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Filozofski vestnik | Volume XLII | Number 2 | 2021 | 159–191 | doi: 10.3986/fv.42.2.08
Alain Badiou’s oeuvre sits uneasily astride a bewildering paradox. Badiou re-
peatedly asserts that the single most imposing impediment to our subjective ac-
cess 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 ‘de-
termination 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 ab-
sente” as Rimbaud writes in Une saison en enfer, is systematically reduced in the 
world of global capitalism to freedom 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 en-
gagement with Marx’s critique of political economy is a veritable empty set. Ba-
diou’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 ep-
iphenomenon, how can a reader hope to formalize 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?
1 Alain Badiou, Number and Numbers, trans. R. Mackay, Cambridge, Polity, 2008, p. 3.
 The research and work on this article was supported by the Czech Science Foundation 
(GAČR) within the project (GA 19-20319S) “From Bolzano to Badiou.” 
2 Alain Badiou, Happiness, trans. A. J. Bartlett and J. Clemens, London, Bloomsbury, 2019, 
p. 43.
* Princeton University, Princeton, New Jersey, USA
Nick Nesbitt*
Capital, Logic of the World
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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
Now, this disinterest is of course odd coming from Badiou, who devotes me-
ticulous care precisely to the formalization 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 brief-
3 Karl Marx, Capital: A Critique of Political Economy, Volume One, trans. B. Fowkes, London, 
Penguin, 1976, p. 125.
4 Alain Badiou, Logics of Worlds. Being and Event, 2, trans. A. Toscano, London, Continuum, 
2009, p. 95.
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capital, logic of the world
est presentation of the Haitian Revolution, and nothing of the essence of slav-
ery and capitalism in the Caribbean, arguably the logics governing these two 
worlds, before and after Toussaint Louverture. Similarly, in Badiou’s “Scholi-
um” 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 dodecophonic composition.
Now, no one can know 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 ex-
position 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 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 here to argue 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 compar-
ative. 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 1994–1995 seminar 
5 Badiou, Happiness, p. 63.
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recently translated to English as Lacan: Anti-philosophy 3.6 Secondly, and while 
I have elsewhere indicated certain general aspects in which Badiou’s ontology 
reproduces certain fundamental gestures of Marx’s materialist critique,7 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 translation and formalization 
of Marx’s Capital. In this view, Capital should quite simply be read as the sys-
tematic 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 dis-
cursive means): the systematic, synthetic demonstration of the necessary forms 
of appearance of commodities in the capitalist social form.
Badiou’s Lacan, Badiou’s (Marx)
While Badiou fully grasps the essential nature of formal demonstration for 
Lacan, his 1994–1995 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 antiphilosophy, 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 symptomat-
ically deaf in these lectures, as elsewhere, to Marx’s scientific discourse – to 
Capital, that is to say. 
6 Alain Badiou, Lacan: Anti-philosophy 3, trans. K. Reinhard and S. Spitzer, New York, Co-
lumbia University Press, 2013.
7 Nick Nesbitt, “The Concept of the Commodity: Badiou and Marx, 1968/1989”, in J. N. 
Berankova, M. Hauser, and N. Nesbitt (eds.), Revolutions for the Future: May 68 and the 
Prague Spring, Lyon, Suture, 2020, pp. 122–139.
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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 uncon-
scious, a demonstration that Badiou suggestively names a “hyperstructural ax-
iomatic”8 – 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 formalization of the categorial structure of capitalism 
understood as social form, as the value-forms of abstract labor, 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, citing 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 impo-
tence 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.9
 
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 
8 Badiou, Lacan: Anti-philosophy 3, p. 203.
9 Jacques Lacan, “Radiophonie”, cited at Badiou, Lacan: Anti-philosophy 3, 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 at Alain Badiou, Le Séminaire. Lacan: L’antiphilosophie 3, 1994-1995, Paris, Fayard, 
2013, p. 155.)
