Truth, Subject and Philosophy in Badiou’s Ontology of the Multiple

By Jonathan Arriola




ABSTRACT

In the following paper we explore Badiou’s ontology of the multiple. Drawing upon the major mathematical revolutions that took place at the end of the 19th century and the beginning of the 20th century, the French philosopher argues that, contrarily to what the Western tradition has defended, ontology must abandon the primacy of the One in the apprehension of being. Bent on the idea that mathematics is ontology and that Set Theory provides a pathway to the being of being, Badiou affirms that being is multiple and that, accordingly, it is necessary to lay out a new ontology. This assertion leads Badiou to reformulate the notion of truth and, along with it, to rethink the role of philosophy in the sophistic era of feeble thinking and the death of Reason.

1.  Badiou’s Ontology

“God is truly dead, as are all the categories that used to
depend on it in the order of the thinking of being.
The pass that is ours is a Platonism of the multiple.”

Badiou, Manifesto for Philosophy

When set against the predominant tendency of contemporary French philosophy and, more generally, of the Continental tradition in the last decades, Badiou’s philosophy stands out because it clearly goes against the current. Although his thought, as we will see, is fabricated with the bricks of very old ideas, albeit reformulated in a modern argot, his philosophy could be nonetheless considered highly subversive when we take into consideration that it contradicts in many ways the core of the philosophical programs developed since Heidegger’s reappraisal of ontology and Althusserean structuralism. Three of them are of particular relevance in the context of this paper. Firstly, Badiou reaffirms a systematic approach for philosophy amidst the postmodern exaltation of difference, the Other and its congenital contempt for any gesture of totalization. Secondly, he reassesses the ontological role of mathematics in contrast with the privileged status the latter Heidegger had yielded to the poem in safeguarding the “ontological difference” between Being and being. And, thirdly, Badiou redignifies the category of Truth (and truths) against the hegemony of the so-called “feeble thinking”, which gained momentum after the dogmatic terror of National-socialism and Stalinism, and, above all, against the many auguries announcing the end of philosophy. 
Nevertheless, Badiou’s philosophy, however explicitly anti-postmodern in many respects, doesn’t constitute a return to a classical modern philosophical system, aiming at totalizing reality and that thus disregards the role of difference, the importance of the poem and the plurality of truths. Rather, in a movement that remembers pretty much the Hegelian Aufhebung, Badiou intends to overcome post-modernity while integrating some of their fundamental claims in a broader thought that would re-enable philosophy to perform its task, i. g. to restore the category of Truth and its traditional exigencies of eternity, evidence and stringency. Hence, by means of his central concept of “event”, Badiou’s philosophy manages to make room for the appearance difference and multiplicity, while preserving the strong systemic vocation of his philosophy, however in a non-Hegelian and non-structuralist manner. Likewise, by defending the existence of four conditions of philosophy (art, politics, love and science) Badiou acknowledges the role of poem, in the form of art, and the different truth-procedures, inherent to each condition, that compose the world of appearance.
In order to better understand how this works in his thought and it is necessary to deepen in his general ontology.
First of all we must say that Badiou’s ontology rejects transcendence, offering thus a purely immanent account, which fulfills Heidegger’s ontological maxim of avoiding falling in theology or metaphysics when inquiring being qua being. However, one of the most remarkable aspects of Badiou’s ontology is that it goes beyond the positive study of being insofar as it also seeks to think, however problematic that might be, at first glance, its negative moment. Put it simply, his ontology is twofold: it concerns, on the one hand, Being qua being and, on the other, Being qua not being.
Badiou introduces the negativity in his ontological scheme by means of resorting to the mathematical figure of the “empty set”, representing the fundamental void that is common to all sets and which Badiou sees as the latent possibility of non-Being to manifest itself in the realm of appearances. This leads us directly to the basic axiom of Badiou’s system: namely, that mathematics is ontology[1]. Indeed, mathematics is for Badiou that which describes the dominion of Being qua being and not being. But, in reality, not all of mathematics has for Badiou ontological implications. Rather, the French philosopher only accords to set theory such ontological status.
The reason why Badiou equates set theory with ontology is that, in his view, set theory alone offers a pure formal doctrine of the multiple. In effect, contradicting the Greek tradition that dominated Western thinking emphasizing the ontological unity of being as opposed to the plurality of concrete beings, Badiou avers that Being in itself is multiple, inconsistent and irreducible.
As it is known, Parmenides, advancing Plato’s theory of ideas, argued that everything that truly is, is both One and immutable, thereby negating the ontological possibility of plurality and change and, as a result, conceiving of the reality perceived by the senses as ultimately false. Having such monist thesis as a basis, the Greek philosopher assured that being, insofar as it is immutable and timeless, is only thinkable in the terms of the logical discourse. In Parmenides’ view, being is invariably submitted to the principle of no-contradiction for it cannot be that what is, is not or is another thing than itself. In that way, his philosophy equates being with thinking.  
