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* https://orcid.org/ 0009-0009-1910-2027 | mnaderi000@gmail.com
Filozofski vestnik | Volume XLIII | Number 3 | 2022 | 7–51 | cc by-nc-nd 4.0 | doi: 10.3986/FV.43.3.01
Reza Naderi*
The Place of the Subject in Badiou’s Theory
of Discipline
Badiou and the Theory of Discipline
The main motivation for the theory of discipline resides in Badiou’s desire to 
answer the following question: if there are forms of human inquiry that we can 
call thinking, what are the conditions in which these forms can acquire max-
imality? What are the conditions in which the solutions to particular impass-
es might appear as a restriction on the space of what we can actually think 
and conceive? We think this is the motivation that has led Badiou throughout 
his career, as a logician, as a political thinker, as a militant, and as a philoso-
pher. In other words, Badiou’s encounter with various subject matters has al-
ways been from the point of view of examining whether the subject matter in 
question struggles with any internal or external commitments that suture them 
to avowed or unavowed presuppositions. Badiou’s category of truth should be 
placed within such a context.
For Badiou, truth is that point where a subject matter, which we call a discipline, 
is pushed beyond its own point of impasse. This impasse, upon closer examina-
tion, is always caused by the subject matter being sutured to explicit or implicit 
presuppositions. Badiou’s answer to this is very simple: de-suture from opinion. 
How do we know that thought is able to de-suture from opinion? Because math-
ematics exists! Mathematics is the singular form of thought that has been able 
to rupture with doxa. So, the effective, historical, and independent existence of 
mathematics provides a paradigm for the possibility of being able to de-suture 
from opinion. This constitutes Badiou’s philosophical programme for our time: 
a return to classicism, and in particular to Plato, and the essence of this return 
is to re-establish mathematics as the paradigm of thinking for philosophy. In 
effect, in Badiou’s assessment, we are still living in the Romantic era, in the era 
of poets, inaugurated by Hegel. The mark of this era is precisely the banishment 
of mathematics as the paradigm for thinking and its replacement with poetry. 
Under the reign of poets, we are no longer eternal, but mortals bound to fini-
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reza naderi
tude. The gravest consequence of the banishment of mathematics is the banish-
ment of the category of infinite as the basis of our thinking.
For Badiou, thinking maximally is possible only if first and foremost we are com-
mitted to the infinite. In that sense, all forms of genuine thinking occur with this 
commitment in place, even if philosophy may operate differently and under the 
dominance of the finite, as it does today. A discipline is one way of formalizing 
rigorous thinking that distinguishes itself by such a commitment. A discipline is 
a space within which pure thinking becomes actual, within which the commit-
ment to the infinite happens in three concomitant and compossible dimensions.
First is the dimension that determines the space of thinking with no reference to 
its exterior. There is the inside of the discipline, but there is no outside. Hence, 
the discipline is not defined by what is exterior to it, because the discipline does 
not recognize its exterior as something that exists. I call this dimension of the 
discipline its interiority. A discipline is defined by an interiority that does not 
have exteriority, or in Lacan’s language, the Other of the discipline is extimate. 
Second, a discipline does not begin according to a principle or ground. While 
disciplines do not recognize anything external to themselves, they are able to 
recognize each other. Hence, they carve out a space of operations for them-
selves. Such a space is not created at the expense of other disciplines, but is 
born anew by the discipline itself. We think this takes place when thought op-
erates in an axiomatic register. Axioms are precisely presuppositions that are 
avowed. They are generalities, not generalizations. In that sense, while they are 
independent of each other, and one does not provide a ground for the other, to-
gether they create a space for thinking that is groundless and principle-free. I 
call this dimension of a discipline its beginning. According to this dimension, 
all disciplines are axiomatic forms of thinking. Axioms have emerged in order to 
make possible thinking in its interiority.
Third, disciplines progress. They advance when they are challenged by im-
passes that they can formulate in their internal language. Disciplines are his-
torical sites, which means that they are evental. As per Gödel, the “real” of 
any sufficiently complex axiomatic system is that it is possible to build state-
ments (known as Gödel statements) that are undecidable within that system. 
Mathematics teaches us that it is around these points (the undecidable state-
9
the place of the subject in badiou’s theory of discipline
ments) that a revolution in a discipline usually takes place. A great example 
of this is the famous Continuum Hypothesis. I call the tendency in disciplines 
to push beyond their points of undecidability and towards the maximality of 
thinking the novelty of disciplines. 
These three dimensions of disciplines, their beginning, interiority, and novelty, 
are concomitant and compossible, and the condition of their possibility is com-
mitment to the infinite.
Disciplinary thinking is akin to dialectical thinking in that both carve out a 
space for thinking as an interiority. Dialectical thinking is also only concerned 
with the interiority of the One, with unfolding discontinuities within a coherent 
logical space. But for the discipline, there is no One other than the closure of a 
space of operations that is circumscribed by its axioms – it is not dependent on 
some initial grounds or fundamental derivation of its logic. Disciplinary think-
ing is also akin to dialectics in the dimension of novelty. Dialectics is never the 
result of supplementation from outside. However, unlike dialectical thinking, 
novelty is not the result of the sublation of two to one. It always begins with 
the One of the discipline and splits this into what the discipline discerns and 
“in-discerns” about itself. It is precisely within the category of novelty and the 
orientation towards what is possible that the discipline manifests its character 
as a wholly subjective process without an object. Within the theory of discipline, 
the subjective is an index of the dimension of novelty.
The dimension of beginning is where discipline is most different from dialec-
tics. Thinking the beginning presents an inherent discontinuity because this 
thinking must perform an irremediable break from the sovereignty of doxa, one 
that is more akin to producing creative hypotheses and critical interventions. 
Axiomatic thinking is the only mode of thinking proper to this violent disconti-
nuity; it is the only mode of thought that makes its own presuppositions explicit – 
rather than the presuppositions of the doxa. Axiomatic set theory provides a 
way of thinking the dialectic of the universal and particular through generalities 
rather than generalization. The relation between the particular and the univer-
sal has usually been thought through generalization: the particular was think-
able by being categorized under the universal. In contrast, axiomatic thinking 
approaches a situation through a set of generalities (axioms) whose deductive 
power allows us to show what makes a situation thinkable. If the particular is 
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unthinkable according to the system of sentences drawn from given axioms, 
then we add a new axiom that is consistent with the others so that this particu-
lar becomes thinkable. Moreover, by relying on ideas rather than ideals, we can 
experiment with the formal system directly, even in advance of the demands of 
the real; the real of the formal system is its own consistency. This form of deduc-
tive reasoning is impossible under the regime of generalization, since generali-
zations are related to one another (and ultimately derived from a super-genre), 
whereas generalities are independent of one another. On the other hand, the 
dialectic is generally ambivalent to what it begins with, and is therefore suscep-
tible to generalization and requires a fixed foundation. As a result, dialectical 
thinking appears as a region or restriction of disciplinary thinking.
A formal system is part of every discipline. But since a discipline is a homogene-
ous region of thought, every part of this region can think its other parts. The best 
example of this is mathematics. A region of mathematics, say geometry, can be 
the object of formalization for another part, such as algebra, according to which 
the latter part can think (i.e. formalize) the former part. But by no means does 
this permanently fixate one part as the object and the other part as the subject 
since geometry can equally formalize algebra. In model theoretical language, 
the parts of a discipline can act as both a formal system and the model for a 
formal system. Disciplinary practice gains huge insight into its parts, and ulti-
mately the discipline as a whole, by being able to think a part through another 
part of the discipline. This means that through disciplinary theories “about” a 
discipline, the discipline produces more of its own. This becomes clearer when a 
discipline is compared to a discourse. Discourses, for example the philosophy of 
science, have disciplines, such as science, as their subject but do not produce, 
nor claim to produce, disciplinary theories themselves. In all their forms, dis-
courses attempt to find from outside of a given discipline the unifying principle 
according to which the discipline can be defined and organized. Discourses, in 
that sense, transcend the disciplines they study. In contrast, the assertions that 
a discipline produces about itself are part of the discipline itself. Discipline is 
immanence. It embeds what it thinks. 
Disciplines are also highly experimental. What constitutes the so-called “ob-
jects” of a disciplinary practice are elements of the model that satisfy the prop-
ositions of a formal system. But recall that what is now a model for a formal 
system could later be a formal system in its own right. In this sense, a discipline 
11
the place of the subject in badiou’s theory of discipline
does not distinguish between subject and object. The experimentality of disci-
plines also stems from this character. The set of propositions that constitute a 
formal system always refers to a set. That is, the sentences within that system 
always seek interpretations within sets of objects of different kinds. The fact that 
the sentences of a formal system require interpretation implies that those sen-
tences are not universally valid or invalid in the same way that logical sentences 
are. This means that in the last instance, those sentences are axiomatic in na-
ture; they are produced according to decisions that are not based on some prior 
self-evident principles. However, the opposite of this is also true: every axiomat-
ic system requires a structure for its interpretation. This points to an extraordi-
nary experimental vocation of formalism, and in that sense the material struc-
tures, from machines to laboratories, are thoroughly formal. The experimental 
nature of disciplines is due to their axiomatic nature. Axioms are responsible for 
the rigorous experimental protocol of formal systems. 
The axiomatic nature of disciplines makes them evental. There are conditions 
under which the formal systems contained in a discipline clash with each oth-
er and with the discipline’s founding axioms. This is a mathematical certainty. 
It is under those circumstances that a discipline is subjectivized. It thinks its 
own foundation and through this, under certain conditions, it expands those 
foundations to open up new territories for its thinking. For this subjectivation, 
a substantial part of the body of a discipline (from theories to models and prac-
titioners, to pens and paper, to signs and syntagma) must be activated towards 
the new possibilities that lie around the discipline’s evental site – which points 
towards a new existence that was not there. If enough of the discipline’s body 
is activated in this way, then the discipline can redefine itself to expand its ter-
ritory and to absorb the new possibilities into its domain. The discipline thus 
expands. But prior to this, from a logical standpoint, the condition for this sub-
jectivation is precisely the practice within a discipline by which parts of the dis-
cipline appear and are interpreted by other parts of the discipline. That is, prior 
to any subjectivation, and as its logical condition, there is an objective phenom-
enology that is in effect and which constitutes “the life” of the discipline.
The Place of the Subject
Before we elaborate on the ways in which the idea of the infinite reconstructs the 
category of the subject, it is useful to understand why this category has such a 
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reza naderi
central place in Badiou’s thought. Indeed, why do we need a new thinking of the 
subject in the first place? Badiou’s answer is that the subject is that operator of 
philosophy from which, in our time, the compossibility of Badiou’s four generic 
procedures is drawn. 
We recall from Manifesto for Philosophy1 that, for Badiou, philosophy is the 
space for the compossibility of all four generic procedures: it is where these ge-
neric procedures together form a philosophical vision compatible with each par-
ticular condition. This means the following three things:
1. That there is an operation in philosophy that brings together the four condi-
tions and helps us comprehend a certain philosophical period.
2. Such comprehension enables us to examine the philosophical period we are 
in, whose name, according to Badiou, is modern philosophy.
3. The period we call modernity has not ended, and thereby modern philosophy 
continues.
Philosophy has conceptual operators by which it configures its conditions. This 
configuration is what orients thought in each epoch, and it is the way philosophy 
thinks about a given epoch, as associated with a particular configuration. To un-
derstand these operators of philosophy, the first thing to note is that one of these 
conditions, or generic procedures, is always closest to an evental site and serves 
as the main referent for the deployment of the compossibility of the conditions.2 
Such was the case for Plato, Badiou proclaims. There were two events within the 
situation relevant to Plato: the emergence of the city-state and the shift in the 
theory of sizes from the Pythagoreans, based on arithmetic, to the geometrical 
and continuous method of Eudoxus. Plato invented this configuration capability 
of philosophy and thereby created, for the first time, a space for both conditions: 
the operator of this configuration was the theory of Forms – operable across 
both politics and mathematics. At the same time, this operator bestowed a sus-
picious status on poetry and made love an indiscernible – that which is neither 
discourse (logos) nor knowledge (epistémé).