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philosophical imaginary? No, says Lacan, because we must maintain that the “logic 
of this shift” must “hasten the act.”10
The first point to note in Lacan’s original statement is his indication of Marx’s re-
fusal of “truth” and “well-being”. This formulation reiterates Lacan’s post-May 
‘68 rejection of traditional, Leninist Marxism, as both a moralism of the prole-
tariat as the universal class, and Bolshevism as a mere programmatic redistribu-
tionism of wealth. It is Lacan’s rejection of the Leninist misreading of Marx’s cri-
tique, the reduction of the critique of political economy to an ideological moral-
ism of the working class in the form of a politicized redistribution of the wealth 
of production, in short, Left Ricardianism.11 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 prole-
tarian 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 ideo-
logical, as what he calls here the “impotent imaginary.” Virtually no attention, 
including Badiou’s presentation, has been devoted to a number of brief but in-
cisive 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 formalization 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 articu-
lating his own structural demonstration of the nature of the unconscious, had 
occurred long before, in the 1950s seminars, a period of his thought Badiou stu-
diously ignores in these seminars.
10 Badiou, Lacan: Anti-philosophy 3, p. 132. My emphasis.
11 This program 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.
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In this passage, Badiou reads in Lacan’s assertion a rejection of philosophy (“no 
clamor of being or nothingness”), revealingly identifying Marx as an antiphi-
losopher of the same stripe as Lacan himself. In this vein, in order to analyze 
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 elev-
enth 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 antiphilosophers, they are, as Badiou points out re-
garding Lacan, different from all others in that for both, the rejection of philoso-
phies of truth is enacted in the name of the rigor of scientific, apodictic demon-
stration; for Lacan, the demonstration of the structure of the unconscious, for 
Marx, the demonstration of the structure of capitalism.12
Badiou cites Lacan in a further development of what I would call Lacan’s scien-
tific antiphilosophy: “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 demon-
strating it.”13 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 Nietzs-
chean 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 knowl-
edge that Spinoza terms the general and the intuitive (the imaginary remaining 
12 In articulating his critique of Freudian Ego-psychology, Lacan had striven to give a mate-
rialist 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 Sym-
bolic. 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.” Jacques Lacan, The Ego in Freud’s Theory 
and in the Technique of Psychanalysis, 1954-1955. The Seminar of Jacques Lacan, Book II, 
trans. S. Tomaselli, New York, Norton, 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 mean-
ing into which we are thrown, to be interpellated as subjects of Capital. 
13 Jacques Lacan, “Radiophonie”, cited at Badiou, Lacan: Anti-philosophy 3, 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 at Badiou, Lacan: 
L’antiphilosophie, p. 178.)
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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 antiphilosopher, Spinoza nonetheless remained the crucial formative phil-
osophical reference for Lacan, prior to Hegel and Kojève, most explicitly in the 
1932 dissertation, where the entire presentation is framed by citations and anal-
yses of key propositions from the Ethics. No less is Spinoza the crucial refer-
ence 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 dialec-
tics 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 un-
knowable. Here we take the measure of the anti-dialectical dimension of every 
anti-philosophy: the point of the 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, we witness across the development 
of the 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, in which what Jacques Bidet has called various Hegelian theoretical im-
pediments (the identity and non-identity of production and consumption, for 
example, or the merely apparent contradiction between the exchange of equiv-
alents and the realization 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).
14 Badiou, Lacan: Anti-philosophy 3, p. 152.
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Adequate knowledge, knowledge of both the general laws governing the uncon-
scious as well as of the essence of any singular case, governs Lacan’s under-
standing of analysis. While in the Écrits and seminars Lacan develops a sys-
tematic exposition of the structure of the unconscious, it is no accident that we 
are left, as Badiou laments toward the end of the 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 under-
standing of the singular essence of that case, a process which indeed requires, 
along with the scientific mastery of general laws, an improvisational genius at-
tendant 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 never-
theless does not end up being the absolute unknowable but is instead exposed 
to being demonstrated.”16 “Demonstration” is arguably the key epistemologi-
cal concept in the French tradition from Cavailles 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 demon-
stration 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 
15 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 inven-
tion 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 univer-
sal 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 Al-
thusser revealingly calls in clinical terms their “treatment”, as distinct from any empirical 
or experimental verification. See Louis Althusser, “The Only Materialist Tradition, Part I: 
Spinoza”, in W. Montag and T. Stolze (eds.), The New Spinoza, Minneapolis, University of 
Minnesota Press, 1997, pp. 3–20.
16 Badiou, Lacan: Anti-philosophy 3, p. 151.
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Badiou’s final gesture: “Should we say,” Badiou concludes, “that Marx substi-
tuted 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 an-
nounce 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 extraordi-
nary indifference given the systematic, logicist nature of Badiou’s philosophy 
– in scientific knowledge of the object. It is at this point that Badiou’s interpre-
tation 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.