Conversely, Badiou defends the meta-ontological claim, underpinning all his system, that l’Un n’est pas and as a result will challenge the very idea of a binary logic which presupposes the Parmedian conception of being as one and immutable. To do such a thing, Badiou resorts to the major revolutions in mathematics that took place in the second half of 19th century and the beginning of the 20th.  
Particularly important for Badiou’s thinking is Georg Cantor’s discovery of the infinite multiples. The core of Cantor’s breakthrough was his demonstration that multiples are inconsistent with one and other and thus totally irreducible to a unique and all encompassing One. Against the longstanding tradition in mathematics, which used to think the infinite in terms of potentiality, Cantor shows that there are actually different levels of infinite, indicating that infinite is not one but rather multiple. Through a series of mathematical demonstrations, which were striking and therefore very resisted by mathematicians at first, Cantor proves the existence of an, allow me the wordplay, “infinite hierarchy of infinites”, composed of countless sets of infinites, each of them infinitely larger than the other and forming accordingly a very complex structure impossible to be articulated in a coherent whole, given its irreducible parts.
By demonstrating that infinite does not depend on a grand One, one overarching set, Cantor showed how important set theory was in the readdressing of the basis of mathematics. In this manner, Cantor redeemed set theory from the marginal place it had been assigned since Antiquity. The task of (re)thinking mathematics from the standpoint of the multiple, that is, of set theory, was to be performed, first, albeit unsuccessfully, by Gottlob Frege, and a little bit latter by Zermelo and Fraenkel, who, by drawing upon Cantor’s work, proceeded to elaborate an axiomatization of set theory and to provide by means of it with a formal foundation of mathematics, which came to be recognized as the most common one.
Among the axioms the Zermelo-Fraenkel theory postulates, there is one that is of especial relevance for Badiou’s ontology of the multiple since institute the prohibition of self-belonging in the realm of sets: namely, the axiom of foundation (or regularity). Echoing Russell’s famous paradox formulated in 1901 against Frege’s set theory, Zermelo-Fraenkel axiom of foundation deems as impossible the fact that a set belongs to itself as an element. For Badiou, that represents the formal proof of the inexistence of a totalizing One and therefore constitutes a straightforward attack to all thinking that departs from supposedly all inclusive and self-contained ideas, such as God, Nation or Nature or any other form of Absolute. As Alex Ling puts it: “pure multiplicity is for Badiou anterior to the one; inconsistency precedes consistency.” (Barlett, A. J.; Clemens, 2010 : 49)
On the other hand, the Zermelo-Fraenkel set theory contemplates an exception for the axiom of foundation and that is the represented by the most singular set: the empty set. This set is the only one which belongs to all sets and therefore is at the same time part and set. Needless to say that Badiou’s draws ontological implications from it too. Indeed, he interprets the empty set as the possibility of a “new” occurrence to happen in all given multiple. Hence for the French philosopher the empty set formalizes what he calls as “event”. The “event” represents in Badiou’s program the limits of the thinkable, that which is impossible to say and to name by ontology insofar as it exceeds the parameters of the system into where it bursts. And we say burst because, as we have already mentioned, the set theory has a paradoxical status with regard to all multiples. It belongs to a determinate multiple inasmuch as it is an element of it but, at the same time, it does not belong to it, since that the empty set represents the possibility of the new to come in. Thereby, no multiple can ever be a closed system because its bears with itself the possibility of a radical rupture: the event, which the empty set represents.  
At this point, it is necessary to clarify that Badiou’s ontology works in two levels: the situation and the state of situation[2]. The former is the space of pure presentation, where there is no sense at all, being the sphere of the “il y a”, and which constitutes an area of exploration of how the next infinite will be. The situation is a space of transcendence within the system of Badiou. However, it is transcendence in the immanence. Therefore, rather than an ontological space, the situation would be a meta-ontological realm as it provides the formal conditions from which the state of situation will acquire its constitution -as well as the possibility to reconfigure itself by means of the excess introduced by the event, as we will see later. In effect, the state of situation is the level of (re)presentation of the inconsistent or consistent multiples and, consequently, it is the place where different possible worlds gain concrete appearance. Rather than just one ontology, what we have at this level is fourfold ontological structure, each one with its own logic and truth-procedures: love (the amorous encounter of two), science (the matema), politics (political invention trough a political movement) and art (the poem or any artistic invention).