1 Alain Badiou, Manifesto for Philosophy, trans. N. Madarasz, Albany, State University of 
New York Press, 1999.
2 Ibid., p. 41.
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the place of the subject in badiou’s theory of discipline
A philosophical period is one in which “a certain configuration, specified by a 
dominant condition, persists. Throughout such a period, the operators of com-
possibility depend on this specification. A period creates a nexus out of the four 
generic procedures, in the singular post-evental state in which a generic proce-
dure is inscribed into the space of thinking and circulation that philosophically 
serves as the determination of the time.”3 In the case of Plato, Forms are under 
the domination of the matheme (and thus mathematics acts as the dominating 
condition over politics). Plato asserts this in his Republic by having the gover-
nor educated in arithmetic and geometry. At the same time, imitative poetry is 
kept at bay, as that form of art that demonstrates the flexibility of language to 
sustain sophistry.
The question for us is now whether there is a modern period of philosophy. The 
postmodern declaration in some way corroborates this: the modern period did 
exist and is now over, according to the postmodern philosophers. If so, then the 
question is: What was (or still is) the operator of the configuration of the modern 
period? To understand that, Badiou first enumerates three distinct episodes that 
should fall in such a period:
1. Europe’s classical age, of Descartes and Leibniz, in which the mathematical 
condition was dominant under the Galilean event, whose intervention intro-
duced the infinite into the matheme.
2. Europe’s romantic age, of Rousseau and Hegel, in which the historic-politi-
cal condition was dominant under the event of the French Revolution.
3. Europe’s post-romantic age, of Nietzsche and Heidegger, in which art, with 
poetry at its heart, was the dominant condition. Badiou does not name an 
event for this episode, but mentions that the return to art was “through an 
anti-Platonic retroaction, in the operators by which philosophy designated 
our time as that of a forgetful nihilism.”4 
In this temporal sequence, we observe a movement of principle, from which the 
compossibility of the generic procedure is drawn, from the three conditions in-
volved in these episodes: science dominant in the first, politics in the second, 
and art in the third. But within this displacement, there is still an invariant, 
3 Ibid., p. 42.
4 Ibid., p. 43.
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reza naderi
from Descartes up to Nietzsche, Freud, Husserl, and Lacan. This invariant is the 
theme of the subject. This theme endured devastating destruction by Heidegger 
and his followers, but was subsequently recast within Marxism (the subject of 
revolution) and psychoanalysis (the subject of the clinic). 
This means, for Badiou, that the category of the subject stands for the operator 
of the configuration that designates the period that we call modernity.
According to Badiou, such is the question of the fate of philosophy: Is our time 
up to the task of upholding and reinserting the category of the subject back into 
philosophical discourse, now dominated by linguistic and analytical traditions? 
Our thesis points to the new orientation of thought constituted by the Cantorian 
invention and axiomatic thought as that which overhauls the thinking of the 
subject, which we sketch by closely tracking it through the theory of discipline. 
As much as the Cantorian revolution has caused a total reorientation of thought, 
in Badiou’s eyes, another disorientation had already been at the essence of what 
he names the Age of Poets, whose central figures, from Hölderlin to Celan, be-
gan to think outside the categories of the object and the subject. But, there is a 
difference: while the Age of Poets did disorient thought by playing down the role 
of knowledge in the thinking of truths, today we need a reorientation. Therein 
lies the difference between Heidegger and Badiou. While for Heidegger the des-
titution of metaphysics, and the opposition of knowledge and truth, on their 
own, inform an orientation of thought according to which the philosopher will 
only need to harken to the poet, for Badiou there still remains one more step; a 
step that our poets were unable – or perhaps lacked the conviction – to take. 
This step consists of an effort to rethink in the lineage of Cartesian meditation. 
So, while a disorientation of thought had already been accomplished in at least 
continental Europe, the reorientation is something that remains a task for phi-
losophy. In summary, philosophy must affirm that “Disorientation can be con-
ceptualized.”5 Badiou maintains that the category of the subject is the key to this 
conceptualization and reorientation.
That is why, throughout his career, Badiou’s interventions have always taken 
place around the question of the subject: What can philosophy say (or not say) 
5 Ibid., p. 74.
15
the place of the subject in badiou’s theory of discipline
about the subject? The category of the subject has been a (if not the) central cat-
egory of Badiou’s philosophy. Early in his career, and in reaction to the proposal 
that grounds science in general, and the foundation of mathematics in particu-
lar, on the repressed figure of the subject, in his seminal essay “Mark and Lack”6 
Badiou affirms that science has no subject because science does not have a lack 
that it cannot fill itself. In other words, Miller is wrong to look for some place 
within the signifying chain in order to metaphysically or metaphorically estab-
lish the primitive of the Lacanian psychoanalytical subject. The discipline of 
science does not rely on something exterior to the discipline.
Having banished the subject from the discipline (of science), in Theory of the 
Subject7 Badiou ruminates on another aporia: How can we think novelty in a 
structure? This thinking took us from the analysis of Hegel’s Logic and the rela-
tion of Something and Other to the notion of periodization. We saw that while 
Hegel’s Logic contains resources to think novelty beyond mere circularity, and 
hence according to the schema of periodization, he does not have an explicit 
enough categorization of the two dialectics, which Badiou denoted as structur-
al dialectic (SD) and historical dialectic (HD). Badiou finds a more advanced 
theorization in Lacan. In this regard, he thinks that the great dialectician after 
Hegel was not Marx, Lenin, Sartre, or Althusser, but Lacan. According to late 
Lacan, an understanding of jouissance and the signifier requires a logic similar 
to what Badiou calls HD, in that the relation of these two is no longer that of a 
situation (language) and the situated (speech), which is captured through the 
structural logic of whole-part. Instead, language itself is situated and a source 
of exception. Singularity and regularity are both generated through the practice 
of language. Therefore, the relation between jouissance and signifier is better 
captured through the relation of forces, which is the central grammar of the his-
torical dialectic. 
While Lacan’s thought can make irregularity thinkable, its model is based on 
the clinic. Badiou takes this theory and transposes it to the model that supports 
politics: the State, masses, and classes. While this theory justifies irregularity 
as a force with the same legitimacy and potency as the force of structure, in the 
6 Alain Badiou, “Mark and Lack: On Zero”, in P. Hallward and K. Peden (eds.), Concept and 
Form Volume One, London, New York, Verso, 2012, pp. 159–185.
7 Alain Badiou, Theory of the Subject, trans. B. Bosteels, London, Continuum, 2009.
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reza naderi
life of an individual subject in the clinic, the analysis must finally find a cure in 
the structure of one’s symbolic constitution. By changing the model from a cor-
relate of analysis to a correlate of politics, Badiou expands the scope in which 
the concept of consistency emanates and operates. In the Lacanian model, con-
sistency belongs to the imaginary register: while the knot is in the real, its effect 
is registered in the imaginary as consistency. When the knot is cut, this effect of 
consistency is also destroyed, as the knot is the cause (in the real) and the con-
sistency is the effect (in the imaginary). There is an inconsistency here: from the 
way the singularity of the jouissance comes to cohabit the very constitution of 
the regularity of the language – this regularity being in fact the retroactive effect 
of singularity – we come back to the primacy of regularity again, which is pro-
tected by the knot. But why such a compromise? The answer, in my view, is that 
the model operative in analysis is insufficient to sustain the radicalism of which 
the theory is capable. Using the model for politics, Badiou shows that the real of 
the masses is not only thinkable, it is the source of consistency, the source of a 
newfound regularity. What Lacan’s thought was capable of – the relation of sin-
gularity and regularity – had to eventually recoil in the face of the weak model 
to which he had to apply it – a model that was too limited to sustain the conse-
quences of what was possible to think. And here was precisely where the subject 
as the black sheep of materialism came into the picture: the real of the (political) 
subject (i.e. the masses) is the provider and guarantor of consistency.
What does the move from interiority to novelty tell us about the category of the 
subject? The logic of the signifier borrowed its conception of the subject from 
outside of the logic of structure. In other words, it performed an ideological con-
struction of this category. Badiou dismissed this conception of the subject by 
maintaining that the structure is an absolute interiority whose consistency is 
not dependent on anything from outside. The logic of force, however, reinsti-
tutes the subject, but this time within the constitution of the structure itself. This 
way, while maintaining the absolute interiority of structure, a gap is opened up 
within the structure itself which harbors the subject – the subject is anchored in 
the very gap between the surface of the law and the real of the forces that the law 
“in-discerns”, but in whose qualitative distinctions it depends. Subjectivization 
constitutes the moment when this qualitative indiscernible erupts to the sur-
face, and the subjective process is that which keeps this eruption at the level of 
the ongoing operations of the structure. Novelty is the consistency brought forth 
by the subjective process, and thereby belongs to the category of the subject. 
17
the place of the subject in badiou’s theory of discipline
From this, we now understand why Badiou’s salient philosophical undertaking 
during this phase of his career is captured within a book entitled Theory of the 
Subject: novelty is a category that requires a theory about the embedded subject. 
The subject is that which fastens the interiority and novelty within the boundary 
of a discipline. 
Hence, for Badiou, the Age of Poets establishes that access to truth presuppos-
es the destitution of the category of object as what presents the being: object, 
in this view, is a correlate of knowledge and not of being or truth. For Badiou, 
the task of philosophy is to sharpen the achievement of poets from Hölderlin 
to Celan, whose insights take philosophy in an opposite direction from what 
the philosophical avatar of that age, Heidegger, had pronounced. In fact, con-
trary to what Heidegger had surmised from the poets, the destitution of the ob-
ject does not mean the destitution of the subject. Rather, it enjoins us to think 
the subject independently, without a vis-a-vis. For Badiou, the ability to think 
the subject without object consists of a possible renaissance for philosophy.8 
While Heidegger and the post-structural milieu were pronouncing the end of 
the subject, Marxism and psychoanalysis proposed its restoration. But both 
schools, ironically similar to Heidegger, missed the great insight of the poets 
and restored the subject at the expense of also restoring a form of object and 
objectivity (the proletariat and the object of desire). So, while their return to the 
category of the subject was warranted, their construction still owes too much to 
objectivity. For Badiou then, the task of philosophy involves a complete commit-
ment to the withdrawal of the object, while traversing those theories that either 
abandon the subject along with the object, or buttress the subject while still be-
ing unable to forgo the object.
Below, we will examine one of these traversals, and it should come as no sur-
prise that the philosopher whose thoughts are material to his task is none other 
than Lacan. Nor should it come as a surprise that, in our view, the main coor-
dinates of this traversal are two pivotal thoughts: Badiou’s commitment to the 
maximality of thinking and the idea of infinity. 
Accordingly, we picked two encounters with Lacan involving the category of 
the subject, both definitive of what Badiou intends for this category. The first 
8 Badiou, Manifesto for Philosophy, p. 93.
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reza naderi
encounter is the very last meditation of Being and Event9, and the second is 
“Subject and Infinity”.10 Our reading of these texts will take place through our 
main theoretical apparatus: the discipline at whose center is the idea of infini-
ty. Through this, it will become evident, during the first encounter, that Lacan’s 
formulation of the subject of the unconscious owes too much to the wrong side 
of Descartes: it owes too much to the I in I think. The proposal of this chapter 
begins by showing that Lacan’s theory of the subject relies too heavily on the 
count-as-one of an individual, and thereby it is not capable of overcoming the 
Sartrean reflexive subject. Disciplinary thinking shifts the emphasis from I to 
think, or more precisely, “being thinks”. The real, which is the it, is still a deriv-
ative of Descartes’, rather than a recomposition of thought from the ground up. 