Even more surprising, it is Badiou himself who makes precisely this point, pre-
sented in terms of traditional Marxism’s lack of engagement with Marx’s cat-
egorial demonstration, when he summarizes 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 demonstra-
tion on Badiou’s part and the rush to pronounce the imperative of the political 
act, Marx himself is reduced to a mere (hysterical) political activist, and revo-
lutionary 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 
17 Ibid., p. 132.
18 Ibid., p. 110.
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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 val-
orisation, is reduced to mere imaginary ideological semblance, both in tradition-
al 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 com-
plexity 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 organize 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: 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 formalization 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 formal-
ization.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 subcat-
egory of the capitalist real – for example in capitalism’s dependence upon ab-
stract labor as the substance of value. The essential conclusion of Reading Capi-
tal 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 formalized 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, 
19 Ibid., p. 118, translation modified by N. N.
20 Alain Badiou, À la recherche du réel perdu, Paris, Fayard, 2015.
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toward the construction of a post-capitalist transnationalism, one that surpass-
es the mortal crisis of valorization that is the actuality of posthuman capitalism 
and its real and attendant threat of anthropocenic catastrophe. 
Badiou himself eloquently describes such an orientation as our finite participa-
tion 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
“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 lim-
its of Badiou’s philosophical and political critique: on the one hand, Badiou 
clearly and repeatedly states the obvious, that the overarching and predomi-
nant 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 semi-
nars, 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 sev-
21 Badiou, Number and Numbers, p. 214.
22 Alain Badiou, “Comment vivre et penser en un temps d’absolu désorientation?”, talk given 
at La Commune Aubervilliers, October 4, 2021. Transcription available at http://www.en-
tretemps.asso.fr/Badiou/21-22.html?fbclid=IwAR1oOVauXtOuGfACRHIjSXrDLmBzDgRf87r
pEQx0kTe__gzC-5PakoiHack, accessed 21 November 2021. My translation.
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en books and dozens of chapters, alongside the analyses of worlds from paint-
ing 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 analyze 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 ab-
surd 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. 
To reread Capital after Logics of Worlds, to read its three volumes as a logic of 
capital, is 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 labor 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.24 
To answer this question will require that Badiou reconceive the ontological sta-
tus 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 
23 Badiou, Logics of Worlds, p. 55.
24 Translated as Alain Badiou, Briefings on Existence: A Short Treatise on Transitory Ontology, 
trans. N. Madarasz, Albany, State University of New York Press, 2006, p. 153, translation 
modified by N . N.
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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 localized.”25
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.”26 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 calcula-
tion.”27 In Badiou’s reading, Aristotle’s logic remains ontologically determined 
(“For Aristotle, ontology prescribes logic”) in a manner analogous to that of Fre-
ge, whom Badiou had critiqued in the crucial Meditation 3 of Being and Event.28
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 con-
trast, 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 subse-
25 Alain Badiou, Sometimes, We Are Eternal, Lyon, Suture, 2019, pp. 103, 105.
26 Badiou, Briefings on Existence, p. 105.
27 Ibid., p. 102, translation modified by N. N.
28 See Nesbitt, “The Concept of the Commodity”.
29 Marx, Capital, Vol. 1, p. 532.
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capital, logic of the world
quently replace with “worlds” in Logics) each necessarily bears its own singular 
logic as an immanent, “internal dimension.”30
Key to this categorial reconceptualization 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 unique-
ly 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 formalize 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, la-
bor, or commodities and their value as such, understood transhistorically. Each 
of these and other categories of political economy always necessarily exist with-
in a historically and conceptually distinct “social form” (gesellschaftlich Form) 
(feudalism, capitalism, communism, etc.).32
30 Badiou, Briefings on Existence, p. 113.
31 Ibid., p. 161, translation modified by N. N.
32 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 catego-
rial reinterpretation, therefore, must focus on Marx’s distinction between value and mate-
rial 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.” Moishe 
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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 characterization of 
a thinkable ontological state induces certain logical properties, which are them-
selves 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 reduc-
tion 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 be-
comes 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 
Postone, Time, Labor, and Social Domination: A Reinterpretation of Marx’s Critical Theory, 
Cambridge, Cambridge University Press, 1993, pp. 17, 123.