2.  The Renewal of Truth

As he explicitly states in his Manifest pour la Philosophie, Badiou wants to reassess the philosophical importance of the notion of Truth and, with it, reassess the value of philosophy and its sense in the 21st century. Above all, what Badiou seeks is to redeem Truth from the numerous invectives that it has undergone by postmodernists, which in the wake of Nietzsche’s attack on Platonism and of the totalitarian trauma, declared the depletion of the concept of Truth and thereby commended philosophy to death. In sharp contrast to such postmodernist’s sentence, Badiou insists on the modern claim that Truth must be the “central category” of philosophy. By this means, Badiou aims at rehabilitating philosophy and combat nihilism, in the form of a radical relativism, which beats at the very heart of the postmodern program[3]. Indeed, post-modernity can be seen as a child of the second Wittgenstein, whose conclusion in Philosophical Investigations, asserting that all philosophical problems are, at bottom, problems of language, marked the course of philosophy in the sense of relativism from the Second World War on.[4]
For Badiou, the result of this understanding of philosophy in just linguistic terms is that it replaces truth and error for speech and silence as the main problem of philosophy, paving the way for relativism to dominate the scene. By enthroning difference and language in lieu of truth, Badiou sees post-modernity as equivalent to modern sophism since it declares “… that there are only conventions, rules, types of discourse, language games” (119).   
On the other hand, in Badiou eyes the blind sacralization of truth, which is the opposite number of postmodern conviction, also entails great dangers, perhaps more evil ones than those brought by sophistic relativism. In effect, if with sophism, we have indifference to truth, with dogmatism, we have intolerance.
Furthermore, the canonization of truth is not whatsoever foreign to philosophy’s history. On the contrary, from the very beginning of Western thought, countless philosophers, starting with Plato, have systematically incurred in what Badiou calls the “disaster”, that is, they have embraced the thoroughly misconceived idea that it is philosophy, and only it, the kind of thinking in charge of producing truth. The French philosopher put it as follows:

It is no longer legitimate to say, as does the dogmatist, that there is a solo locus of Truth and that this locus is revealed by philosophy itself. Such a retort is excessive, overstrung and disastrous. (1999: 133)