In this sense, we will investigate the thesis that the true motivation of Descartes’ 
cogito ergo sum is disciplinary thinking, in which the new category of the sub-
ject will arise.
The second encounter takes place around Lacan’s treatment of infinity. Lacan 
actually had engaged with Cantor in Seminar XIX, but makes it very clear that, 
for him, actual infinities are imaginary. However, Cantor is still useful to Lacan: 
the concept of actual multiplicity, understood as a set, authorizes psychoanaly-
sis to speak of what the latter calls a unary trait. The theory of sets thinks multi-
ples without totalization; it only thinks the unicity of each multiple. Lacan points 
out how psychoanalysis is still stuck with Freudian doctrine, because it needs 
a representation of otherness. However, this requires a unifying otherness. So, 
we can never operate in the model of the psychic apparatus with the idea that 
something of otherness is captured by the structure. In Badiou’s terminology, 
nothing of the outplace is preserved as an outplace by the place. We are author-
ized to move further and no longer think identification and representation only 
in these terms, because Cantorian mathematics has shown us that multiplicity 
without unity, and only with unicity, is perfectly thinkable. We can distinguish 
between multiplicities, without unintentionally unifying them. So, the exten-
sive treatment of multiplicities authorizes us to think otherness without sub-
suming it as a finite multiple under a common property. Therefore, for Lacan, 
9 Alain Badiou, “Meditation Thirty-Seven: Descartes/Lacan”, in Being and Event, trans. O. 
Feltham, London, Continuum, pp. 431–435.
10 Alain Badiou, “Subject and Infinity”, in Conditions, London, Continuum, trans. S. Corco-
ran, pp. 211–227.
19
the place of the subject in badiou’s theory of discipline
the gift of Cantor is the power to think unicity, which preserves otherness. This 
is what Lacan means by the unary trait, which states that something of the oth-
erness is preserved by a trait. But, in Seminar XX, as we shall see shortly while 
reading Badiou’s intervention, Lacan still maintains that the infinite must be 
thought of as inaccessible, something fictitious. The fact that we can think con-
sistently about actual infinities and derive positive results from such thinking 
is totally out of Lacan’s reach, not because it is unthinkable, but because Lacan 
has no name for that which is both inaccessible and consistent. This includes 
the fact that infinity is totally mis-measured by finitude, and is totally indiscern-
ible from the standpoint of countable situations, but is still thinkable. These two 
positions, in successive seminars of Lacan, are, of course, inconsistent. Lacan 
accepts that it is possible to think the unicity of the multiplicity in extension 
(that is, in their existence), while claiming that we cannot accept actual infinity. 
For this study, the Cartesian and Cantorian frameworks are combined: there is 
a way to think of the cogito and infinity within the same framework, which we 
call discipline. We claim that a rejuvenated understanding of the subject, in line 
with Badiou’s work, involves a reconstruction of the subject using the idea of 
the infinite, and through this reconstruction we find that it is not the I or it that 
thinks, but the discipline itself. Let us now elaborate on these points.
The Subject and Cogito
For Lacan, the imperative to return to Freud was doubled by the directive to also 
return to Descartes. How can these two imperatives work together, Badiou asks. 
He provides the answer as follows:
The key to the matter resides in the statement that the subject of psychoanaly-
sis is none other than the subject of science. This identity, however, can only be 
grasped by attempting to think the subject in its place. What localizes the subject 
is the point at which Freud can only be understood within the heritage of the Car-
tesian gesture, and at which he subverts, via dislocation, the latter’s pure coinci-
dence with self, its reflexive transparency.11
11 Badiou, Being and Event, p. 431.
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reza naderi
Understanding the subject in its place is the key to understanding how the sub-
ject of the unconscious can only be understood as the cogito. How does Lacan 
link the Cartesian subject and the subject of psychoanalysis? What does the 
term subject mean for Lacan? He provides a thesis: the subject is the Cartesian 
subject, i.e. the subject of the cogito or the statement “I think.” Lacan makes this 
point explicit in his Seminar XI:12
I dare to state as a truth that the Freudian field was possible only a certain time 
after the emergence of the Cartesian subject, in so far as modern science began 
only after Descartes made his inaugural step.
It is on this step that depends the fact that one can call upon the subject to re-en-
ter himself in the unconscious – for, after all, it is important to know who one is 
calling. It is not the soul, either mortal or immortal, which has been with us for so 
long, nor some shade, some double, some phantom, nor even some supposed psy-
cho-spherical shell, the locus of the defenses and other such simplified notions. It 
is the subject who is called – there is only he, therefore, who can be chosen.
In order to understand the Freudian concepts, one must set out on the basis that 
it is the subject who is called – the subject of Cartesian origin.13 
Let us first make four quick remarks about the cogito that we think are salient to 
the present discussion.
Firstly, cogito is the subject of thought. It is only because the subject thinks that 
it is certain about itself. In addition, cogito is a subject of certainty. It is certain 
about its own existence, not about its essential being, but its existence as it pre-
sents itself in thinking: the mere fact of thinking is what the subject as cogito is 
certain about.
Secondly, the subject of cogito, which is the subject of thought and certainty, 
is not a subject of truth. The cogito suspends any considerations of truth: the 
12 Jacques Lacan, The Four Fundamental Concepts of Psychoanalysis, The Seminar of Jacques 
Lacan, Book XI, London, trans. A. Sheridan, New York, W. W. Norton & Company, Inc., 
1998.
13 Ibid., p. 47.
21
the place of the subject in badiou’s theory of discipline
subject’s thoughts can be true or false, they can be hallucinations, dreams or 
mistakes. Regardless, the truth status of these thoughts do not change the op-
eration “I think”.
Thirdly, the statement “I think therefore I am” rips away any particularity of what 
a subject is. A subject is, insofar as it thinks, and that eliminates all qualities and 
marks of empirical or substantial individuality, whether corporeal or non-cor-
poreal. This emptiness at the core of the subject, marked by “I think therefore I 
am,” is what makes it possible for it to engage with/in the world through a pro-
cess that is devoid of any presuppositions – the process that we call the modern 
scientific process. In this sense, cogito is the true subject of science.
Fourthly, the statement “I think therefore I am” enunciates the fact that, in-
sofar as I cannot doubt that the process of thinking is occurring, I am certain 
that I am. But the existence that is being affirmed is not the existence of a sub-
stance, but a process, since at this point, Descartes has not yet deduced a sub-
stance form in “I am”. The Cartesian subject is thus the subject of the process of 
thought (the subject of enunciation) rather than the subject in the Aristotelian 
sense (the subject I in the statement “I am”, or the subject of a statement) that is 
backed by a substance. The subject is in the enunciation, not in the statement. 
What then are the grounds for Lacan claiming that the subject of psychoanaly-
sis is the same as the subject of science, which is the Cartesian subject? In what 
sense is Freud Cartesian? 
At the outset, we observe that the subject of psychoanalysis, what the practice 
refers to as the analysand – the person who asks for therapy – seems to be very 
different from the subject of the cogito. An analysand is firstly the one who suf-
fers: if there is a cogito for the analysand, it seems to be more like: “I suffer there-
fore I am”! It appears that the subject of psychoanalysis is the subject of affects, 
not thoughts. In addition, the analysand is not the subject of certainty. On the 
contrary, an analysand is someone who mostly doubts: she does not know what 
is happening to her. She suffers but does not know why. An analysand, one who 
says “I suffer therefore I am”, is therefore also a subject of doubt. The analysand 
who suffers and doubts about the cause of her suffering, also wants to know 
about the true reasons behind this suffering. An analysand is therefore not am-
bivalent to the truth.
22
reza naderi
What does the Freudian process do for such an analysand? It transforms the 
subject of suffering into a subject of thought. This process is called free associ-
ation, through which the analysand is to speak her thoughts; to say what she is 
otherwise silently thinking. Free association transforms the subject of suffering 
into a subject of thinking, which is a step closer to the subject of cogito.
But an asymmetry exists herein: as the therapy brings more of the subject’s af-
fects into spoken words, and transforms the subject of affect into the subject of 
thoughts, it does not necessarily bring about certainty. In fact, just the opposite! 
To the analysand, the thoughts that she speaks about during free association 
may remain incoherent, inconsistent, insignificant, and meaningless. The anal-
ysand doubts the truth of her thoughts, and here lies the asymmetry between 
Descartes and Freud: for psychoanalysis, the moment of doubt is the moment 
that the subject of the unconscious comes to be. This was the case with Freud’s 
discovery of the unconscious itself: it was his doubts about his dream thoughts 
that first suggested to him the existence and efficacy of the unconscious. Lacan 
mentions this point, and the parallel between Descartes’ and Freud’s experi-
ence, in the following way:
In a precisely similar way, Freud, when he doubts – for they are his dreams, and it 
is he who, at the outset, doubts – is assured that a thought is there, which is un-
conscious, which means that it reveals itself as absent. As soon as he comes to deal 
with others, it is to this place that he summons the I think through which the sub-
ject will reveal himself. In short, he is sure that this thought is there alone with all 
his I am, if I may put it like this, provided, and this is someone thinks in his place. 
It is here that the dissymmetry between Freud and Descartes is revealed. It is not 
in the initial method of certainty grounded on the subject. It stems from the fact 
that the subject is ‘at home’ in this field of the unconscious. It is because Freud 
declares the certainty of the unconscious that the progress by which he changed 
the world for us was made.14
The dissymmetry pointed out by Lacan pertains to certainty: in psychoanalysis, 
the certainty is not found in the subject of thought, i.e. in the analysand, but is 
situated in the Other, or the analyst. It is the analyst who is responsible for the 
14 Ibid., p. 36.
23
the place of the subject in badiou’s theory of discipline
presence of the unconscious.15 Therefore, the difference between Descartes and 
Freud, according to Lacan, can be summarized as follows:
We know, thanks to Freud, that the subject of the unconscious manifests itself, 
that it thinks before it attains certainty.16
In the end, the Cartesian subject is a conscious subject defined by its mastery 
over the process of thought. On the contrary, the psychoanalytic subject is sub-
jected to language and the signifier. Both subjects exist insofar as they think, or 
more precisely, speak; both of their existences depend on speech and are in rela-
tion to the signifier, but these relations to the signifier are inverted with respect 
to each other. The relation of cogito is that of the mastery of the signifier, and the 
relation of the subject as unconscious is that of slavery to the signifier. In that 
sense, one may say that Freud is Cartesian insofar as he adopts the notion of the 
Cartesian subject, but it is a subverted subject. 
There is another way in which the subject of the unconscious is a subversion of 
the subject of cogito: the existence of a substantial being becomes the existence 
of a process – the subversion of the home of the subject from the statement to the 
enunciation. This introduces a measure of ex-centricity, a divide, which Freud 
sought to exhibit in the relation of the subject to itself and to the whole experi-
ence of therapy. In Écrits,17 Lacan highlights the difference between where I am 
presented by my thought (the subject of statement) versus where my thought is 
(the subject of enunciation), which is captured in his re-transcription of “cogito 
ergo sum”: ubi cogito, ibi sum.18 
The subject of psychoanalysis, therefore, looks like a generalization of the 
Cartesian subject: first, the two moments of thinking/doubting and being/cer-
tainty are not at the same place in therapy (as we shall shortly see in Lacan’s us-
15 The role of the Other in acquiring the certainty is also emphasized by Lacan in the case of 
the Cartesian cogito: Descartes, although he affirms the presence of the thinking subject, 
has to assume that the truth of even this affirmation is dependent on an Other who is not 
deceptive.
