the structure of the unconscious, it is no accident that we are left, as Badiou laments toward the end of his seminar, without a theory of the act. For the analytic act occurs on the register of Spinoza’s third, intuitive mode of knowledge, as the knowledge of the singular essence of any given case. We cannot know what to do in the case of a given, real analysis, no matter how adequate our knowledge of the laws governing the structure of the unconscious may be. We can only approach the real of a given subject via an adequate understanding of the singular essence of that case, a process that indeed requires, along with the scientific mastery of general laws, an improvisational genius attendant to Spinoza’s third genre of knowledge.15
Badiou’s commentary is revealing: ‘Although the real, as distinct from reality, is exempted from the knowable, which is the essence of reality, the real nevertheless does not end up being the absolute unknowable but is instead exposed to being demonstrated’.16 ‘Demonstration’ is arguably the key epistemological concept in the French tradition from Cavaillès and Koyré to Althusser and Badiou himself. Beyond the knowable and the unknowable, lies not the will to power, or language games, but the adequate, asubjective, apodictic demonstration of the essential necessity governing an object of knowledge such as the unconscious.
All this is, I think, a fully adequate reading of these two typically enigmatic Lacanian pronouncements that Badiou cites. The problem, however, arises in Badiou’s final gesture: ‘Should we say’, Badiou concludes, ‘that Marx substituted a science or knowledge for the philosophical imaginary? No, says Lacan, because we must maintain that the “logic of this shift” must “hasten the act” ’.17 Where in the original text Lacan loads his typically baroque pronouncement with ambiguous negatives and subjunctive conditionals (‘Be there where I announce that the unconscious reigns, but not to say that the logic of this turn may not hasten to the act’) Badiou declares an unambiguous imperative to proceed directly to the political act itself. This ‘devoir’ (‘we must [on doit] maintain that the logic of this shift must [doit] hasten the act’), this obligation Badiou imposes on Lacan’s ambiguity betrays a problematic disinterest – in fact an extraordinary indifference given the systematic, logicist nature of Badiou’s philosophy – in scientific knowledge of the object. It is at this point that Badiou’s interpretation becomes not merely problematic, but wholly symptomatic, symptomatic of a general oblivion and lack of engagement not only with Lacan’s scientific discourse on the structure of the unconscious from the 1950s, but above all with Marx’s Capital specifically.
Surprisingly, it is Badiou himself who unintentionally makes precisely this point – presented here as a symptom of traditional Marxism’s lack of engagement with Marx’s categorial demonstration – when he summarises Lacan’s critique of the political Marx in the following terms: ‘Politics is glued to meaning, and, insofar as it’s glued to meaning, it makes an imaginary, or if you will, religious, hole in the real of Capital’.18
In the absence of any substantial engagement with Marx’s scientific demonstration on Badiou’s part and the rush to pronounce the imperative of the political act, Marx remains a mere (hysterical) political activist, and revolutionary desire remains ‘stuck’ to mere ideological meaning, overdetermined by the empty, even ‘religious’ hope of moving beyond capitalism to something called communism.
Strictly speaking, there is no discourse of politics. And it’s because there isn’t any that, in fact, politics always makes a hole in the discourses. And more precisely in what, in these discourses, is based on imaginary consistency, or, in other words, is based on semblance.19
The complexity of social form, of capitalism as the social logic of compulsory valorisation, is reduced to mere imaginary ideological semblance, both in traditional Marxism (as Lacan and Badiou both note), as well as in Badiou’s own suturing of politics to the Idea of Communism.
In the face of the immense theoretical complexity and simultaneous abstraction of Badiou’s logic of worlds and events, how is one to know where the weak points and sites lie in the capitalist system, what constitutes its weakest links and limits? How to organise and articulate political militancy without an adequate understanding of the social form that is its object? The result of such reflexive politics invites the very conclusion Lacan never tired of bestowing on the pseudo-events of May ’68 as the mere acting out of imaginary desires sutured immediately to the inflammatory act and the messianic hope that the system would magically crumble: ‘Sous les pavés, la plage’.
This brings us directly and imperatively to the limits of any formalisation of the world of capital, to the very problem Badiou terms the ‘recherche du réel perdu’, the search for the capitalist real. There is, in other words, a capitalist Real, in the strong, Lacanian sense of the term. In À la recherche du réel perdu, Badiou draws on Lacan to argue that the capitalist ‘real’ is no mere empirical, ready-at-hand substance or experience of the everyday; instead, the capitalist real consists of the very impasse or impossible limit of capital understood as a process of formalisation.20 I would argue, though, that a more appropriate proper name for this real is not equality, as Badiou suggests. Equality is certainly a necessary subcategory of the capitalist real – for example in capitalism’s dependence upon abstract labour as the substance of value. The essential conclusion of Reading Capital still holds: we do not yet truly live as more than the subjects (Träger) of what Marx named the ‘automatic subject’: subjects of the general social structure of compulsion that he formalised as the system of Capital. To live, then, beyond mere fleeting intimations of life in evental moments such as 1789 and 1804, the Paris Commune and May ’68, requires the deployment of a politics adequate to the demands of such events as a general possibility, the transformation of the transcendental categories of social structuration and subjectivity themselves, toward the construction of a post-capitalist transnationalism, one that surpasses the mortal crisis of valorisation that is the actuality of posthuman capitalism and its real and attendant threat of anthropocenic catastrophe.