However, Badiou argues that this deep tendency of Western philosophy to see itself as the sole locus of truth, had its utmost expression in the totalitarian episodes of Nazism, Imperial parliamentary democracy and Stalinism, which claimed to be the guardian of some “sublimated bodies”, either Race, Civilization and/or Proletariat. In Badiou’s vision, terror is thereby the natural consequence of an inappropriate divinization of truth. In effect, when a truth is proclaimed as being complete and holly, then the dignity of other possible truths is immediately excluded: they are condemned as illegitimate and moreover as contemptible. Ethics become thereby the servant of such sacralized truth and of the sublimated body it supposedly illuminates. On the contrary, everything that stands outside or against such enthroned truth, either be it the Jews, the Communist, the immigrant, the Uncivilized, etc. become the object of persecution as they are equalized to the incarnation itself of impurity and error. By reducing the irremediably multiplicity of the names of truth to a single, all-inclusive and eternal name[5], for instance, the idea of Good, terror arises as an urgent necessity, as the sole possibility that could enforce the divinized form of truth into reality itself. In that manner, disaster sets in.

In Badiou’s eyes, the origins of all substantialization of truth, which is it at the basis of all dogmatic stance, lay in a deep misunderstanding of being qua being. Indeed, according to his ontology, truth is not a being and cannot ever be a being. For the French philosopher, truth’s nature is heterogeneous and multiple[6] and it is so in a twofold sense[7]. First, because it cannot be thought apart from the four conditions as they have each own their own truth-procedure. In that sense, truth is immanent, thus historical, as it is always the truth of a situation. And second, truth’s nature is heterogeneous because, as a result of the latter, it can always be another thing: in other words, truth is never definitive or fixed. In effect, the event, along with the subject and the truth that arise with it, structures a determinate state of situation but, qua void, it remains always open to the new, acquiring new forms and making an appearance in the (phenomological) world. To negate this is to negate the nature of truth itself. Given its close relationship with philosophy, to reject the very possibility of an authentic philosophical thinking. Nevertheless, the fact that truth, for Badiou, is multiple and heterogeneous does not mean that truth is plural, as the Ancient or Modern sophists claim. According to Badiou, multiplicity is not equal to pluralism, for the latter implies that there are, in reality, no objective truths and therefore that all construed truths are equally valid, while the former points to the acknowledgment that truths arise within the four truth-procedures of each condition.

The latter leads us to another crucial thesis of Badiou’s ontological system, which, he argues, was already implicit in Plato’s aporetic dialogues: namely, that truth, formally expressed, is indeed the void. For truth is, in its pure objectivity, that which is unpresented and unrepresentable[8]. Hence the French philosopher says that truth produces a hole in actual knowledge. In that sense, truth and event, insofar as the latter it is too related with the figure of the void, are intrinsically link, specially when it comes to depict them in formal terms. And that is precisely the point of Badiou’s argumentation when he declares that all truth is post-événementielle, meaning that no truth is structural or axiomatic but rather entirely dependent on a historical and contingent singularity, embodied by the event (1999: 107). Therefore, no nomology of truth can be established since its empty essence obeys no pattern at all: all truths “just” appear in the world. According to Badiou, no further ontological inquiries can be made concerning what is that which causes an evental truth to appear in the world, given that, for him, and plainly put, there are indeed no such causes in the first place. Said otherwise, the truth of an event is, for Badiou, causa sui, namely, the immanent origin of its own existence: consequently, no more fundamental cause, determining its nature, can be elucidated. Thereby, the essentially indiscernible character of truth marks the very limits of Badiou’s immanent ontology. Needless to say, it is identifiable at this point a clear theological moment in Badiou’s proposal. It is a “secular theology” though, insofar as Badiou does not allow transcendence to permeate his ontology and in that manner recognizes no God. Rather, the theological aspect of his thought lies is in the fact that the event and truth coming into existence is akin to revelation, into which no rational inquiry can fully penetrate.