16 Ibid., p. 37.
17 Jacques Lacan, Écrits, the First Complete Edition in English, trans. B. Fink, London, New 
York, W. W. Norton & Company, Inc., 1999.
18 Ibid., p. 429.
24
reza naderi
age of topological surfaces). Second, the analysand is not the only constituent: 
the object (or the analyst), the couch, and free association are also constituents 
of the subject. Third, the relation of the analysand to analyst changes as the pro-
cess evolves. So, although psychoanalysis still works within the overall frame-
work of the Cartesian subject, it makes this architecture more complex. 
So, when Badiou says that Freud can only be understood (according to Lacan) 
“within the heritage of the Cartesian gesture, and at which he subverts, via dis-
location, the latter’s pure coincidence with self,” we understand this sense of 
within according to the above structure that not only subverts but at the same 
time generalizes what is meant by the category of the subject.
What renders the cogito irrefutable is the form, that one may give it, in which the 
‘where’ insists: ‘Cogito ergo sum’ ubi cogito, ibi sum. The point of the subject is 
that there where it is thought that thinking it must be, it is. The connection be-
tween being and place founds the radical existence of [the] enunciation of [the] 
subject.19 
Badiou continues:
The subject thus finds itself ex-centered from the place of transparency in which it 
pronounces itself to be: yet one is not obliged to read into this a complete rupture 
with Descartes. Lacan signals that he “does not misrecognize” that the conscious 
certitude of existence, at the center of the cogito, is not immanent, but rather 
transcendent. “Transcendent” because the subject cannot coincide with the line 
of identification proposed to it by this certitude. The subject is rather that latter’s 
empty waste.20 
The moment, or place, of certitude is where thought coincides with being. But 
that is not an immanent operation, Badiou claims. How does this stand with 
Lacan?
Lacan, throughout his early carrier after discovering Freud, was in search of a 
framework for articulating Freud’s discoveries on a solid basis that would be sci-
19 Badiou, Being and Event, p. 431.
20 Ibid., pp. 431–432.
25
the place of the subject in badiou’s theory of discipline
entific, while also non-humanist and non-essentialist. This leads Lacan to the 
concept of the split subject. As Badiou remarks, Lacan’s “Science and Truth”21 
is the primary source of this theoretical innovation and serves to highlight the 
important topological characteristics of the split subject. It is in this text that 
Lacan examines the status of the split subject as the true conceptual heir to the 
Freudian discovery of the unconscious, and how the rigor of the Freudian leg-
acy might be maintained through this particular advancement. This, of course, 
amounts to a different reading of Freud’s corpus, in particular from ego psychol-
ogy, popular at the time and recognized by many of Freud’s followers as where 
his legacy should reside. 
Lacan proposes that Freud’s work should be read in anachronological order 
(from later to earlier): from Ichsplatung, to the articles on fetishism (1927) and 
the loss of reality (1924). This allows the reader to grasp how the theory of the 
divided subject is the groundwork for the topography introduced through the 
terms (which Lacan opposes): Ich, Über-Ich, and Es. Lacan introduces the con-
cept/term of subject to assist with the navigation of concepts introduced by 
Freud that, due to their lack of clarity, contributed to the aporia of depth psy-
chology. Lacan professes that he borrowed the term subject from structuralism 
so that he could avoid the tendency to substantialize, or to confuse it with brain, 
mind, ego, or similar substance-like constructs. He asserts that Freud’s second 
topography (ego, superego, and id) is best understood by thinking it through the 
concept of subject.
Freud’s scienticism, although not completely adopted by Lacan, has very impor-
tant consequences for the fate of psychoanalysis, one that should be preserved 
and continued. Lacan says that it is impossible to imagine psychoanalysis as a 
practice and the Freudian unconscious as a discovery without the birth of science 
in the 17th century, the century of geniuses. Lacan seems to allude to a science 
which could be applied to psychoanalysis, but one with a notion of subject (as a 
split between knowledge and truth and as the “two sides” of the Möbius strip). 
This notion will render irrelevant all humanist references in psychoanalysis. 
As a practice whose main focus is human suffering, psychoanalysis should be 
fraught with humanist references, distinguishing it from the hard sciences. But 
21 See “Science and Truth”, in Lacan, Écrits, pp. 726–745.
26
reza naderi
Lacan does not like this proximal notion, and thereby stresses that “human-
ist references become superfluous in science, the subject cutting them short.”22 
This portrays the tightrope that Lacan walks between humanist and scientific 
domains, and, at least in this particular text, in relation to the Freudian legacy 
as well as reasons that are his own, he approximates psychoanalysis more to-
ward science than humanism. As evidence, his references to two historical an-
ecdotes show how a scientific posture for psychoanalysis (which Freud was also 
in favor of) helped psychoanalysis gain popular acceptance, and furthermore, 
inspired Freud to look for a scientific formulation of human behavior, which led 
him to the discovery of the unconscious. Lacan sees the root of the latter inspi-
ration in the scientific tendency to formulate all physiology, both mental and 
physical, by the laws of thermodynamics. Lacan persists on a certain path that, 
in his view, helped Freud investigate the unconscious with scientific rigor. This 
is the same path that set Freud apart from Jung, and from ego psychology, which 
was popular among American Freudians at his time. Lacan finds it important to 
draw a line with these tendencies, and suggests an alternative formulation from 
another field of study: linguistics. Borrowing from the structuralist approach, 
Lacan introduces the subject, around which the unconscious can be elaborated 
and further developed, with a rigor analogous to scientific method, and without 
recourse to an object, which is the way in which both scientific (physics, chem-
istry, etc.) and non-scientific (Jung, ego psychology, etc.) approaches tended to 
conduct their studies.
Lacan specifically distinguishes the subject of enunciation from the subject of 
science, something only discernible from within the context of linguistics, and 
this is why he promotes this as a model for psychoanalysis. How can this simi-
larity be mapped? Here is a short suggestion by Lacan:
It is in the realm of logic that the theory’s various refractive indices appear in re-
lation to the subject of science. They differ as regards the lexicon, syntactic mor-
phemes, and sentential syntax.23
In other words, in linguistics, there is recognition at the level of the basic op-
erators of discourse (lexicon, syntax, etc.) with relation to the subject of enun-
22 Ibid., p. 728.
23 Ibid., p. 731.
27
the place of the subject in badiou’s theory of discipline
ciation and the subject of science (which we take to be the subject within the 
statement). 
It is also important to point out that a science can be understood finally as a text 
about a particular subject. The subject appears in this text, the same way that I 
appears in “I think therefore I am.” The I in this text is “the subject of science” 
partly because it is what a text is about – i.e. when a physics text discusses ob-
jects in motion, for example. Science is ambivalent to enunciation; what is im-
portant is the text itself. Compared to the sciences, the position of psychoanaly-
sis is peculiar, as it primarily engages with the textual material of speech while 
its proper subject is the analysand. As such, while the speech (or text) is where 
the subject of other sciences will solely reside, the subject of psychoanalysis is 
where the speech is enunciated from.
Lacan’s ingenious proposal is that there is nothing but speech, so if there is a 
where for the subject of enunciation, it is speech itself (so there is no depth psy-
chology, no mind, soul, etc.). The subject of enunciation can only be found in 
what has been enunciated. This sounds enigmatic: How can that which enun-
ciates be in the enunciated? Here is where Lacan’s genius strikes again, by sug-
gesting that the structure of speech should be viewed as a Möbius strip: speech 
is structured such that the two subjects (the subject of the statement and the 
subject of speech) constitute the two sides of this strip, and the split subject is 
the very split of the two surfaces. Psychoanalysis is the practice that is capable 
of analysing the two-sidedness of speech, so that the subject of enunciation can 
be traced there.
How does psychoanalysis do this? This is where another of Lacan’s famous for-
mulations enters. Lacan declares that the unconscious is structured like lan-
guage: that is, the unconscious is subject to linguistic operations. Therefore, 
the analysis in psychoanalysis is the practice of decoding those linguistic oper-
ations that allow us to recognize the specific discourse produced by the analy-
sand’s unconscious, which is incidentally intermixed with the analysand’s con-
scious speech. That is why, as we pointed out in the foregoing, psychoanalysis 
employs the method of free association. In this method, the analysand speaks 
freely of thoughts as they come to her mind, and through the course of analy-
sis, the analyst begins to recognize those patterns that express unconscious 
thoughts.
28
reza naderi
We finally come back to this: both conscious and unconscious thoughts, both 
subjects, are found in speech, in the same text that is the vocation of the scienc-
es, as the I appears in “I think therefore I am.” This is perhaps yet another way 
to understand why the subject of psychoanalysis is finally the same subject of 
the sciences. And this is how, for psychoanalysis, truth and knowledge are final-
ly sutured within the same medium. Science can never suture knowledge and 
truth: this much is certain following Gödel’s proof. In Lacan’s model, truth and 
knowledge are seen as two sides of the same strip, traversable through speech, 
and no longer localized within the same domain and thus subject to Gödel’s 
incompleteness theorem: topology sutures what arithmetic could not. This is 
what Badiou alludes to in the quote above: certitude, knowledge about a subject 
can never be immanent to where the truth of the subject is – this truth cannot 
be obtained through or culminate in the former certitude – they belong to two 
sides of the strip only sutured through speech: certainty is never the vocation of 
the subject of unconscious.
The Lacanian subject is, therefore, a topological structure, where the truth of 
the subject is a void subtracted of all knowledge, yet maintained in a structure 
that is intertwined with the same conscious subject. This is what a split subject 
is, the split between (the subject of) truth and (the subject of) knowledge (if you 
cannot unite them, as per Gödel, keep them separate, but within one structure, 
aka a Möbius strip).
Lacan, in his Seminar XIV and Seminar XV, developed a schema to describe the 
relation of thinking and existing, as in the statement “I think therefore I am.”24 
In this schema, the two sides of the statement, i.e. I think and I am, have no in-
tersection: no part of one belongs to the other; in other words, the thinking be-
ing is without existence and the existent being does not think.25 It is impossible 
to have both thinking and existing at the same time. This schema is a way, in a 
logical form, to account for the torsion within the structure of the split subject, 
which became thinkable through the topology of the Möbius strip. It is easy to 
see how the split subject supports the modalities of I am, underwriting con-
24 Here we use Bruce Fink’s representation of Lacan’s schema. See Bruce Fink, The Lacanian 
Subject, Between Language and Jouissance, Princeton, New Jersey, Princeton University 
Press, 1995, pp. 44–48.
25 Fink, and perhaps Lacan too, contrasts thinking with being, but we chose to contrast 
thinking with existing instead, for reasons that should be obvious.
29
the place of the subject in badiou’s theory of discipline
scious knowledge and the certitude about who the subject (of the statement) is, 
and I think, underwriting the signifier, the unconscious thought, and the truth of 
the subject (of enunciation) at the same time. In fact, the only issue that remains 
concerns therefore, there is no relation between the two, other than both belong-
ing to the same structural torsion that Lacan calls the split subject. This sense 
of therefore will not find any place in this logical interpretation of the Cartesian 
subject. Below, we will discover that the elimination of therefore proves to be an 
important step in positioning the torsion of thinking and being, not inside the 
subject, but inside the discipline.
Now, when Badiou emphasizes the localization of the void, he absolutely tar-
gets the center of this debate, because Lacan’s project is precisely an attempt to 
suture the truth of the Cartesian subject (i.e. the void of knowledge, as we said 
before, not merely in “I think”, but the mere process of thinking, that is, the pure 
act of enunciation) with the knowledge of I am, which is the conscious subject. 
In this sense, Lacan’s project of split-subject could be understood as the com-
ing to maturity of the Cartesian project in a pure formal structure. Why is it im-
portant for Lacan to suture the void and knowledge into a subjective structure? 