Badiou eloquently describes such an orientation as our finite participation in the infinity of Number, real and true life, that is, beyond the tyranny of mere numericality:
To think Number … restores us, either through mathematics, which is the history of eternity, or through some faithful and restrained scrutiny of what is happening, to a supernumerary hazard from which a truth originates, always heterogeneous to Capital and therefore to the slavery of the numerical. It is a question, at once, of delivering Number from the tyranny of numbers, and of releasing some truths from it. … It proceeds, effectively and theoretically, to the downfall of numbers, which are the law of the order of our situation.21
2 ‘Qu’en est-il de la logique?’: Reading Logics of Worlds After Capital
Let me restate in the most deliberate terms the paradox that determines the limits of Badiou’s philosophical and political critique: On the one hand, Badiou clearly and repeatedly states the obvious, that the overarching and predominant form of contemporary global social relations is, quite simply, capitalism. Most recently, for example, Badiou has repeated this in the form of an axiomatic truism: ‘Allow me to begin … from a perfectly banal conviction: the dominant socio-economic structure, which is today in place at a global scale, is capitalism. Everyone, or nearly so, agrees’.22 Who could disagree? On the other hand, while I have argued above that the corresponding absence of any concrete analysis of the capitalist social form on Badiou’s part occasionally, as in the Lacan seminars, reaches symptomatic proportions, the one moment where one would most expect such an engagement with ‘the dominant socio-economic structure’ that governs the contemporary world is precisely in Badiou’s second magnum opus, Logics of Worlds. Instead, in the vast complexity of its 638 pages comprising seven books and dozens of chapters, alongside the analyses of worlds from painting to poetry, mathematics to music, love and revolutions past and present, the word capitalism appears exactly once, in a banal and utterly indeterminate aside, when Badiou early on castigates the nouveaux philosophes of the 1970s for their ideological role in the unleashing of ‘an unbridled capitalism’.23
Stated as such, this stunning absence from a book proposing to analyse with abundant examples the logic governing the forms of appearance of things in any world would amount to no more than a final pièce de conviction in an absurd and illegitimate condemnation of the author of some 200 books for not having talked about a topic of particular interest to this reader; were it not that Logics of Worlds, without ever explicitly mentioning capitalism, in fact provides the means precisely and adequately to understand the philosophical status of Marx’s critique of the political economy of capitalism as a materialist logic. It is as if Logics of Worlds objectively takes up the long-forgotten conclusion of Althusser’s 1947 thesis ‘On Content in Thought of G.W.F. Hegel’. There, Althusser called for a reading of Capital as transcendental analytic of the capitalist social form, a reading that it would be left to Badiou to take up six decades later: ‘The transcendental which conditions the a priori activity (theoretical or practical) of man’, Althusser writes in his conclusion, ‘has, now, conquered its nature: it is the concrete historical totality. … In the fundamental structure of the human totality, Marx gives us the table of human categories that govern our time. Capital is our transcendental analytic’.24
Here again, Badiou seems to displace Althusser’s explicit, 1947 invocation of Marx’s Capital as transcendental analytic into a theoretically generic domain of representation, as if Logics of Worlds conducted its dreamwork upon the conclusion of Althusser’s ‘On Content in Thought of G.W.F. Hegel’. To reread Capital after Logics of Worlds, to analyse the latter as the abstraction of the former, is to read Marx’s three volumes as a logic of capital, to account for its status as an utterly contemporary presentation of a materialist logic of the dominant structure of the world.
In this vein, Badiou recasts and precisely delimits logic, after Aristotle, Kant, and Hegel, after the linguistic turn of analytic philosophy, as what he calls the ‘science of the forms of appearance’ (la science de l’apparaître) of objects in any world. In the case of capitalism, following Marx, this will mean quite simply to grasp the precise ontological status of the critique of political economy, understood as the science of the necessary forms of appearance of value in the capitalist social form, as, in other words, Marx’s monetary labour theory of value.
‘Qu’en est-il de la logique?’, ‘What then of logic?’ Badiou asks in his theoretical prolegomenon to Logics of Worlds, the 1998 Court traité d’ontologie transitoire.25 To answer this question will require that Badiou reconceive the ontological status of logic – this is the project of the Short Treatise – which will then allow him to deploy this new, categorial logic of the forms of appearance of things in any given world in Logics of Worlds. Badiou is forced to turn to the problematic status of logic in the wake of Being and Event because, he argues, that book left unaddressed a crucial aspect of any ontology: the being-there, existence, and forms of appearance of beings that manifest themselves in any determinate situation:
My goal [in Logics of Worlds] is to define what existence is … and to introduce the fundamental philosophical difference between being [the subject of Being and Event] and existence … Logics of Worlds is the logic of existence. It establishes the possibility of the logic of existence; that is, the possibility of different forms of singularity, of different forms of relationship between a multiplicity and a world in which this multiplicity is localised.26
To ‘establish the possibility of the logic of existence’, Badiou first steps back in the Short Treatise to condense the problem of logic in the form of an axiomatic decision between ‘Plato or Aristotle’.27 Either logic remains integrally linked to the Idea of mathematical truths, as it does for Plato, he argues, or, in the case of Aristotle, ‘thought is the [mere] construction of an adequate descriptive framework’, the weaving together, in the form of demonstrations that construct a ‘purely ideal’ set of admissible consecutions, an aesthetic ‘art of calculation’.28 In Badiou’s reading, Aristotle’s logic remains ontologically determined (‘For Aristotle, ontology prescribes logic’) in a manner analogous to that of Frege, whom (as discussed in the previous chapter) Badiou had criticised in the crucial Meditation 3 of Being and Event.
Badiou’s initial presentation would seem to relegate Aristotelean logic to the dustbin of the history of philosophy, but in fact, surprisingly (and crucially in the case of Marx, for whom Aristotle, not Plato, stands as ‘the greatest thinker of Antiquity’29), this refoundation of logic as a categorial science of appearances will ultimately refashion Aristotle for a contemporary logic of worlds. To do so, Badiou must address the immediate object of his critique, the linguistic turn of logic since Bolzano and Frege. Badiou formulates this critique as a second contrast, one that forces an axiomatic philosophical orientation: logic will either be understood as the syntax of a linguistic semantics or, as Badiou will propose, as a categorial logic, in which among plural ‘universes’ (a term he will subsequently replace with ‘worlds’ in Logics) each necessarily bears its own singular logic as an immanent, ‘internal dimension’.30
Key to this categorial reconceptualisation of logic is the notion of the plurality of worlds and their attendant logics (as the title Logics of Worlds will forcefully proclaim). Given that, as Russell’s Paradox first determined, there exists no set of all sets, no totality of worlds (what Badiou will call in Logics the ‘universe’ of worlds), there can correspondingly exist no single logic that would govern the existence of all beings. Instead, logics in their plurality must be conceived of as necessarily local:
It is an essential property of the existent qua existent [de l’étant en tant qu’étant] that there can exist no totality of beings, in so far as they are thought uniquely from their beingness (étantité). A crucial consequence of this property is that every ontological investigation is irremediably local. In fact, there can exist no demonstration or intuition bearing upon Being as the totality of beings, or even as the general site in which beings are disposed.31
This plurality of logics that Badiou will formalise in Logics of Worlds is not only a necessary characteristic of any adequate materialist logic since Cantor, but, I would add, indicates the relevance of a categorial logic to Marx’s critique of political economy. Any world and its attendant logic of the existence of beings must, Badiou argues, necessarily be local and contingent; there exists, Marx argues analogously, no overarching ontology or anthropology of production, labour, or commodities and their value as such, understood transhistorically; each of these and other categories of political economy always necessarily exist within a historically and conceptually distinct ‘social form’ (gesellschaftlich Form) (feudalism, capitalism, communism, etc.).32
The principal consequence of Badiou’s categorial reformulation of logic as a plurality of situated logics is therefore that to the description of any given world there correlates a specific structure of logic: ‘The descriptive characterisation of a thinkable ontological state induces certain logical properties, which are themselves presented in the space of Being, or the universe, that thought describes’.33 This categorial reformulation allows Badiou to escape the formalist dead-end of the linguistic turn of modern logic34 and to construct a novel ‘contemporary theory of logic’. When logic is no longer understood as a normative syntax, but instead as an ‘immanent characteristic’ of possible worlds, it escapes its reduction to the status of a formal science of adequate discourse, to regain instead the ontological dimension it had born from Aristotle to Hegel, but now relegated to its limited and proper domain, as the science of possible worlds according to the ‘cohesion’ or necessary forms of appearance therein.