33 Badiou, Briefings on Existence, p. 113, translation modified by N. N. 
34 “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 Poin-
caré and Brunschvicg, was cast upon what they called ‘logistics.’” Ibid., pp. 159–160.
35 Badiou defines appearance as follows: “what links a being to the constraint of a lo-
cal or situated exposure of its manifold-being we will call the ‘appearing’ of this being 
[l’apparaître de cet étant ].” Ibid., p. 162, translation modified by N. N.
36 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 sub-
ject. 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 by N. N.
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capital, logic of the world
world can both be in its 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
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 con-
cepts 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, appre-
hended not as pure multiplicity, but according to the laws governing its appear-
ance or “localization” 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 localized by 
37 Badiou, Logics of Worlds, pp. 100–101. “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 localization for 
the being-there of any being whatever.” Ibid., p. 102.
38 Ibid., p. 95.
39 Ibid., 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. Ibid., p. 173. 
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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 “tran-
scendental”.41
Reasserting in the wake of Russell’s paradox the inexistence of totality as a nec-
essary and governing condition of any contemporary materialist logic, Logics 
analyzes 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 
formalize the concept of world in the order of thought, to grasp the real struc-
40 Ibid., pp. 121–122.
41 In explicit contrast to the Kantian transcendental subject, Badiou’s materialist logic is rad-
ically 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.” Ibid., p. 101.
42 Russell’s 1902 Paradox, Badiou summarizes, “means that it is not true that to a well-de-
fined 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).” Ibid., p. 153.
43 “We will call universe the (empty) concept of a being of the Whole.” Ibid., p. 102.
44 “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.
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turation that allows for the manifestation of objects as they appear in sensuous 
lived experience.
The concept of the transcendental enables Badiou to pass, logically, from the 
inconsistency of any set in its abstract, “neutral” multiplicity, to account for the 
consistency in the existence 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 labor), 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 summarized.
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 abstrac-
tion 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 commod-
ities, each existing in sheer externality to all others within this set. “The com-
modity 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 unsell-
able, 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 mul-
45 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.” 
Ibid., p. 99.
46 Marx, Capital, Vol. 1, p. 125.
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tiplicity 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 
analyzing 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 dif-
fering 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 quan-
tity will appear 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 characterizes a necessary quantification as the degree of 
difference between any two things that appear in a world. “The logic of appear-
ing,” he writes, “necessarily regulates degrees of difference, of a being with re-
spect 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 
47 Badiou, Logics of Worlds, p. 155.
48 Heinrich analyzes in extraordinary detail the various levels of abstraction in Marx’s presen-
tation across the initial chapters of Capital, pointing out for example that in Chapter One 
(which I am discussing here), “Marx is analyzing 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.” Michael Heinrich, How to 
Read Marx’s Capital, trans. A. Locascio, New York, Monthly Review Press, 2021, p. 53.
49 Badiou, Logics of Worlds, p. 118.
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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 of-
ten 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 ex-
changeable, 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 labor power, and, 
furthermore, demonstrated how the formal equality of commodity exchange is 
nonetheless able to create surplus value. Money, in the form of exchange val-
ue (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 socialization of all private labor. Marx for 
the first time distinguished transhistorical, material-physiological processes 
of commodity production (concrete labor) from their specific social forms in a 
commodity-based society (as abstract labor, the “substance” of value). In this 
fashion, he demonstrated why in a society governed by commodity exchange, 
labor must take the historically distinct form of a monetary exchange value that 
Marx termed labor power. To count as a value in the capitalist social form, a con-
crete 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 ex-
change, but is essential and absolutely necessary to the nature of the commod-
50 Ibid., p. 119.
51 Ibid., p. 102. 
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ity.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 commod-
ities 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 so-
cial 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 ex-
change-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 labor,55 indicates a further point of 
congruence of Badiou’s abstract logic of worlds with Marx’s systematic demon-
52 See Patrick Murray, The Mismeasure of Wealth: Essays on Marx and Social Form, Chicago, 
Haymarket, 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.” Ibid., p. 278. Marx vehe-
mently rejected and critiqued such monetary nominalism of Proudhon and his followers 
such as Darrimon in the first section of the Grundrisse.
53 “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. Impor-
tantly, 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, How to 
Read Marx’s Capital, p. 143.
54 “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, Paisian 
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 at Murray, The Mismeasure of 
Wealth, p. 471. See Heinrich, How to Read Marx’s Capital, pp. 92–143, for an extraordi-
narily meticulous, word-by-word analysis of Marx’s demonstration of the logical and ma-
terialist necessity governing Marx’s monetary labor theory of value. 