The answer seems obvious: because of the alternative results in various kinds 
of depth psychology; the void is placed either in a chemical/biological brain, or 
in transcendental substances such as the mind, the soul, pure practical reason, 
common consciousness, etc.
At this point then, we are faced with a decision as to the location of thinking. 
Descartes originally attributed this to the Cartesian ego as the human subject, 
which is entirely transparent and transcendental. With Freud, we find that the 
thinking thing is not precisely in the same place as that to which the statement 
of certainty refers. So, we at least have two places: a place of thinking (enun-
ciation, doubt) and a place of being (statement, certainty). Lacan provided an 
architecture for this spaltung based on the structuralist theory of language. 
Speech is where both certainty and doubt, being and thinking, are woven to-
gether, whose topological paradigm could be thought in terms of a Möbius strip. 
In this architecture, the subject is the very split between thinking and being 
as the two surfaces of the strip. The two sides share nothing with each other: 
there is an empty lacuna that acts as the mere differentiation between being and 
thinking, which Lacan dubs the subject. How does this model measure up to our 
disciplinary requirements? 
30
reza naderi
What Lacan accomplishes is extraordinary as he avoided the metaphysical and 
humanist presumptions looming behind the subject from Descartes to Sartre, and 
at the same time he was able to extend structural causality by distinguishing the 
law from the cause. This opened opened up a gap within the structure between 
the automatic unfolding of the signifier (automaton) and the agency that evades 
formalization (Tuchè) – which we could name subjective causality, to distinguish 
it from structural causality. Despite this, however, Lacan’s notion of the subject, 
similar to his forerunners, still remained sutured to the I of I think. Speech, which 
is ultimately the place of the subject, is ineluctably one’s speech: for Descartes, 
as well as for Freud, Sartre, Husserl, and Lacan, thinking is ultimately sutured 
to the human individual. Miller, as seen at the very beginning of this study, had 
realized this and attempted to generalize the category of the subject such that 
it becomes the latent and repressed core of the logic of structure. According to 
the latter thematization, and inspired by Lacan’s innovations, Miller argued that 
not just one’s speech but any discourse, such as science or politics, is structured 
around a repressed kernel. Structure itself is not-all. Every structure forecloses or 
bars an element that paradoxically makes the structure consistent. Badiou uses 
this important discovery by Lacan: structure is not the place of consistency and 
stability, it is precisely the place of instability. This instability is the main reason 
for the metonymy of signifiers – inaugurated by a traumatic loss of jouissance. 
Accordingly, the subject is not constitutive of just an un-symbolizable excrement 
of the structure, but as Žižek puts it, “‘subject’ designates the contingency of an 
Act that sustains the very ontological order of being. ‘Subject’ does not open up a 
hole in the full order of Being: ‘subject’ is the contingent-excessive gesture that 
constitutes the very universal order of Being.”26
We call Lacan’s position modest because we think Lacan was justified in putting 
a disciplinary constraint on the reconstruction of the concept of cogito as a mere 
differentiation with a claim to universality. That is, ultimately, Lacan chooses 
to stick to I think, with the emphasis on the I, for the same reason that psycho-
analysis is the only rigorous theoretical field where the statement “I love you” 
is relevant. The I in “I love you” connects to individuals. This move is justified 
precisely for the same reason that, in the procedure of love, the reference to 
the individual body still counts in a way that does not in any other procedure. 
26 Slavoj Žižek, The Ticklish Subject, The Absent Centre of Political Ontology, London, Verso, 
2000, p. 160.
31
the place of the subject in badiou’s theory of discipline
So, Lacan is correct in asserting that if we care how people come to be desiring 
subjects, how they come to inhabit their bodies, and how they come to desire 
other bodies, as psychoanalysis does, we must remain faithful to the idea of the 
Cartesian subject. Because of this, the I is a relevant concept, and a more gen-
eral construction of the concept should not erase it, as psychoanalysis in the 
end is concerned with how thinking and the body encounter each other in an 
individual. We call this a disciplinary constraint because it makes the practice 
of psychoanalysis possible. In other words, seen through the lens of the discipli-
nary theory in which we are engaged, psychoanalysis as a practice is that which 
subjectifies. It is not the case, however, that the subject in the clinic involves 
only the analysand. Rather, it involves the whole experience of the analysis, in-
cluding the sessions, the free association, the analyst, the transference, the the-
ory, as well as the analysand. In other words, thinking and being reside in a sit-
uation that we call analysis, or in our parlance, within the concrete discipline 
we call the psychoanalytical situation. The psychoanalytic cure is therefore not 
the end of the discipline per se, but rather it only eliminates the dependency of 
the disciplinary subject on the external facets of the analysis: the sessions and 
the analyst. This is where the analysand is now capable of participating in the 
subjective experience, which is the discipline itself. That is where the constraint 
put on the individual human body becomes material to the practice of psychoa-
nalysis – it becomes the boundary of what will have been the elusive cure.
The issue that arises is thereby not the constraints set in order to circumscribe 
the disciplinary practice, but rather concerns the generalization of the con-
straints as a rule of thinking as such. In Badiou’s parlance, it is the suturing of 
thought to a particular condition of truth. This suturing, although heavily sug-
gested by Lacan himself throughout his work, was never transformed by him 
into a programme, but, by his exceptional reader, his son-in-law-to-be, and the 
future heir to his theoretical legacy, Jacques-Alain Miller.
The other, and more important issue, regarding this generalization, which 
makes the conception of the subject in psychoanalysis unsuitable for us, is that 
the suturing of the subject to the chain of signifiers has the inaugural assump-
tion of a lost or impossible object. Why is this important? Because the concep-
tion of the subject for both Lacan and Miller, as the case was for the philoso-
phers before them, is effectively mediated through the object, and this does not 
bode well from either the perspective of axiomatic thought, or Badiou’s perspec-
32
reza naderi
tive, which holds philosophy responsible for thinking our era through the cate-
gory of an objectless subject.27
In fact, the conception of an objectless subject is precisely what the theory of 
discipline posits: the discipline is the cogito; it is the discipline that thinks, not 
the I. It is only within the movement of thought, whose coordinates traverse ac-
tors, artifacts, assumptions, theories, discourses, and experimentations spread 
across a disciplinary landscape, that subjective thinking can take place. The 
discipline thinks its own being through axioms, which means disciplines can 
think their beginnings. As we have discussed in detail in the previous section, 
the main difference between dialectical and disciplinary thinking is that a dis-
cipline can think its own beginning, but a dialectic cannot – as axioms are the 
only viable means of thinking the beginning, through a violent rupture from pre-
sumptions based on opinions. And it is precisely through the thinking of begin-
ning that the thinking of truths finds legitimacy, as the latter goes beyond what 
the discipline could think through its beginning: thinking truths is precisely 
thinking beyond the point of the impasse of the beginning. But that is the other 
aspect of axiomatic thinking: that it can summon itself to carry out the task yet 
again. An example of this convocation under the event of infinity in Zermelo–
Fraenkel set theory (ZF). ZF (which includes the Axiom of Infinity) as a set of 
axioms could in fact recoil, as it did, in the face of the infinity event toward the 
foreclosure of infinity under the assumption of constructivism. This is the event 
operating as the cause. But, at the same time, the fidelity to the infinity event 
can orient thought toward the assumption of the generic, where event now oper-
ates as consistency. Ontology cannot decide between the two, itself falling short 
in the face of being’s excess. This manifests the movement of axiomatic thought 
in two modalities: conveyance and composition. When the discipline conveys a 
concept, such as the generic, it does so by positing a new generality that sup-
plements the set of previously posited generalities that had carved the being of 
the discipline. In the compositional mode, however, the discipline experiments 
with the avowed generality using the material available to it in the situation of 
27 This assertion is certainly true for the subject of castration, as the universal operator of 
subjectivation for Lacan. But, in his theory of sexuation, Lacan does develop a conception 
of the subject that is not wholly determined by castration alone. Properly speaking, that 
subject could be considered to be an objectless subject. We will examine that sense of sub-
jectivity in Lacan in the next section.
33
the place of the subject in badiou’s theory of discipline
which it is a discipline. This we have dubbed the discussion of the token, or the 
material condition of a truth multiple.
For example, when the concept of the party in power, as a consequence of the 
Lenin event, recoiled to an organized State, as an abstraction of the socialist soci-
ety after the October Revolution (event as cause), Mao offered a different concep-
tion of the socialist state and the relation of the Party to the masses in which the 
Party, as an abstraction of the State, was supplemented by the Cultural Revolution 
(event as consistency). At this level, the Cultural Revolution is a generality that 
merely supplemented the original set of axioms that defined the discipline of so-
cialist revolutionary politics conveyed by Lenin. The Cultural Revolution is the 
conveyor of a new set of axioms (Lenin’s party + the Cultural Revolution, akin 
to ZF + infinity). However, this generality was put to work in the real situation of 
Chinese society. This experimentation amounted to having every cadre tend to 
crops for six months. The implementation of the generality or idea is the compo-
sitional modality through which an instance of the truth is approximated within 
the discipline. The debate in the politburo, the organization of brigades, the new 
regiments for the cadres, were all part of the implementation of the supplement-
ed generality towards the truth of the Leninist doctrine of the dictatorship of the 
proletariat, the creation of soviets, and the dismantling of the State. 
On this basis, we propose to think of the objectless subject as the discipline in its 
compositional modality. In that sense, the cogito, the “I think”, is the discipline 
when perceived compositionally. In contrast, the being of discipline is always its 
modality in conveyance; it is what the discipline conveys of itself. As a result, “I 
am” is the marker of the thinking of the discipline over its beginning, its thinking 
over its being. Using this grammar, the phrase “I think therefore I am” conjoins 
the two modalities of the discipline. This is, in my view, what Lazarus meant for 
the discipline of politics: politics thinks its own thought. This is also what Badiou 
said about the discipline of science when he proclaimed that there is no subject 
of science: there is no subject of science because primarily there is no object of 
science. Science is that thinking which aims for its own interiority – at least sci-
ence in the Bachelardian sense. Badiou further claims that art and love are re-
gions of thinking that manifest the same characteristics as politics and science. 
Thought in this way, we construe Badiou’s exposition of the subject in Being 
and Event within the above general disciplinary landscape. The relation of the 
34
reza naderi
subject to an event from one end, and to truth from the other, is best under-
stood when we place that relation in the context of the dual modalities of the 
discipline. In that sense, Badiou has provided a more elaborate framework for 
how the compositional logic operates. In “Meditation 23”, Badiou introduced 
the problem of double origins concerning procedures of fidelity. This problem re-
ferred to the naming of the event, which is the first step in an intervention. And 
the second is the operator of connection, the procedure of truth itself. The oper-
ator of fidelity emerges consecutively to an interventional nomination. Badiou 
calls this emergence of the operator of fidelity subjectivization. Thereby, subjec-
tivization is an emergence of the Two: it is connected to the evental site through 
the intervention and it is connected to the situation through the operator of fi-
delity. Every intervention performs a naming, which puts into circulation a su-
pernumerary name. But every such naming leads to a consecutive counting – a 
count that is different than the count-as-one of the presentation, and the count-
as-one of the State. 