The final consequence of this reformulation is thus that the remit of logic becomes necessarily limited to the ontological domain of existence, with logic understood specifically as the science of the necessary forms of appearance of any existing object in a given world.35 Since a necessary aspect of Being is that it must take on forms of appearance,36 and since in this view ‘the essence of appearance is relation’, categorial logic can thus demonstrate how any given world can both be pure, inconsistent multiplicity (as Being and Event had described), as well as intrinsically determined as the existence of beings and their attendant and necessary forms of appearance. This affirmation of the strict equivalence of logic and appearance then becomes a shibboleth in Logics of Worlds (‘ “Logic” and “appearance” are one and the same thing’) such that for Badiou the compass of any given logic, as it governs the existence of things in any singular world as such (rather than a particular world or social form such as capitalism), remains strictly limited to the laws that determine the ‘cohesion of appearing’.37
3 Logics of (Capitalist) Worlds
Following his refoundation of contemporary logic as the science of appearing (‘science de l’apparaître’) in the Short Treatise, Logics of Worlds sets itself the consequent task of grasping ‘the requirements of a contemporary materialism’ in the form of a systematic ‘materialist logic’.38 To do so, Badiou sets forth in the crucial second book of Logics what he calls a ‘Greater Logic’ (Grande logique), which he defines as ‘a materialist theory of the coherence of what appears’.39 This Greater Logic takes the form of an exposition and demonstration of the concepts required for the apprehension of the existence, or ‘being-there’ (être-là) (Badiou uses the terms interchangeably) of any multiplicity whatsoever. If Being and Event had articulated Badiou’s understanding of ontology as such, Logics turns to the subordinate problem of the ‘worldly’ existence of any being, apprehended not as pure multiplicity, but according to the laws governing its appearance or ‘localisation’ in the form of a general theory of objects and relations:
The mathematical theory of the pure multiple doubtless exhausts the question of the being of a being, except for the fact that its appearing – logically localised by its relations to other beings – is not ontologically deducible. We therefore need a special logical machinery to account for the intra-worldly cohesion of appearing.40
It is thus the task of Logics’ Greater Logic to set forth this ‘logical machinery’ in the form of a novel series of concepts or ‘logical operators’, the functions that provide any world with its singular coherent forms of appearance, the most important of which for this task is what Badiou names, after Kant, the ‘transcendental’.41
Reasserting in the wake of Russell’s paradox the inexistence of totality as a necessary and governing condition of any contemporary materialist logic, Logics analyses both worlds and their attendant logics in their plurality.42 One of the few significant differences between the refoundation of logic in the Short Treatise and its systematic exposition in Logics is a terminological one. Where the Short Treatise spoke ambiguously of multiple ‘universes’, in Logics Badiou reserves this term to indicate not a world but only the inexistence of the Whole figured as an empty set or void (le vide).43 In its place, he substitutes the more precise term of ‘world’, and crucially indicates by this not a material, extensive space to be filled with beings, but instead only the governing logic of that world.44 This is to formalise the concept of world in the order of thought, to grasp the real structuration that allows for the manifestation of objects as they appear in sensuous lived experience.
It is the concept of the transcendental that then enables Badiou to pass, logically, from the inconsistency of any set in its abstract, ‘neutral’ multiplicity, to account for the existential consistency of any object in a given world. Badiou develops this process in four steps, steps that correspond, in the abstract, to Marx’s initial and familiar demonstration of the basic categories of the commodity form in the first three chapters of Capital: use-value, exchange-value, value as such and its substance (abstract labour), along with the necessary form of appearance of any commodity, the price-form. These steps, given their high degree of abstraction in Logics of Worlds, can be rapidly summarised.
Badiou’s demonstration sets off from the ontological standpoint of Being and Event, and its description of the abstract multiplicity of the elements of any set in its bare neutrality.45 To this corresponds Marx’s concept of the commodity’s use-value: every commodity possesses, and must possess if it is to be sold, its singular identity. The set of all commodities in the capitalist social form consists of an infinite variety of things, each of which – at this general level of abstraction of use-values as such – exists in its singularity, unique unto itself, in its abstract nature as use-value devoid of any systematic relation to other commodities, each existing in sheer externality to all others within this set. ‘The commodity is, first of all’, Marx writes, ‘an external object, a thing which through its qualities satisfies human needs of whatever kind’.46 The set of commodities taken solely as use-values refers each use-value to its singular possession of any given quality whatsoever, the only requirement being the most abstract one, that a commodity in fact have some use-value of whatever kind (lest it be unsellable, and thus, in the capitalist social form, worthless). Were we to reproduce capitalism analytically in this fashion as a structured totality of the Symbolic, a Badiouian rearticulation of the opening sentence of Capital might thus read: ‘The wealth of a society subject to the logic of the world of capitalism appears as a consistent multiplicity of commodities’. To posit being as the abstract multiplicity of the objects in any world entails for Logics of Worlds no more than a passing reference to Being and Event (‘A multiple is only identical to itself, and it is a law of being-qua-being’).47 Marx similarly spends a mere three paragraphs analysing the use-value of commodities.