A.   Event, Subject and Truth
 
In order to illustrate the close triadic relation between event, truth and subject that lies at the very heart of Badiou’s ontology, the French philosopher resorts to the example of Saint Paul’s conversion to the Christian faith, who operates by reducing the universal truth of Christianity to the singular event of Jesus’ Resurrection. The episode is paradigmatic inasmuch as it portraits the logic and the sequence of emergence of all evental truth. Although truth’s appearance into the world is itself lawless and random, for Badiou, the ontological structure regulating its development, as that of being, is recurrent.  
Indeed, regardless of their particularities, all truths begin with a historical eruption. In the case of Saint Paul, such eruption is incarnated by his mystical and thoroughly unforeseeable –thence the randomness of truth- encounter with the divinity, prompting his conversion from paganism to Christianity. In a similar vein, Einstein’s groundbreaking relativity theory founded a new paradigm in the realm of science by ruling out the longstanding Euclidian comprehension of space. For their part, politics and love are not the same after, for instance, the event of Marxist communism, who, drawing upon Hegel’s dialectic, strongly criticized the formalism and ahistoricity of liberalism, and Freud “discovery” of the unconscious, which challenged the Cartesian idea that the subject is “one” and “self-transparent”.

One of the paradoxes of truth is that, despite its singular localization and strong historical nature, it has nevertheless an irrevocable universal vocation: furthermore, this universality is, in Badiou’s conception, the distinctive mark of any authentic truth. By reconfiguring the state of situation, truths have consequences that necessarily go beyond the particular time and space in which they were born. For instance, the emergence of a truth can lead to a reinterpretation of the past as well as it can affect the way the future is conceived. Moreover, an evental truth might also irradiate consequences for other state of situations: namely, it has the potential of becoming general.   

On the other hand, event and evental truth have the particularity of giving birth to a new subjectivity. Thus, for Badiou, the subject is neither an essence nor an individual. It is rather a process which must be understood in relation to the irruption of the event. However, it is the decision of this in status nascendi subject to be loyal to the truth that the event reveals what consolidates himself as a new form of subjectivity. In that sense, it is worth noting that the decision founds the subject since the subject does not exist before it. Thereby, the subjectivization process comprises two instances. On the one hand, it encompasses the objective conditions of possibility for its arising, that is, the opening of an event in the world. On the other, the (pre) subjective ones, pointing to the decision of the incoming-subject to name the event and to be loyal to it. Again, this is visible in the case of Saint Paul, who appropriates for himself the event by deciding to evangelize once the miracle of Jesus’ Resurrection touched him. By that means, he molded a new subject upon which the Catholic Church will be built.



B.   Philosophy and Truth

“What is proper to philosophy is not the production of universal truths,
but rather the organization of their synthetic reception
by forging and reformulating the category of truth”
Badiou, Saint Paul.

Philosophy has a very important role to play in the context of Badiou’s ontology. As we have latter pointed out, one of Badiou’s main goals was to rule out the sophistic relativistic stance, defending the impossibility of accessing being qua being, which deemed philosophy’s main task, that is, the seeking of truth, as wholly unfeasible and fruitless. By recovering truth as a worthy category of thought, Badiou opens the paths for philosophy to come in again into the ontological scene. However, the relation of philosophy with truth is not the same as that which the Greek tradition and modernity had formerly envisioned. To put it straightforwardly: for Badiou, philosophy does not produce truths. Rather, truths are exclusively produced within the four conditions and in accordance to their own particular truth-procedures. These procedures enable to think the fundaments of being.


The role of philosophy in this context is to analyze the locus where truths occur but it should keep away of enthroning itself as the source of them. By this means, Badiou wants to avoid the temptation of mistaking the production of truth with philosophy itself, as dogmatists do, and therefore of falling into the “disaster”, when philosophy transforms itself into terror and bigotry. In that sense, by ascribing to the conditions the production of truth, Badiou conceives of them as restrictions for philosophy insofar as it must abstain itself from reclaiming exclusive sovereignty over the realm of truth, thus mistaking its ontological place. But at the same time, these conditions are that which allow philosophy to emerge.