This counting is the second aspect of the subjectivization – the operator of fidel-
ity. Subjectivization, designated by a proper name: St. Paul, Lenin, Cantor, is the 
coming together of a name, which names the event, and an operator of fidelity, 
which is the generic procedure of a simple encounter. However, subjectivization 
is neither only one or the other, but something in excess. From the perspective 
of the situation and its state, the name has no significance. The insignificance of 
the proper name of the subject is an attestation to the fact that subjectivization 
is connected to the occurrence of the void. The Two, in our view, should be un-
derstood as a commitment to the maximality of thinking, which is occasioned by 
events and as that which invokes this maximality. This maximality is then exer-
cised by experimentation in thinking. By being able to issue statements whose 
truth will go beyond the established system, thought demands and occasions its 
extension. Therefore, we see a very clear resemblance between Lautman’s views 
with respect to the way that generalities are identified or named, and how new 
theories are developed based on the inauguration of those generalities. Here 
we see the clear role of subjectivization, from one end caused by an event (the 
cause) and from the other oriented toward a truth (consistency). Ontology does 
not speak of this relation. As we have repeated time and again, ontology deals 
with the being of the generic as an impasse of the knowledge of the situation: 
the being of truth in general, whereas subjectivation is where a singular truth 
comes to exist in a situation, in relation to the occurrence of an event. The being 
35
the place of the subject in badiou’s theory of discipline
of truth is compatible with ontology: ontology does not speak of truth but does 
speak of the generic and its being. 
But this much we knew from Lacan too: we already knew that the real has a be-
ing. If the generic is the name of the real as truth, what does the association of 
the generic and the real give us that we did not have before? How do we think 
more of the real by utilizing the name generic or indiscernible? In two ways: be-
cause the real is not just an impasse to the knowledge of a situation, it is the 
source of its novelty too – the situation could change and the real of the situa-
tion is the guarantor of the possibility of this change. Accordingly, the relation 
of the real and the interiority of the situation is not only of the category of cause, 
but also of the category of consistency. This attests to the connection of truth 
and consistency – whose inner relation belongs to the disciplinary relation of 
novelty and interiority. But, the generic, although providing a guarantee of the 
being of truth, does not speak of the existence of a truth in a given situation. 
Badiou’s philosophical edifice, starting from the possibility of an event and the 
existence of its evental site, to the act of intervention and the procedures of fi-
delity, speaks to the existence of a truth associated with a particular evental site. 
We can also refer to the latter as the local possibility of a truth. So, when Badiou 
says the “local status of a generic procedure” has dependence on “a simple en-
counter,” we understand the above sense of the locality of a truth, vs. the onto-
logical globality of the being of the truth that pertains to every historical situa-
tion in which an event decrees its void.28 
What constitutes a simple encounter? A finite set of enquiries, + or -, subsequent 
to the fixation of the name of an event, starting from its evental site. This proce-
dure is so simple that it is non-prescriptive of the trajectory it should take: the 
encounter is completely aleatory. Although its effect is prescriptive (+/- results), 
its trajectory is not. That is how it is simple: it is an aleatory and unplanned en-
counter. The only thing that we can say about this encounter is that its trajectory 
starts from an evental site. Therefore, in its locality, we have a procedure whose 
genesis and progression are constituted by aleatory, non-prescriptive, and law-
less encounters. Each encounter enriches the one or the other set of enquiries 
with the names of the elements according to whether or not they are affected by 
the name of the event.
28 Badiou, Being and Event, p. 324.
36
reza naderi
From the perspective of this simple encounter, the truth (of that encounter) ap-
pears as an ideal: “a truth is the ideal assemblage of all the evaluations, it is a 
complete part of the situation.”29 We can perhaps say that the ontological being 
of truth as a complete generic subset of the situation appears to the locality of 
the above simple operations as an unachievable ideal.
This leads to a thought: If the subject is the discipline in its compositional mode, 
and if discipline is infinite, then what does the association of the discipline and 
the subject tell us about the subject? Is the subject finite or infinite? Here is 
where the conception of the locality is important. The subject is related to the 
locality of an event and the locality of a procedure. As everything local is finite, 
the locality of what determines the subject would mean that it is also a finite 
multiple. Using this conception of locality, Badiou provides a definition of the 
subject in which the subjection is qualifiable and unqualifiable at the same time:
Thought in its operation, the subject is qualifiable, despite being singular: it can 
be resolved into a name (ex) and an operator (□). Thought in its multiple-being, 
that is, as the terms which appear with their indexes in effective enquiries, the 
subject is unqualifiable, insofar as these terms are arbitrary with regard to the 
double qualification which is its own.30 
What does being qualifiable mean? To me, the term qualifiable shall mean that 
the term subject is defined by a formula or predicate. The name guarantees the 
singularity of the subject: the singular name of the event is the source from 
which the subject inherits its singularity in the situation. The qualification (and 
thereby the predicative aspect) of the subject comes from the operation of fideli-
ty. Furthermore, the matter of the subject is comprised of the terms submitted to 
enquiry at a given moment. Due to the aforementioned locality of the enquiry, 
the matter of the subject is unqualifiable. That is, the matter of the subject has 
no definable relation to the operation that indexes the terms of the enquiry (as + 
or -). This means that the multiple terms that constitute the matter of the subject 
is arbitrary and lawless. But the locality and thereby arbitrary nature of the en-
quiries that constitute the the matter of the subject make the subject necessarily 
finite: locality means finitude, and every finite multiple is discernible and there-
29 Ibid., p. 324.
30 Ibid., p. 395.
37
the place of the subject in badiou’s theory of discipline
by belongs to the realm of knowledge. This means that the matter of the subject 
is not co-extensive with truth, despite the fact that “a truth proceeds solely via 
the assemblage of those enquiries,” it always surpasses the finite support of the 
subjectivization that makes the truth proceed.31
The finitude of the subject is not in contention with the infinitude of the truth. 
The local configuration of an instance of the truth is always finite, because of its 
locality. But the truth, as an idea that supplements the thought of the discipline, 
is infinite in its extension and in how the discipline is conveyed.
What is the importance of all this? We believe that the category of the subject 
whose vicissitudes are discussed in Being and Event gives us the framework of 
how the discipline operates in its compositional modality, whereas ontology, 
and in general axiomatic thinking, constitutes the working of the discipline in 
its modality of conveyance. The discipline is a region of thinking that has no 
object. Its ground refers to no objectivization. The important claim is thus this: 
understanding the subject as what belongs to a modality of the discipline as a 
whole should give us a concept of the subject with no object. A non-referential 
and non-objective category.
The journey is quite amazing here: as the Cartesian subject is the original tem-
plate according to which the psychoanalytical subject is constituted, the roots 
of the latter is evidently in philosophy, matured and ripened in psychoanalyti-
cal theory. Now we have a philosophy that takes the concept of the subject from 
psychoanalysis back into philosophy, by keeping the same commitment to for-
malism in defining its constitution.
This periodization is none other than the great philosophical exchange through 
the history of modern thought, and more specifically in our era between philos-
ophy and psychoanalysis. For both, there is a truth, but whereas for philoso-
phy the being of truth is trans-individual and eternal, for psychoanalysis, truth 
is singularly placed in the subject’s unconscious. In addition, we now have a 
new possibility for conceptualizing the subject that emerges from the concept of 
discipline, from which we can also ingest Badiou’s theorization of this concept 
from Being and Event. 
31 Ibid., p. 395.
38
reza naderi
But what does this theory, based on the concept of discipline, give us that the 
theory of the subject in Being and Event did not? Why do we need a different 
formalization aside from, or in addition to, the formalization that Badiou pro-
vides? The concept of discipline speaks to three crucial conceptual apparatus-
es in Badiou’s enterprise: firstly, it speaks to his Platonism through the com-
mitment to the maximality of thinking; secondly, it speaks to his fidelity to the 
Cantor event through the commitment to the idea of infinity; and thirdly, to his 
revolutionary politics through the commitment to the category of the subject. 
The discipline comes together in these three apparatuses, which gives a new 
logic that is more general than the dialectic. This generality allows us to final-
ly see that what the category of the subject names at the historical level (the 
operator of compossibility in modernity), discipline names at the ontological 
level, that is, the trans-historical level (the conditions of thinking that make 
the thought of immanence, novelty, and the beginning compossible in gener-
al). In a way, we could even think of the Platonic form as a local name whose 
global instance is discipline. Therefore, “discipline thinks” is a trans-historical 
statement, whose name in modernity is “subject thinks” (and “form thinks” in 
antiquity).
Therefore, we are quickly arriving at a point where, with the concept of disci-
pline, we are able to merge the Cartesian and Cantorian frameworks towards a 
revived understanding of the cogito, in the tradition of Parmenides as discipline 
in composition. And this, we believe, is the proper reconceptualization of the 
Cartesian meditation after the Age of Poets.
The Subject and Infinity
Lacan, in his theory of sexuation, develops two subjective logics: man and 
woman, each with its own determinations. This grounds a singular truth in 
psychoanalysis: there is no sexual relationship. This theory is of utmost impor-
tance to us for two reasons: first, in the position of woman, we can effective-
ly recognize a partially objectless determination of the subject. Furthermore, 
Lacan proceeds to introduce infinity as the proper determination of this object-
less subject. The focus of this section is precisely the encounter between Badiou 
and Lacan regarding the sense of infinity employed here. This encounter takes 
39
the place of the subject in badiou’s theory of discipline
place in a surprisingly obscure text called “Subject and Infinity”32, in which 
Badiou mostly comments on a single passage from Lacan’s Seminar XX (Chapter 
VIII, entitled “Knowledge and Truth”).33 The text Badiou quotes is as follows:
In that logic, on the basis of the fact that one can write ‘not-every [pas-tout] x is 
inscribed in Φx’, one deduces by way of implication that there is an x that con-
tradicts it. But that is true on one sole condition, which is that, in the whole or 
the not-whole in question, we are dealing with the finite. Regarding that which is 
finite, there is not simply an implication but a strict equivalence. It is enough for 
there to be one that contradicts the universalizing formula for us to have to abol-
ish that formula and transform it into a particular. The not-whole becomes the 
equivalent of that which, in Aristotelian logic, is enunciated on the basis of the 
particular. There is an exception. But we could, on the contrary, be dealing with 
the infinite. Then it is no longer from the perspective of extension that we must 
take up the not-whole [pas-toute]. When I say that woman is not-whole and that 
that is why I cannot say Woman, it is precisely because I raise the question [je 
mets en question] of a jouissance that, with respect to everything that can be used 
in the function Φx, is in the realm of the infinite.34
Now, as soon as you are dealing with an infinite set, you cannot posit that the not-
whole implies the existence of something that is produced on the basis of a nega-
tion or contradiction. You can, at a pinch, posit it as an indeterminate existence. 
But, as we know from the extension of mathematical logic, from that mathemat-
ical logic which is qualified as intuitionist, to posit a ‘there exists’, one must also 
be able to construct it, that is, know how to find where that existence is.35
Lacan affirms the Aristotelian conclusion that the negation of a universal state-
ment is equivalent to a particular negative statement. If I say “not all apples are 
red,” I imply that there is at least one apple that is not red. In logical notation:
32 The original French title of this essay is The Position of the Infinite in the Split of the Subject, 
which is a far more crucial and interesting title than the one chosen for its English publica-
tion. This title almost summarizes the topic of this study.
33 Jacques Lacan, Encore: On Feminine Sexuality, the Limits of Love and Knowledge, The 
Seminar of Jacques Lacan, Book XX, 1972–1973, trans. B. Fink, London, New Yok, W. W. 
Norton & Company, Inc., 1999.
34 The marginal page number of the quote is 94 (which is the page number Badiou cites).
35 Lacan, Encore: On Feminine Sexuality, the Limits of Love and Knowledge, pp. 211–212.
40
reza naderi
¬ ( x): f(x) = x: ¬f(x)
But Lacan puts a proviso on this. He says that this equivalency only works when 
x belongs to a finite set. In a finite set, when I posit ¬ ( x): f(x), I must be able to 
find an x such that I could say x: ¬f(x). But Lacan thinks that this cannot be the 
case if x belongs to an infinite set. In an infinite set, there is no guarantee that I 
could find such an x. At most, I can say that such an x is probable but not deter-
minate. But why does that make this equivalency less true in the case of the in-
finite? This is where Lacan appeals to intuitionist logic. In intuitionist logic, the 
existence of something is only guaranteed if that something can be constructed 
or demonstrated in a mathematical proof. This points to an explicit disparity in 
Lacan’s text when dealing with two different logics, Aristotelian and intuition-
ist, which we will return to later in this section.