Exchange-value, in turn, is the crucial category that in Marx’s demonstration initially explains how commodities can enter into relation with one another: the commodity form requires that materially distinct commodities, commodities differing in their nature as use-values, possess identical exchange-values (in their relative amounts) in order to be exchangeable one for the other. Crucially, and even in Marx’s initial, abstract examples of simple exchange logically prior to the price form (‘a quarter of wheat for example, is exchanged for x boot-polish, y silk or z gold’), each exchange requires a definite, numerical quantity through which it relates to all others.48 While it is only with the price form that this quantity will appear and thus exist as identical – if in the barter example ‘x boot-polish, y silk or z gold’, the variables x, y, and z all constitute different amounts, the dollar value of two exchangeable commodities must be identical – the key point to note here is simply the necessity of this numerical count.
Badiou analogously characterises a necessary quantification as the degree of difference between any two things that appear in a world. ‘The logic of appearing’, he writes, ‘necessarily regulates degrees of difference, of a being with respect to itself and of the same with respect to others. These degrees bear witness to the marking of a multiple-being by its coming-into-situation in a world’.49 Badiou argues that every object that exists in a world bears a certain degree of strength of its appearance in relation to all other existing things in that world. It is this relational logic of a world that ‘regulates’ the local manifestation of an object, ‘affecting a being with a variable degree of identity (and consequently of difference) to the other beings of the same world’.50 While Badiou argues that this logic of the transcendental holds for any world whatsoever, his examples often remain obscure (what do we learn from an analysis of the relative strengths of appearance of the objects – leaves, a wall, a shadow – in a painting?), in the case of capitalism, it is luminously clear that every commodity, to be exchangeable, must bear a numerary exchange-value that precisely determines its ‘strength of appearance’ in the world of commodities and their exchange, in other words, its numerical price or exchange-value. ‘There must exist values of identity which indicate, for a given world, to what extent a multiple-being is identical to itself or to some other being of the same world’.51
Marx asked for the first time why under capitalism labour must appear as what he called its ‘value-form’ (Wertform), manifest as the price of labour power (wage), and, furthermore, demonstrated how the formal equality of commodity exchange is nonetheless able to create surplus value. Money, in the form of exchange-value (manifest as the price form), in this view, is no mere convention, but the key relational intermediary that governs and regulates social interaction under capitalism, crucially enabling the socialisation of all private labour. Marx for the first time distinguished transhistorical, material-physiological processes of commodity production (concrete labour) from their specific social forms in a commodity-based society (as abstract labour, the ‘substance’ of value). In this fashion, he demonstrated why in a society governed by commodity exchange, labour must take the historically distinct form of a monetary exchange-value that Marx termed labour power. To count as a value in the capitalist social form, a concrete object or service must necessarily, by definition, have an exchange-value, a value that can and must be manifested in the form of a price. A commodity without a price is simply not a commodity, regardless of whether we treasure or despise it.
The price form of a commodity, Marx crucially shows in the first three sections of Capital, is no mere nominal contrivance or clever invention to facilitate exchange, but is essential and absolutely necessary to the nature of the commodity.52 Since the capitalist social form is axiomatically defined, in Marx’s view, by the predominance of commodities and commodity relations, a thing without an exchange-value simply cannot appear as a thing of value within that social form.53 There is nothing mystical in Marx’s mundane observation: that commodities require a price form is simply another of the necessary consequences of Marx’s initial premise in the first sentence of Capital.54 A thing on the store-shelf without a price, for example, simply cannot be exchanged for money, it remains a tangible thing, perhaps even a privately useful thing, but, under capitalist social relations, it cannot take the social form of an exchangeable commodity.
Marx is not content to describe the dual nature of the commodity as use- and exchange-value; he asks, furthermore, what is it that a numerical exchange-value actually measures? What, in other words, constitutes the substance of value of a commodity? Marx’s famous answer, abstract labour,55 indicates a further point of congruence of Badiou’s abstract logic of worlds with Marx’s systematic demonstration of the singular logic of the capitalist social form, as what Badiou calls the scale (échelle) of evaluation of the strength of appearance of any object. An object’s indexification to a transcendental, what Badiou calls its ‘function of appearance’, must, he argues, offer a numerical measure of something. What, in other words, does the degree of a transcendental measure? Badiou’s answer is perfectly agnostic, given the abstract level of his analysis, and yet its relevance to Marx’s analysis of the substance of value in the capitalist social form is uncanny:
But what are the values of the function of appearing? What measures the degree of identity between two appearances of multiplicities? Here too there is no general or totalising answer. The scale of evaluation of appearing, and thus the logic of a world, depends on the singularity of that world itself. What we can say is that in every world such a scale exists, and it is this scale that we call the transcendental.56
Translating Badiou’s jargon to Marx’s analysis, we can say that the quantitative degree of strength of an object, what Marx calls a commodity’s exchange-value, is the monetary form of appearance of the substance of value of that commodity, what Badiou terms the scale of values inhering in any world. In capitalism, this scale is simply the price or exchange-value of any commodity.
Capitalist society, Marx argues, is that specific historical epoch in which every thing and relation that counts as a value must bear a monetary price. ‘In this form’, Marx concludes, ‘when they are all counted as comparable with the [general equivalent, money], all commodities appear not only as qualitatively equal, as values in general, but also as values of quantitatively comparable magnitude’. Any commodity, under the general, monetary form of value, can thus relate to any other through its equation with the universal equivalent: X (quantity) of (any given commodity) a = $ 1. This, the general capitalist form of appearance of value, is quite simply the price form: in Marx’s example, ‘20 yards of linen = 2 £’.57
Here we should note that Badiou furthermore argues, again analogously to Marx, that the existence of the things composing any world forms a relational system; no single thing (such as a commodity) can exist on its own. Rather, the logic of the necessary forms of appearance of things in a world necessitates a relational order: ‘What is measured or evaluated by the transcendental organisation of a world is in fact the degree of intensity of the difference of appearance of two beings in this world, and not an intensity of appearance considered [ontologically] “in itself” ’.58 Badiou’s transcendental logic of appearance of any world demands that each thing that appears in that world do so in relation to all other things; the intensity of appearance of one thing must be relational, ‘measured by the intensity of appearance of one of them’.59 This ‘conjunction’, Badiou states, is ‘carried’ by one of the two things in relation. The parallelism with Marx’s analysis is here as well uncanny: in Marx’s derivation of the necessity of the price form of appearance of any commodity in the capitalist social form, he famously begins by defining exchange-value as a necessarily relational determination.