55 “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, Capital, Vol. 1, p. 129.
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stration 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 rele-
vance 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 gener-
al or totalizing 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 transcen-
dental.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 mag-
nitude.” Any commodity, under the general, monetary form of value, can thus 
relate to any other through its equation with the universal equivalent: X (quanti-
ty) of (any given commodity) a = $1. This, the general capitalist form of appear-
ance of value, is quite simply the price form: in Marx’s example, “20 yards of 
linen = 2£”.57
56 Badiou, Logics of Worlds, p. 156.
57 Marx, Capital, Vol. 1, pp. 159, 163. Emphasis added by N. N.
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Here we should note that Badiou furthermore argues, again analogously to 
Marx, that the existence of the things composing any world forms a relation-
al system; no single thing can exist on its own. Rather, the logic of the neces-
sary forms of appearance of things in a world necessitates a relational order: 
“What is measured or evaluated by the transcendental organization 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 anal-
ysis 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 com-
plex analysis of the relational nature of the commodity can be summarized 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 cap-
italist mode of production prevails appears as an ‘immense collection of com-
modities’; the individual commodity appears as its elementary form. Our inves-
tigation therefore begins with the analysis of the commodity.”60 Marx thus asks 
his reader to accept, initially and without prior logical derivation, that in capi-
talism – the immediate form of appearance of which is the massive accumula-
tion 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, dis-
tinguished 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 in-
vestigate not specific individual commodities, as did classical economics, but 
58 Badiou, Logics of Worlds, p. 123.
59 Ibid., p. 126.
60 Marx, Capital, Vol. 1, p. 125.
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capital, logic of the world
the total mass of commodities, an undifferentiated, “immense heap” (ungeheure 
Warensammlung), in relation to which Marx will analyze individual commodi-
ties 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 accumu-
lation and generalization 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 appear-
ance 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 monetarized 
whenever possible), but they do not and cannot count as commodified values 
when the capitalist social form predominates: they can have no value in capi-
talism 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 gen-
eral, rather than any specific concrete form of labour), this must mean that value 
61 See Fred Moseley’s penetrating analysis of this point in Money and Totality: A Macro-Mon-
etary Interpretation of Marx’s Logic in “Capital” and the End of the “Transformation Prob-
lem”, Chicago, Haymarket, 2017.
62 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.” Karl Marx, Later Political Writings, T. Carver (ed.), Cambridge, Cambridge 
University Press, 1996, pp. 241–242. Emphasis added by N. N.
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nick nesbitt
“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 so-
cial 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:
1) One commodity (sugar, cotton, indigo) taken in isolation cannot have an ex-
change 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 relative-
ly, in a relative form, in some other, second commodity.64
2) This “relative form” of the expression of value, which Marx analyzes in great 
detail,65 simply describes how one commodity can come to have its value ex-
pressed 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 commodi-
ty 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 in so far 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). 
3) 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-
63 Marx, Capital, Vol. 1, p. 139.
64 “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”. Ibid., p. 140.
65 Ibid., pp. 139–154.
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capital, logic of the world
form,” the form of appearance adequate to the capitalist social form. A society 
in which only two commodities are exchanged simply is “insufficient” to deter-
mine 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-en-
compassing, and all commodities stand “in a relation […] with the whole world 
of commodities [as] an endless sequence.”66
4) 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, in so far 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 characterized by the general predominance of 
commodities and commodification.
Badiou’s abstract summary of the relational nature of any system of the tran-
scendental 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 capi-
talist social form. “The transcendental values,” Badiou concludes,
do not directly measure intensities of appearance ‘in themselves’, but rather dif-
ferences (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
66 Ibid., p. 155.
67 Ibid., p. 158.
68 Badiou, Logics of Worlds, p. 127.
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nick nesbitt
The logic of the forms of appearance of existence in any world, Badiou argues, 
can be succinctly summarized at this high level of abstraction with only three 
basic operations: 1) the determination of a minimum value for any thing to ap-
pear 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 neces-
sity of the monetary price form to allow for the universal exchangeability of any 
and all commodities one for another). The degree of congruence between Badi-
ou’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.