But why does Lacan use this logical jargon? The issue is that the function Φ, 
which stands for castration, is a universal function in psychoanalysis. Castra-
tion is a process through which a speaking (i.e. human) subject is made. As 
such, if x is a subject, in psychoanalysis, then (analytically) Φ(x) holds. The is-
sue is that if Φ(x) is true, then how can we at the same time assert ¬ ( x), Φ(x)? 
When Lacan says woman is not-all, and on that basis he concludes that there 
is no Woman, it suggests that, while there is a universal genus of Man that all 
particular men fall under, Woman is not such a genus, there is no generalization 
under which particular women fall, and thus there is no Woman.36
The passage we cited above is from the 8th session of Lacan’s Seminar XX. The 
passage was produced after the main lecture was over (apparently there was a 
quarter of an hour still remaining and Lacan continued talking). Lacan, who 
was excited about a lecture delivered by François Recanati four months prior 
to that date (during the first session, entitled On Jouissance), provides some re-
36 One can only be a man if one assumes that there is an exception to castration in the set 
called Other. Woman is (one of the names of) that exception, and so is actually part of the 
masculine logic. It is important to highlight the dependence men have on Woman, and 
how this dependence does not go both ways.
41
the place of the subject in badiou’s theory of discipline
marks regarding “the schema Recanati had to erase earlier,” which apparently 
had to do with Aristotelian logic and the topic of not-all (pas-toute) 37:
Masculine Feminine
x: ~Φx
x: Φx
~ x: ~Φx
~ x: Φx
 
S
Φ 
 
              S(A) 
a 
                                  Woman
Lacan’s Formulae of Sexuation
This not-whole (pas-toute), in classical logic, seems to imply the existence of the 
One that constitutes (fait) an exception. Henceforth, it would be there that we 
would see the emergence in an abyss – and you will see why I qualify it thusly – 
of that existence, that at-least-one existence that, with regard to the function Φx, 
is inscribed in order to speak it (s’inscrit pour la dire). For the property of what is 
said is being, as I said earlier. But the property of the act of saying is to ex-sist in 
relation to any statement (dit) whatsoever.
The question then arises whether, given a not-whole, an objection to the univer-
sal, something can result that would be enunciated as a particular that contra-
dicts the universal – you can see that I am remaining here at the level of Aristo-
telian logic.38
It appears to us that Lacan’s argument, comprised of both this and the previous 
quote, can be divided into three parts. First, he acknowledges that in Aristotelian 
logic, when one speaks of “not-all x satisfy Φ(x)”, one also implies that there ex-
ists an x that contradicts Φ(x). If I assume Φ is “is red”, then the expression “not 
all apples are red” means that we can find an apple that is not red. Lacan then 
adds that this is only true if we are dealing with the finite. In the case of x be-
37 We are using “not-all”, which is what is widely used in the literature, and “not-whole”, 
which is used in Badiou’s “Subject and Infinity”and Seminar XX as the translation of pas-
toute, interchangeably.
38 Ibid., p. 102.
42
reza naderi
longs to a finite set, the existence of a particular x such that ¬Φ(x) is not only 
an implication, but also an equivalence. Such a condition is not necessary in 
predicate logic. In fact, as far as predicate logic is concerned, the equivalence of 
“not-every” and “there exists” is universally true regardless of the scope of x.39 
In the next part of his argument, Lacan considers the possibility of x to se-
lect over an infinite domain, and he says the following: “then it is no longer 
from the perspective of extension that we must take up the not-whole [pas-toute]. 
When I say that woman is not-whole and that that is why I cannot say Woman, 
it is precisely because I raise the question of a jouissance that, with respect to 
everything that can be used in the function Φx, is the realm of the infinite.”40 
Lacan makes a turn here. He says that, in dealing with an infinite, not-whole 
domain, the logic in question should no longer be approached from the per-
spective of extension. What does this mean? Here is a possible reading: When 
I say “not all apples are red,” I am referring to the sets of all apples. But when I 
say: “not all of an apple is red,” the not-all does not refer extensionally; it refers 
to a single apple and says that not-all of that single apple is subject to the func-
tion is-red. It appears, solely based on this passage from Lacan, that the sense 
in which he wants to use the quantifier not-all suddenly shifts from an external 
scope (not every x) to an internal scope (not every part of x). 
In the third part of the argument, Lacan is completely submerged in the dis-
course of the infinite: a point that pertains to the dialectic of existence and 
ex-sistence.41 Lacan says this: if we say “not all of x is Φ(x)” (based on an in-
ternal domain of x) and the domain is infinite (which is the case when Lacan 
speaks of woman’s jouissance), we do not thereby conclude that there exists an 
x such that Φ is not true for it. In the context of jouissance, Lacan asserts that, 
unlike man’s jouissance, not all of woman’s jouissance is determined by the 
39 For example, see https://en.wikipedia.org/wiki/First-order_logic#Provable_identities, ac-
cessed 23 February 2022.
40 Lacan, Encore: On Feminine Sexuality, the Limits of Love and Knowledge, pp. 211–212. 
Emphasis added.
41 For Lacan, existence is only possible in the symbolic register. We may refer to things that 
do not exist (i.e. they are not within the symbolic register), but this reference does not 
mean that they exist. Lacan’s term for the sense of being of things that we can speak of but 
do not exist (i.e. they are not in the symbolic register) is “ex-sist”. Lacan borrows this term 
from Heidegger.
43
the place of the subject in badiou’s theory of discipline
phallus: this is made obvious by the double arrow to the crossed-out Woman 
(Woman) in the diagram, which illustrates that Woman has two partners, the 
phallus and S(A), the signifier of the inexistent/inconsistent Other. Therefore, 
the assertion that “not all x such that Φ(x)”, in my view, should mean that part 
of x, woman’s jouissance, is determined by its relation to the signifier of the 
Other, but by writing S(A), Lacan indicates that he does not affirm the existence 
of the Other. Intuitionist logic can afford that to Lacan: it allows us to keep S(A) 
at the level of ex-sistence instead of existence. This reading is confirmed by the 
second passage we quoted from Seminar XX, which is just before the original 
passage quoted herein. A little before the passage we cited, Lacan says:
Is there One or not? In other words, this not-whole (pas-toute), in classical log-
ic, seems to imply the existence of the One that constitutes (fait) an exception.42
Therefore, when we say “not all x is Φ(x)”, the question is: are we confirming, 
as Aristotelian logic requires us to do, that “there exists an x such that ¬Φ(x)”? 
We know that the Primal Father is the referent of the One in the above quote: 
there is a One who is not subject to the effect of castration. What is the existen-
tial status of the Primal Father? That is precisely what takes us to the next part 
of this quote:
Henceforth, it would be there that we would see the emergence in an abyss – and 
you will see why I qualify it thusly – of that existence, that at-least-one existence 
that, with regard to the function Φx, is inscribed in order to speak it (s’inscrit pour 
la dire). For the property of what is said is being, as I said earlier. But the property of 
the act of saying is to ex-sist in relation to any statement (dit) whatsoever.43
What is implied by the not-all is precisely what allows us to speak of something 
that is not under Φ, but at the same time, this not-all does not force us to commit 
to “there exists”, thanks to the intuitionist logic. In the end, we have a pure sig-
nifier for the Other, which has no existential commitment.
42 Ibid., p. 102.
43 Ibid., p. 102, my emphasis.
44
reza naderi
In his Seminar XIX,44 Lacan had previously adopted a different strategy toward 
the same end, by elaborating on a proposition that has a similar construction: 
“Il y a de l’Un” (“There is something of the One,” or “Sometimes there is One”), 
which he contracts as Yad’lun. After affirming the “Aristotelian angle” for the 
contradiction between “the statement that for all x, x fulfils in Φx the function of 
an argument, and the fact that there some x that can fulfil the place of argument 
only in the enunciation that is the exact negation of the former,” he proceeds to 
say: “I’m daring to advance something that is plainly lacking in the aforemen-
tioned logic. I am able to do so to the extent that the term existence has quite cer-
tainly changed meaning since then.” How has the sense of “existence” changed? 
When we say “There exists an x, at-least-one, lends a value that can be qualified 
as true to what is posited as a function.” In this sense, we can say: “There is a dis-
tance between this and natural existence, which I will not name otherwise today, 
for want of a better word.” This sense of existence is what Lacan attributes to the 
One, and it is why Lacan finds Cantor’s invention of sets so useful: “the main-
spring of set theory hinges entirely on how the One – that there is – of the set is 
distinct from the One of the element.”45 In Lacan’s mind, set theory supplies a 
sense of one (or oneness) without having to ground it in the one of being, or the 
existential sense of oneness and sameness (as we have seen Plato had attributed 
to Parmenides). Instead, the commitment to the one is grounded in the being of 
multiples, and as in set theory, there are nothing but multiples:
It is in this respect that it is, let’s say, inadequate in the Platonic dialogue to make 
anything whatsoever of the existent participate in the realm of the like-for-like. 
Without the crossing-through whereby the One is initially constituted, the notion 
of like-for-like would not appear in any way whatsoever.46
So, when Lacan refers to “there exists”, this does not refer to the sense of exist-
ence from Aristotelian predicate logic. Instead, borrowing from set theory, he is 
“daring to advance” the existential sense of the standard quantifiers.
44 Jacques Lacan, … or Worse, The Seminars of Jacques Lacan, Book XIX, 1971–1972, trans. 
A.R. Price, Cambridge, Polity Press, 2018.
45 Ibid., pp. 120–124. 
46 Ibid., p. 125.
45
the place of the subject in badiou’s theory of discipline
This new “logic”, proffering a sense of “existence” distinct from “natural exist-
ence”, is the same sense that Lacan wishes to leverage when he speaks of the 
“infinite” field of woman’s jouissance – the not-all. At the bottom part of the dia-
gram, Woman is connected to Φ and S(A). S(A) is that not-all which, at the same 
time that it signifies the non-existing Other, plays a part in formulating feminine 
sexuality. Using the foregoing interpretation, the sexuality (jouissance) of every 
woman is subject to the effects of castration, but castration does not fully deter-
mine a woman’s sexuality (jouissance): it is a necessary, but not sufficient, con-
dition. This is obvious from the first formula on top of the right side of the above 
figure that says ¬ x: ¬Φ(x): there is no woman who is not affected by castration, 
which means all women are affected by castration, but that is not all that deter-
mines their sexuality (unlike men). The key to this interpretation is, as we have 
said, to posit an internally scoped sense of the quantifier. However, in the sense 
of not-all, “there exists” does not predicate the existence of a thing outside of 
the effect of castration. That is why Lacan takes recourse in intuitionist logic, 
since what he wants in the end is a logic where the affirmation of not-all does 
not result in a “there-exists”:
For an intuitionist, therefore, from the statement ‘not for every x Φ(x)” there is 
no reason to conclude that ‘there exists x such that not-Φ(x)”. On this point intu-
itionism coincides perfectly with Lacan’s aim.47
In intuitionist logic, the traditional concept of truth is qualified by the concept of 
constructive provability: a method of proof that works by demonstrating the ex-
istence of an object by creating or providing a method for creating it. Therefore, 
while predicate logic finds the proposition “not all x such that Φ(x)” to be equiv-
alent to the proposition “there exists an x such that ¬Φ(x)”, such that the truth 
of one will imply the truth of the other, intuitionist logic does not consider these 
equivalent. Therefore, the truth of the former proposition does not imply the 
same for the latter: the existential statement must be independently construct-
ed. This is, as Badiou points out in his commentary on Seminar XIX, exactly 
the effect that Lacan is seeking: woman, the not-all, has a relation to the phal-