While Badiou’s abstract point can be briefly stated as such, Marx’s more complex analysis of the relational nature of the commodity can be summarised in four crucial steps of his argument. In the famous opening sentence of Capital, Marx chooses to begin his demonstration with an axiomatic declaration of the nature of the capitalist social form: ‘The wealth of societies in which the capitalist mode of production prevails appears as an ‘immense collection of commodities’; the individual commodity appears as its elementary form. Our investigation therefore begins with the analysis of the commodity’.60 Marx thus asks his reader to accept axiomatically, initially and without prior logical derivation, that in capitalism – the immediate form of appearance of which is the massive accumulation of commodities – the predominant form of existence as well as the relations among existing things are those laws that govern the exchange of commodities. This is to say that the capitalist social form is, minimally but essentially, distinguished from other social forms by the predominance of both commodities and commodified social relations. His analysis, his initial statement informs the reader, will take as its object this specific social form, and furthermore will investigate not specific individual commodities, as did classical economics, but the total mass of commodities, an undifferentiated, ‘immense heap’ (ungeheure Warensammlung), in relation to which Marx will analyse individual commodities as identical subdivisions or ‘aliquot parts’.61 Marx initiates in this manner not a semantics of capital nor a representation of the structure of capitalism, but instead undertakes a logical demonstration of the essential nature of the real (commodified) social forms of relation in capitalism, to construct, under the aspect of thought (rather than sensuous material extension), as the logic of this world or social form, actual capitalist social relations.62
One could imagine other axiomatic definitions of capitalism. Marx chooses an initial, readily acceptable proposition (that capitalism appears as the accumulation and generalisation of commodities and commodified relations) and from it, the many implications he will demonstrate in his critique follow necessarily. More specifically, if the reader accepts that the predominant form of appearance of capitalism is the accumulation of commodities, this already implies, as Marx will demonstrate, that only commodified things bearing a monetary price form can appear as values under the capitalist social form. Non-commodified things and relations certainly continue to exist (though tend to be monetarised whenever possible), but they do not and cannot count as commodified values when the capitalist social form predominates: they can have no value in capitalism since they have no value-form and thus cannot be objects of commodity exchange.
If, as Marx proposes, the substance of value is social (as abstract labour in general, rather than any specific concrete form of labour), this must mean that value ‘can only appear [as exchange-value] in the social relation between commodity and commodity’. Marx argues that it is only when two (or more) commodities actually confront each other in the exchange process that they take on the social form specific to capitalism, a commonplace value-form of which ‘everyone knows [:] the money-form’.63 To do so, he demonstrates that the value of labour must be expressed not simply as an isolated exchange-value, but must take the specific form of appearance of the universal equivalent, money. To do so, Marx systematically develops his analysis of the social nature of commodity relations:
One commodity (sugar, cotton, indigo) taken in isolation cannot have an exchange-value expressed by itself, since this would be to ‘exchange’ one thing for the same. The exchange-value of a commodity can only be expressed relatively, in a relative form, in some other, second commodity.64
This ‘relative form’ of the expression of value, which Marx analyses in great detail,65 simply describes how one commodity can come to have its value expressed in another commodity. There must, by this reasoning, exist a minimal relation between (at least) two commodities for the substance of value (abstract labour) to find expression (as an exchange-value). Only then does the commodity take a form (in its equivalent) that is distinct from its material, natural form as a use-value, a dual form that Marx has already shown any thing must possess to count as an exchangeable commodity. The social nature of this binary relation lies not merely in the comparison of these two things (as exchange-values). The social aspect of the commodity form finds its first (logical) mode of expression in this simple relative form of relation insofar as the substance of that value (which Marx has argued is abstract, rather than any specific concrete labour), what exchange-value is actually measuring or expressing, is given real concrete form in the social act of equating these materially distinct concrete practices when two use-values (linen, coats) are equated (X coats = Y yards of linen).
This simple relative form of value, however, is ‘insufficient’, Marx notes, and ‘must undergo a series of metamorphoses before it can ripen into the price-form’, the form of appearance adequate to the capitalist social form. A society in which only two commodities are exchanged simply is ‘insufficient’ to determine the capitalist social form as Marx has axiomatically defined it from the first sentence of Capital. In what Marx calls the ‘expanded relative form of value’, a commodity expresses its value not just in a single opposing commodity, but in each and every other commodity; there thus arises an infinite sequence of relative values. The social relation of any given commodity now becomes all-encompassing, and all commodities stand ‘in a relation … with the whole world of commodities [as] an endless sequence’.66
Commodities consequently must find their adequate form of expression in one single commodity, a general equivalent that is socially specified to stand apart and to serve as the measure or expression of value (traditionally, gold). It is finally in this general form of value that commodities achieve their full social form of expression, insofar as only this universal equivalent ‘permit[s] them to appear to each other as exchange-values’.67 This general, social form of relation to all other commodities is therefore necessary given the axiomatic assumption that the capitalist social form is characterised by the general predominance of commodities and commodification.
Badiou’s abstract summary of the relational nature of any system of the transcendental valuations governing the strength of appearance of the objects in a world constitutes, therefore, a precise reformulation of Marx’s analysis of the systematic logic governing the forms of appearance of commodities in the capitalist social form. ‘The transcendental values’, Badiou concludes,
do not directly measure intensities of appearance ‘in themselves’, but rather differences (or identities). When we speak of the value of appearance of a being, we are really designating a sort of synthetic summary of the values of transcendental identity between this being, in this world, and all the other beings appearing in the same world.68
The logic of the forms of appearance of existence in any world, Badiou argues, can be succinctly summarised at this high level of abstraction with only three basic operations: 1) the determination of a minimum value for any thing to appear in that world (in capitalism, that a commodity bear a numerical price); 2) that there exist the possibility of conjoining the degrees of value of any two objects (in capitalism, the determination of what Marx calls a relative exchange-value between two commodities); and 3) the possibility of a ‘global synthesis’ of these values among a specific number of multiples (in capitalism, the necessity of the monetary price form to allow for the universal exchangeability of any and all commodities one for another). The degree of congruence between Badiou’s abstract analysis of the logics of worlds and Marx’s analysis of the necessity governing the forms of appearance of commodities in the capitalist social form is uncanny, all the more so as judging at least by his writings, Badiou seems never to have closely studied Marx’s synthetic demonstration of this logic in the third chapter of Capital.