Reading Capital as the Logic of a World
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 ne-
gation, through its various forms. Marx was not improvising when he methodi-
cally, 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 struc-
ture 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. Among 
the greatest accomplishments of Capital, in this view, is to have constructed for 
69 On the putative Hegelian, negative-dialectical structure of Capital, see for example Chris 
Arthur, The New Dialectic and Marx’s Capital, Leiden, Brill, 2002, and F. Moseley and T. 
Smith (eds.), Marx’s Capital and Hegel’s Logic: A Reexamination, Leiden, Brill, 2014.
187
capital, logic of the world
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.”70
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.71 
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 labor) as the determination of what exchange value measures in the 
capitalist social form, Marx’s demonstration of the logic governing the com-
modity form culminates in his demonstration of the necessity of its monetary 
form of appearance.72 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 
70 Marx, Capital, Vol. 1, p. 91.
71 A great many of Marx’s principal propositions in this chapter are articulated in variations 
of this Aristotelean material conditional (as opposed to negative dialectical) form: “It fol-
lows from this that ...”; “If then we disregard the use-value of commodities, only one prop-
erty remains, that of being products of labour”; “If we leave aside the determinate quality 
of productive activity, and therefore the useful character of the labour, what remains is 
its quality of being an expenditure of human labour-power”; “since the magnitude of the 
value of a commodity represents nothing but the quantity of labour embodied in it, it fol-
lows that all commodities, when taken in certain proportions, must be equal in value”; 
“[Commodities’] objective character as values is therefore purely social. From this it fol-
lows self-evidently that [value] can only appear in the social relation between commodity 
and commodity.” Ibid., pp. 127, 128, 134, 136, 139, et passim. Unless I am mistaken, none 
of Marx’s demonstrative formulations in the first three chapters of Capital take the form of 
Hegelian negative dialectical logic, as in the classic example of the beginning of the Logic: 
“Being in general; being, and nothing else, without further determination” which is dia-
lectically sublated to reveal “the unity of being and non-being [or] the identity of identity 
and non-identity.” G. W. F. Hegel, The Science of Logic, trans. G. di Giovanni, Cambridge, 
Cambridge University Press, 2010. pp. 47, 51.
72 I analyze Marx’s demonstration in greater detail, as well as its implications for the nature 
of capitalist slavery specifically, in the second chapter of The Price of Slavery: Capitalism 
and Revolution in the Caribbean, Charlottesville, University of Virginia Press, 2022. See 
also Heinrich, How to Read Marx’s Capital.
188
nick nesbitt
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 
labor-time.”73
As does Badiou in his general theory of the logics of worlds, Marx repeatedly 
emphasizes 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 illu-
sory, 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-ob-
ject, to demonstrate the logical necessity of its monetary form of appearance. 
In arguing that in commodity relations, value must take a monetary form of ap-
pearance, Marx is constructing not an adequate syntax of capital, but a materi-
alist logic of the immanent necessity governing the existence of what counts as 
things and possesses value in the capitalist social form (commodities). 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 com-
modities 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 neces-
sary consequences of this predominance.
The expression of the value of any commodity in the form of the universal equiv-
alent (money) fully abstracts not only from the material use-value of that com-
modity, 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 cap-
italist social form, in the form of the quantitative abstractions of exchange val-
ues. “By this [general] form,” Marx writes, “commodities are, for the first time, 
73 Marx, Capital, Vol. 1, p. 138.
189
capital, logic of the world
really brought into relation with each other as values, or permitted to appear to 
each other as exchange-values.”74 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 the-
ory, 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.75 The categorial logic of Capital, in oth-
er 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 sub-
stance of value as abstract labour, derivable only as a socially validated rela-
tion, Capital unfolds as a category theory of the capitalist social form.76 Marx’s 
unprecedented accomplishment, 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 
74 Ibid., p. 158. Emphasis added by N. N.
75 As Paul Mattick writes, “Marx’s model of the capitalist economy does not yield quantita-
tive 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.” 
Paul Mattick, Theory as Critique: Essays on “Capital”, Chicago, Haymarket, 2019, p. 33.
76 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, Sometimes, We Are Eternal, 
pp. 97–105.
190
nick nesbitt
theoretical formalization 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 enor-
mous complexity of Capital (though Logics contains many extraordinary formu-
lations 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 He-
gel’s Logic arguably 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 universal and transhistorical (He-
gelian) ontology. Instead, following Badiou, it is clear that despite its incom-
pletion, 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.
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