lic function, and nothing more – somewhere means not everywhere; the some-
where – not everywhere – of the woman’s position is expressed as not-whole.48
47 Badiou, Conditions, p. 215.
48 Ibid., p. 215.
46
reza naderi
But is this a temporary alignment with intuitionist logic, or is Lacan an intui-
tionist? Badiou emphatically asserts the former. Lacan neither fully subscribes 
to intuitionist logic (e.g. the renunciation of reductio ad absurdum as per his ap-
proach in the interpretation of symptoms) nor renounces the existence of actu-
al infinites (as per his usage of alephs). He even, in the first passage we quoted 
from Seminar XX, makes use of the Aristotelian logic of finite sets, something 
that an intuitionist would not agree with. The key that Lacan mistakenly sought 
in intuitionist logic does in fact lie on the side of the infinite. This confusing re-
lationship with intuitionism points to another important matter as well. While 
intuitionism is not a branch of logic to which Gödel, Cohen, and Badiou sub-
scribe, it is nevertheless one that many mathematicians have worked fruitfully 
within. This makes the debate between intuitionists and realists in mathemat-
ics an interdisciplinary debate, one that Lacan is not party to. Recall Badiou’s 
detailed analysis of the ideological dispositions that are developed in relation 
to the sciences. As early as ”Mark and Lack”, Badiou had recognized two dif-
ferent representative stances, one transcendental to the sciences, such as epis-
temological theories, and the other immanent to a given science.49 The latter 
stance represents what a science thinks about itself, and despite being ideolog-
ical, is part of that science – furthermore, science already contains the means 
of eradicating such internal ideological representations. Hilbert’s programme 
is evoked as such an ideological representation generated within the practice 
of mathematics itself – subsequently addressed by Gödel’s inconsistency the-
orems. In contrast, we have ideological instances that are produced outside of 
a given science, those that do not pertain to the practice of the science itself. 
Miller’s representation of the logic of the signifier is an example of this tran-
scendental-ideological stance. Likewise, we could say that intuitionism is a rep-
resentative disposition inside the practice of mathematics, and Lacan’s usage of 
intuitionism, like Miller’s, is an ideological disposition that is transcendental to 
the discipline of mathematics.
But there is more. While Miller’s ideological usage of Frege’s logic (itself ideolog-
ical, but nevertheless intra-mathematical) amounts to a consistent programme, 
Lacan’s usage here is not so. As per Lacan’s articulation, we are dealing with 
an infinite field of woman’s jouissance. Somewhere in that infinite field, there 
is also phallic jouissance. But does not the existence of this somewhere, by way 
49 Badiou, “Mark and Lack: On Zero”, pp. 159–185.
47
the place of the subject in badiou’s theory of discipline
of negation, also affirm the existence of the everywhere of the infinite, the not-
whole? Lacan’s answer is no: the not-whole, the everywhere that is infinite, is 
too indeterminate for the finite to be circumscribed by phallic jouissance. This 
thought of Lacan’s is seemingly confirmed by mathematics: there is no dialectic 
between the finite and the infinite – the infinite is the absolute alterity and in-
accessibility with respect to the finite. The paradigm of the absolute alterity of 
the infinite, as we have formerly seen, renders the Hegelian dialectic of the finite 
and the infinite impossible – the infinite is not the negation of the finite, nor its 
sublimation, but its inaccessible determination. According to the paradigm of 
the mathematical infinite, phallic jouissance functions similarly as the succes-
sion operator, such that, despite its unending insistence (an unending chain of 
desires), a circumscribed finite jouissance will never be commensurable to the 
infinite not-whole; the same way that no whole number is commensurable to ω:
This is a crucial adjective, both in set theory and in the logic of the formulas of 
sexuation. This enjoyment of the feminine not-whole is properly the inaccessible 
infinity in which castrated enjoyment is determined.50
But in axiomatic set theory, ω is an actual number, infinite in size, but actual 
nevertheless – i.e. this number exists in the same way that the number 2 exists. 
But actuality is not what Lacan is after. It is enough for him to say that the in-
finite is an inaccessible horizon for the finite. This gives us a good explanation 
as to why feminine enjoyment ultimately has the structure of a fiction: it is a 
fiction of the inaccessible. From here stems the organic relation between this 
enjoyment and God. This is precisely where Lacan drops his association with 
Cantor:
Thus, set theory is designed to restore the status of number. What proves that it 
does indeed restore it, within the perspective that I have been laying out, is that, 
setting out as it does the grounding of the One, and making number lean on this 
as a class of equivalence, set theory thereby manages to highlight what it calls the 
non-denumerable, which is very straightforward, as you are about to see. It’s read-
ily accessible, but to translate it into my vocabulary, I call it, no the non-denumer-
50 Ibid., p. 218.
48
reza naderi
able – an object I would unhesitatingly qualify as mythical – but the impossible 
to denumerate.51 
Lacan takes from set theory what he deems appropriate so he can “advance a 
new logic” to explain the non-existence of the sexual relationship. But the pas-
sage above completely shows his non-axiomatic comprehension of the denu-
merable. The axioms (of Separation, Power Set, Union, Empty Set, etc.) allow 
for the construction of the whole numbers. But none of these foregoing axi-
oms are responsible for the construction of the denumerable itself, because the 
denumerable is not constructible. It exists according to a separate axiom: the 
Axiom of Infinity – using Lacan’s parlance above, ω is readily accessible axio-
matically. Asserting the status of the denumerable as mythical is what makes 
Lacan a pre-Cantorian (and in our parlance, pre-disciplinary) in the end: for 
him (and this is why intuitionism sounds appealing to Lacan), the infinite is ul-
timately the paradigm of inaccessibility. 
The latter point is accentuated by the way Lacan mobilizes Cantor in his treat-
ment of the theory of identification. As we mentioned earlier, Lacan made use of 
the concept of sets in his Seminar IX, on identification, where he wants to move 
beyond Freud’s general theory of how representations associate themselves 
through an economy based on the quantity of excitement. At this point, Lacan 
took advantage of a method different than his usual one. Freud was already 
able to show that what is significant are associations wired in one’s psychic ap-
paratus. In contrast, Lacan wanted to show that, before this can happen, one 
needs to bring into the psychic economy something that has no signification, 
which can represent the lack of representation, that is, desire itself. Therefore, 
the question is: How can one have a representative with no representation? A 
difference with no signification? The problematic that this approach opens, ac-
cording to usual philosophical arguments, is that of the representation of noth-
ing. Lacan needed to show that a relation to some unity, which is also not a rep-
resentation of unification, is thinkable. This was not strictly a psychoanalytical 
problem, but rather a necessary stepping stone in Lacan’s argument. At that 
moment, Lacan found his solution in Cantor’s theory of multiples – because 
a set provides exactly this minimal measure of unicity without having to unify 
what it contains. With this step, Lacan mobilized Cantor in the correct sense: 
51 Lacan, … or Worse, p. 124.
49
the place of the subject in badiou’s theory of discipline
mathematics authorized Lacan to continue thinking maximally. From this, he 
proceeded to develop the concept of a unary trait, as a potentially denumerable 
set, as an addendum and extension to Freud, and to the existing psychoanalyt-
ical theories of the time.
This anecdote shows the positive influence that Lacan received from mathe-
matics, set theory, and axiomatic thought. Here, Lacan does not yet condemn 
Cantor for having mythical or imaginary commitments. It was not psychoanaly-
sis that was interpreting mathematics (as per Miller), but mathematics that was 
interpreting psychoanalysis. But there resides another point in this anecdote. 
We now know that the paradigm that Lacan wanted to move beyond is construc-
tivism, that is, he wanted to move to the paradigm according to which a rep-
resentation of a set does not have to be necessarily constituted by a representa-
tive, or a formula. We also know now that this is only possible by a commitment 
to the Axiom of Infinity that is deeper than what constructivism could afford. In 
other words, what Lacan wanted to achieve is possible not just by a commitment 
to the Axiom of Infinity, but also by a commitment to the genericity of denumer-
able sets: the movement we have been pursuing from Gödel to Cohen.
This finally takes us to the question crucial to our inquiry: What would it mean 
for the subject (in the analytical sense a woman) to have a determination that is 
of the order of the infinite, when this order is not merely fictitious and inacces-
sible? Let us see how Badiou answers this question, which summarizes the crux 
of our endeavor:
Since feminine enjoyment is of the order of the infinite, does it not turn out that, 
rather than having the structure of a fiction, it has the structure of an axiom? A 
woman then would, as the condition of her enjoyment, have to decide the in-
accessible as regards its existence. This axiomatic character of secondary enjoy-
ment in no way contradicts its unutterable character. Granted, the axiom does 
state something, but the decision on this statement, the gesture by which it is in-
scribed are [sic!] not all stated in the axiom itself. The axiom does not express its 
axiomatic dimension, and so the decision that it is remains tacit. Silently, in the 
infinite element of her enjoyment, a woman would have decided that with respect 
to primary or phallic enjoyment there exists an inaccessible point that supple-
ments its effect, and determines her as not-whole with regard to the function Φ. 
It is properly this silent decision that would forever block the sexual relationship 
50
reza naderi
from existing. For, summoned to the place of enjoyment, the position ‘man’ and 
the position ‘woman’ would continue to be separated by that layer (épaisseur) 
without substance (épaisseur) not even of the axiom, but of the axiomatic, and 
thus instituting, dimension of this axiom.52
What is important about the above paradigm shift (or a figure-ground change of 
perspective)? That the real of thinking – as what was thought of as impossible 
and impassable – becomes a positive category, from which new possibilities will 
arise: it is the pass of the real, the real as consistency and as generic.
We can interpret this change of perspective, a disciplinary operator which I call 
regionalization: this operator lays bare the presuppositions embedded in a cer-
tain theoretical edifice. This operator touches upon the themes of beginning, 
novelty, and interiority – and sits at the center of the theory of discipline. This 
operator has been utilized by Badiou, time and again: in his debate with Miller 
regarding the theory of discourse, with Lacan regarding the operation of sub-
jectivation in Logical Time,53 regarding the presuppositions of the doctrines of 
foundation and ground, and finally with regard to the cogito, those presuppo-
sitions that tie us to an objective determination of the subject. It is therefore fit-
ting that we complete our last construction with yet another application of this 
operator by our master. 
If the subject has a determination that is of the order of the infinite, and if we 
abandon the pre-Cantorian presupposition of the infinite as inaccessible – if we 
espouse the idea of the infinite as a (or the) positive category of thought (in our 
time), apropos the Cantorian revolution in mathematics – then this infinite de-
termination does not merely touch upon the real as mythical or mystical, but as 
generic. The essence of the subject is no longer unreachable, but comprised of 
an infinite truth. Following our construction of the subject as a non-relational 
category – subject minus the object – we come to realize that the determination 
of this subject is infinite, and this determination under the idea of infinity and 
axiomatic thought is nothing but an infinite truth. 
52 Badiou, Conditions, p. 211.
53 See “Subjectivizing anticipation, retroaction of the subjective process”, in Badiou, Theory 
of the Subject, pp. 248–253.
51
the place of the subject in badiou’s theory of discipline
If we agree with Badiou that the category of the subject in philosophy has act-
ed as modernity’s operator of compossibility – a constant theme that has been 
present from Descartes (science), to Hegel (politics), to Heidegger (art), and to 
Lacan (love) – and if the return of philosophy will depend on the reworking of 
this category after its destitution in the hands of the linguistic turn, then, in my 
view, this reworking after Badiou must occur through the thought of discipline, 
in whose center we find the commitment to the maximality of thinking, the idea 
of infinity and its capacity for regionalization.
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