4 Reading Capital as the Logic of a World
This book has argued that Marx’s demonstration of the nature of value in the capitalist social form, of its forms of appearance (above all as money), and of the essence of surplus value, are not derived from obscure metaphysical elucubrations (as Marx’s academic and empiricist critics have often asserted), nor from the theoretical reversals of a negative-dialectical (Hegelian) logic.69 Marx’s theory is at heart a materialist logic of the real process of the circuit of capital as it passes, without logical negation, through its various forms. Marx was not improvising when he methodically, revision after revision, constructed the various drafts of Capital from 1861 to 1883, but instead sought the most adequate (logical) form of demonstration to present the conceptual order of the capitalist social form. Though he certainly continued to develop and fine tune the diverse categories of his analysis till his last days, he had already conducted his fundamental ‘inquiry’ into the structure of the capitalist social form to arrive at his central notion of the monetary labour theory of value in the final pages of the Grundrisse notebooks.70 Among the greatest accomplishments of Capital, in this view, is to have constructed for readers the real, dynamic logic of the capitalist social form, the immanent logic of a social form, to reveal, as Marx proudly proclaims in his first Preface from 1867, ‘the natural laws of capitalist production, … these tendencies winning their way through and working themselves out with iron necessity’.71
If capitalism appears as the general accumulation of commodities, and if its predominant form of social relations is that of the exchange of commodities, then, Marx argues, a series of necessary consequences immediately follow. What Marx will argue, in the limpid terms of a synthetic logical demonstration, is that given this predominance, abstract labour, the substance of value, must take a monetary form of appearance. To do so, he takes his reader step by step to discover the essential nature of the commodity form. From the dual nature of the commodity as both use- and exchange-value to the substance of value (abstract labour) as the determination of what exchange-value measures in the capitalist social form, Marx’s demonstration of the logic governing the commodity form culminates in his demonstration of the necessity of its monetary form of appearance. If a thing does not possess this dual form, if, specifically, it does not possess an exchange-value, Marx tells us, it cannot appear as, and thus is not, a commodity. Marx categorically and unambiguously affirms this often-overlooked point: ‘Money as a measure of value is the necessary form of appearance of the measure of value which is immanent in commodities, namely labour-time’.72
As does Badiou in his general theory of the logics of worlds, Marx repeatedly emphasises the criterion of appearance in his analysis, not just critically, but positively. This is to say that the object of his critique of the commodity, the substance of its value, and its various value-forms is not only to reveal the illusory, ideological nature of social relations under the capitalist social form. Marx undertakes in his analysis not just a negative critique of commodity fetishism, but also a positive construction of the commodity in the form of a thought-object, to demonstrate the logical necessity of its monetary form of appearance. In arguing that in commodity relations, value must take a monetary form of appearance, Marx is constructing not an adequate syntax of capital, but a materialist logic of the immanent necessity governing the existence of what counts as a thing and possesses value in the capitalist social form (a commodity). Capital is not a well-ordered linguistic apparatus of semantic analysis that would infer or prove the necessary existence of the capitalist social form and its attendant value-forms; instead, given the a priori existence of this social form, Capital simply reconstructs, in the attribute of thought (as opposed to extension), as the logic of this world, a real object. Marx proceeds in materialist fashion from the unproven, axiomatic and reasonable presupposition that accumulated commodities and generally commodified social relations do in fact exist and prevail, and furthermore define the capitalist social form per se, to then reproduce in thought the real structure of this social form via the demonstration of the necessary consequences of this predominance.
The expression of the value of any commodity in the form of the universal equivalent (money) fully abstracts not only from the material use-value of that commodity, but universally, from the material specificity of all commodities, finally to ‘express what is common to all commodities’: abstract labour. The general form of value thus fully expresses the (commodified) social relations of the capitalist social form, in the form of the quantitative abstractions of exchange-values. ‘By this [general] form’, Marx writes, ‘commodities are, for the first time, really brought into relation with each other as values, or permitted to appear to each other as exchange-values’.73 Here again, Marx underscores in his logic of capital the ‘positive nature’ of a form of appearance that allows for a general social relation – between the commodities people exchange – at the same time that it fetishistically obscures the substance of those exchange-values, abstract labour.
Since Marx’s analysis is not an economic theory, but a critique of economic theory, what the demonstration of the necessity of the quantitative, monetary form of appearance of value reveals are not specific numerical values (the object of econometric analyses, from profit rates to unemployment figures), but rather the nature and substance of the various categories that constitute the forms of appearance of the capitalist social form.74 The categorial logic of Capital, in other words, is not a philosophy of ‘substance’ in the sense of the econometric, analytic manipulation of collections of objects or sets (commodities, profits, employment data, GDP, etc.); rather, from the moment Marx defines the substance of value as abstract labour, derivable only as a socially validated relation, Capital unfolds as a category theory of the capitalist social form.75 Among Marx’s unprecedented accomplishments, in his logic of the forms of appearance of value in capitalism, is to have systematically demonstrated the absolute necessity that value take a monetary form of appearance in commodity society.
The consequence of Badiou’s reformulation of the domain and remit of logic as a categorial science of the necessary forms of appearance and existence of the beings in any given world is that without ever considering Marx’s Capital or even the capitalist social form in general, Badiou has quite surprisingly produced a theoretical formalisation of the object of Marx’s critique of political economy, one that constructs the adequate notion of a materialist logic of capitalism. It is not that Logics of Worlds accounts in the abstract, point by point, for the enormous complexity of Capital (though Logics contains many extraordinary formulations that begin to do just that, only a few of which I have indicated here), but, rather, that Badiou’s materialist logic for the first time adequately accounts for the ontological status of Marx’s critique. For while Marx famously takes leave of philosophy in the eleventh thesis on Feuerbach (‘Philosophers have only interpreted the world, in various ways; the point is to change it’), the various ongoing attempts to map the movement of concepts in Capital back onto Hegel’s Logic cannot account for the theoretical and, indeed ontological specificity of this critique, but instead, implicitly or explicitly, tend to reinscribe Marx’s critique of a singular social form as a monist and transhistorical (Hegelian) ontology. Instead, following Badiou, it is clear that despite its incompletion, Capital constitutes nothing less than the historically and theoretically delimited, adequate, and systematic demonstration of the necessary forms of appearance of value in (and only in) the capitalist social form. In other words, Capital should and indeed must be read and understood as the science of the logic governing our world, the capitalist social form.
Badiou 2008, p. 3.
Badiou 2019, p. 43.
Marx 1976, p. 125.
Badiou 2009, p. 96.
Badiou 2019a, p. 63.
Badiou 2018a.
Badiou 2018a, p. 203.
Jacques Lacan, ‘Radiophonie’, cited in Badiou 2018a, p. 155. Note the tortuous, ambivalent grammar and tense structure of Lacan’s original phrasing: ‘Ce que le marxisme a démontré par sa révolution effective : qu’il n’y a nul progrès à attendre de la vérité ni de bien-être, mais seulement le virage de l’impuissance imaginaire à l’impossible qui s’avère d’être le réel à ne se fonder qu’en logique : soit là où j’avertis que l’inconscient siège, mais pas pour dire que la logique de ce virage n’ait pas à se hâter de l’acte’ (Lacan, cited in Badiou 2013b, p. 155).
Badiou 2018a, p. 132, my emphasis.
This programme is encapsulated by the famous Leninist slogan ‘Communism is Soviet power plus the electrification of the whole country’, the redistribution, that is to say, of the wealth of production under the directives of the dictatorship of the proletariat, while leaving untouched, and even expanding as a general productivist imperative, the general social form that to this day demands the endless valorisation of value.
In articulating his critique of Freudian Ego-psychology, Lacan had striven to give a materialist turn to the notion of the symbolic, one that draws it into more direct proximity to Marx’s Spinozist, materialist dialectic. In his 1954 Seminar II, Lacan displaced the process of signification from the intentionality of a subject, to argue instead that the figures of machine language (cybernetics) offered a perfect illustration of the function of the Symbolic. Lacan there reduces meaning (le sens) to the logical assemblage and concatenation of signs, the purely formal relation of logical marks, such that Lacan can assert that ‘the symbolic world is the world of the machine’ (Lacan 1991, p. 47). The symbolic, as Lacan formulated it at this point, is understood to constitute an asubjective system of codes that are supported, in Lacan’s example, by the materiality of computing (rather than the intentionality of an ego). In this view, the Lacanian symbolic would constitute the asubjective system of meaning into which we are thrown, to be interpellated as subjects of Capital.
Lacan, ‘Radiophonie’, cited in Badiou 2018a, p. 151. ‘Ainsi le réel se distingue de la réalité. Ce, pas pour dire qu’il soit inconnaissable, mais qu’il n’y a pas question de s’y connaître, mais de le démontrer’ (Lacan, cited in Badiou 2013b, p. 178).
Roudinesco 1997, pp. 52–4.
Badiou 2018a, p. 152.
In the third section of ‘L’Unique tradition matérialiste’, Althusser – in the course of a broad reflection on the centrality of Spinoza to his thinking – turns to Spinoza’s invention of an adequate materialist (‘nominalist’) knowledge, a knowledge Althusser argues encompasses Spinoza’s discovery of ‘generic constants or invariants … which arise in the existence of singular “cases” ’. Such constants are to be distinguished from the universal generality of ‘laws’, (which would fall under Spinoza’s second genre of knowledge); equally, it is their genericity as constants of any singular case that allows for what Althusser revealingly calls in clinical terms their ‘treatment’, as distinct from any empirical or experimental verification. See Althusser 1997, pp. 3–20.
Badiou 2018a, p. 151.
Badiou 2018a, p. 132.
Badiou 2018a, p. 110.
Badiou 2018a, p. 118, translation modified.
Badiou 2015.
Badiou 2008, p. 214.
Badiou, ‘Comment vivre et penser en un temps d’absolu désorientation?’, talk given at La Commune Aubervilliers, 4 October 2021. Transcription available at
Badiou 2009, p. 55.
Althusser 2014, p. 169.
Translated as Badiou 2006, p. 153, translation modified.
Badiou 2019, pp. 103, 105.
Badiou 2006, p. 105.
Badiou 2006, p. 102, translation modified.
Marx 1976, p. 532.
Badiou 2006, p. 113.
Badiou 2006, p. 161, translation modified.
This is among the key points Moishe Postone first developed in his influential critique of traditional, Left Ricardian Marxism, to substitute instead a reading of Marx as what he calls a ‘categorial’ critique: ‘I use “categorial” to refer to Marx’s attempt to grasp the forms of modern social life by means of the categories of his mature critique. … A categorial reinterpretation, therefore, must focus on Marx’s distinction between value and material wealth; it must show that value is not essentially a market category in his analysis, and that the “law of value” is not simply one of general economic equilibrium’. Postone 1993, pp. 17, 123.
Badiou 2006, p. 113, translation modified.
‘For a long time I had believed this superseding of Platonism involved a destitution of formal logic as the royal path by which we have access to rational languages. Accordingly, and so deeply French in this respect, I rallied to the suspicion that, in the minds of Poincaré and Brunschvicg, was cast upon what they called “logistics” ’. Badiou 2006, pp. 159–60.
Badiou defines appearance as follows: ‘what links a being to the constraint of a local or situated exposure of its manifold-being we will call the “appearing” of this being [l’apparaître de cet étant]’. Badiou 2006, p. 162, translation modified.
Badiou restates this Hegelian point categorically and without demonstration, but, against both Kant and Hegel, in the form of an asubjective phenomenology: ‘It is the being of the existent to appear [Il est de l’être de l’étant d’apparaître], insofar as the totality of Being does not exist. … Appearing in no way depends on space or time, or more generally on any transcendental field whatsoever. It does not depend on a subject whose constitution would be presupposed. The manifold of beings [L’étant-multiple] does not appear for a subject. Instead, it is rather the essence of a being to appear as soon as, unlocalizable within the whole, it must assert the value of its being-multiple [fasse valoir son être-multiple] from the point of view of a non-whole’. Ibid., translation modified.
Badiou 2009, pp. 100–1. ‘We are speaking here of any appearing whatsoever in any world whatsoever. In other words, our operational phenomenology identifies the condition of possibility for the worldliness of a world, or the logic of the localisation for the being-there of any being whatever’. Badiou 2009, p. 102.
Badiou 2009, p. 95.
Badiou 2009, p. 94. This ‘Greater Logic’ Badiou distinguishes from ‘ordinary logic, [i.e.] the formal calculation of propositions and predicates’ which he considers a mere subset of Greater Logic as such. Badiou 2009, p. 173.
Badiou 2009, pp. 121–2.
In explicit contrast to the Kantian transcendental subject, Badiou’s materialist logic is radically pre-subjective, and necessarily so, since Badiou’s conception of the subject – which Book I of Logics further articulates in the wake of the formal simplicity of the concept in Being and Event – appears in subtraction from the governing logic of any world as the bearer, faithful or otherwise, of an Event: ‘The transcendental that is at stake in this book is altogether anterior to every subjective constitution, for it is an immanent given of any situation whatever. … It is what imposes upon every situated multiplicity the constraint of a logic, which is also the law of its appearing, or the rule in accordance with which the ‘there’ of being-there allows the multiple to come forth as essentially bound’. Badiou 2009, p. 101.
Russell’s 1902 Paradox, Badiou summarises, ‘means that it is not true that to a well-defined concept there necessarily corresponds the set of the objects which fall under this concept. This acts as a (real) obstacle to the sovereignty of language: to a well-defined predicate, which consists within language, there may only correspond a real inconsistency (a deficit of multiple-being)’. Badiou 2009, p. 153.
‘We will call universe the (empty) concept of a being of the Whole’. Badiou 2009, p. 102.
‘A world is not an empty place – akin to Newton’s space – which multiple beings would come to inhabit. For a world is nothing but a logic of being-there, and it is identified with the singularity of this logic’. Ibid.
To initiate his Greater Logic, Badiou explicitly invokes this starting point: ‘Previously, I identified [in Being and Event] situations (worlds) with their strict multiple-neutrality. I now [in Logics of Worlds] also envisage them as the site of the being-there of beings’. Badiou 2009, p. 99.
Marx 1976, p. 125.
Badiou 2009, p. 155.
Heinrich analyses in detail the various levels of abstraction in Marx’s presentation across the initial chapters of Capital, pointing out for example that in Chapter One (which I am discussing here), ‘Marx is analysing a capitalistically produced commodity, which is normally exchanged for money, but he is doing so initially not only in abstraction from capital but also in abstraction from money [as well as from the human subjects that exchange commodities]. For that reason, Marx does not yet mention prices. The relation between the money price that we are familiar with in everyday life and exchange-value still has to be explained. … The object of inquiry, the “commodity”, is not simply drawn from experience. Instead, it is constructed, by means of abstraction’. Heinrich 2021, p. 53.
Badiou 2009, p. 118.
Badiou 2009, p. 119.
Badiou 2009, p. 102.
See Murray 2017, p. 273. ‘For classical labour theory’, Murray writes, ‘labour of whatever social sort was the source of value, and money was an afterthought, a “ceremonial form”, as Ricardo called it; the answer to a merely technical problem’. Murray 2017, p. 278. Marx vehemently rejected and critiqued such monetary nominalism of Proudhon and his followers such as Darrimon in the first section of the Grundrisse.
‘All other commodities relate to [the general equivalent] as their expression of value. It’s only this act of “relating” within the world of commodities that makes a certain commodity into the general equivalent, thus endowing it with the ability to buy everything. Importantly, this “relating” is not at all accidental or arbitrary; it is necessary, for only by relating to a general equivalent can commodities relate to each other as values’. Heinrich 2021, p. 143.
‘The busiest streets of London’, Marx observed matter of factly in the 1859 ‘Contribution to the Critique of Political Economy’, ‘are crowded with shops whose show cases display all the riches of the world, Indian shawls, American revolvers, Chinese porcelain, Parisian corsets, furs from Russia and spices from the tropics, but all of these worldly things bear odious, white paper labels with Arabic numerals and then laconic symbols £ s. d. This is how commodities are presented in circulation’. Cited in Murray 2017, p. 471. See Heinrich 2021, pp. 92–143 for an extraordinarily meticulous, word-by-word analysis of Marx’s demonstration of the logical and materialist necessity governing Marx’s monetary labour theory of value.
‘How, then, is the magnitude of this value to be measured? By means of the quantity of the “value-forming substance”, the labour, contained in the article … The labour that forms the substance of value is equal human labour, the expenditure of identical human labour-power’. Marx 1976, p. 129.
Badiou 2009, p. 156.
Marx 1976, pp. 159, 163, emphasis added.
Badiou 2009, p. 123.
Badiou 2009, p. 126.
Marx 1976, p. 125.
See Fred Moseley’s penetrating analysis of this point in Money and Totality (2017).
As Marx affirms in his ‘Notes on Adolph Wagner’: ‘I do not start out from “concepts”, hence I do not start out from “the concept of value”. … What I start out from is the simplest social form in which the labour-product is presented in contemporary society, and this is the “commodity”. I analyse it, and right from the beginning, in the form in which it appears. Here I find that it is, on the one hand, in its natural form, a useful thing, alias a “use-value”, on the other hand, it is a bearer of exchange-value, and from this viewpoint, it is itself “exchange-value”. Further analysis of the latter shows me that exchange-value is only a “form of appearance”, the autonomous mode of presentation of the value contained in the commodity’. Marx 1996, pp. 241–2, emphasis added.
Marx 1976, p. 139.
‘I cannot’, Marx observes, ‘express the value of linen in linen’, for this would simply express a concrete quantity of this item ‘as an object of utility’. Marx 1976, p. 140.
Marx 1976, pp. 139–54.
Marx 1976, p. 155.
Marx 1976, p. 158.
Badiou 2009, p. 127.
On the putative Hegelian, negative-dialectical structure of Capital, see for example Arthur 2002 and Moseley and Smith 2014.
On Marx’s monetary labour theory of value, see Bellofiore 2018, p. 256.
Marx 1976, p. 91.
Marx 1976, pp. 138.
Marx 1976, p. 158, emphasis added.
As Paul Mattick writes, ‘Marx’s model of the capitalist economy does not yield quantitative results that could be compared with economic data; it is capable neither of accounting for the actual price of goods on the market nor of predicting (or even accounting for) such phenomena as the rates of profit obtaining at one time or another. [Rather,] the phenomena (price representations of labour time) with which it is concerned … serve social functions involving the concealment of real relationships rather than their direct manifestation’. Mattick 2019, p. 33.
See Badiou’s comments on this distinction – in response to Jacques Desanti’s critique of the latent ‘substantialism’ of Being and Event – where he presents Logics of Worlds as a category theory of relations between existing things, in Badiou 2019b, pp. 97–105.