The reason for the latter is that philosophy first and foremost raison d’etre is to make “compossible” the truths that appear in the conditions, offering the vantage point of allowing its collective intelligibility. Just as philosophy must keep away from seeing itself as the sole locus of truth, so, according to Badiou, it must avoid suturing itself to one of its particular conditions too[9]. The suture occurs when philosophy falls under the spell of one of its conditions and at the same time exercises a hegemonic sway over the rest. This serious misunderstanding of philosophy’s role in relation to its conditions has been very frequent in the Western tradition too. As Daniel Bensaid puts it: “In the wake of the ‘Galilean event’, philosophy in the Classical age fell under the domination of its scientific condition. In the aftermath of the French revolution, it came under the sway of its political condition. Lastly, with Nietzsche and Heidegger it withdrew in favor of the poem.” (2004)


The main problem with the suture is, first, that it disregards the ontological discontinuity between the four conditions, thus inappropriately projecting ontological categories to other conditions, and, second, that it undermines the strong systematic nature of philosophical inquiry. For Badiou, philosophy’s work is, above all, to compose and make possible, hence his neologism “compossibilité”, a space where the different generic procedures could be articulated. In other words, philosophy must be capable of thinking conjointly the four conditions without being reduced to any of them. Thus philosophy is wholly different from art, politics, science and love. However, it is in philosophy that the truths of these four non-philosophical conditions can be systematized, reconfigurated and transformed into a philosophical Truth. Indeed,

La philosophie n’existe que quand elle propose une compossibilité de ses conditions, la vocation systématique est inévitable et fait partie de l’essence même de la philosophie. (Badiou 1990 : 25)

3.    Bibliography:

· BADIOU, Alain. Infinite Thought: Truth and the Return of Philosophy. Ed. Continuum: 2004. London.

· BADIOU, Alain. Manifesto for Philosophy. Ed. State University of New York Press. 1999. United States.

· BADIOU, Alain. Saint Paul: The Foundation of Universalism. Ed. Stanford University Press. 1997. United States.

· BADIOU, Alain. L’entretien de Bruxelles. Les Temps Modernes. 526. 1990.

· BARLETT, A. J.; CLEMENS. Justin. Alan Badiou. Key Concepts. Ed. Acumen. 2010. United Kingdom.

· BLAKE, Terence. In: THEORIA, La Revue. Badiou’s Reduction. Retrieved from: http://www.theoria.fr/badious-reduction-1890/

· FELD, Alina. Karl Jaspers and Alain Badiou on the Destiny of Philosophy. In: Existenz. Volume 4, No. 1, Spring 2009. Retrieved from: http://www.bu.edu/paideia/existenz/volumes/Vol.4-1Feld.html

· GÓMEZ, Guillermo. Presentación y Entrevista: Alain Badiou. 2007. Retrieved from: http://www.uia.mx/actividades/publicaciones/iberoforum/3/pdf/carlosg.pdf

· WILDEN, William. Forcing Analogies in Law: Badiou, Set Theory, and Models. In: Cardozo Law Review. 2009. University of Miami Legal Studies Research Paper No. 2009-33. Available at SSRN: http://ssrn.com/abstract=1507933



[1].- Needless to say that such a thesis is anti-Heideggerean in essence given that for the German philosopher mathematics has at its very basis a metaphysical interpretation of Being in terms of presence that ultimately led to the “oblivion of Being” and thus to the rise of modern technology, reification and inauthentic existence.
[2].- Apropos of the situation Alex Ling : “A situation is thus any presented multiplicity whatsoever. Or again, a situation is the constitution of inconsistent multiplicity: it is literally “the place of taking-place” [… pure presentation prior to the structured presentation that is the situation. (Barlett, A. J.; Clemens, 2010 : 50)
[3].- In relation to that, Badiou himself says the following: “Sophistic and postmodern, contemporary philosophy endorses language games, deconstruction, feeble thinking, irremediable heterogeneity, different and differences, the ruin of reason, the fragment or discourse in shreds, thus placing philosophy in an impasse.” (1999:135)
[4].-Of course that is not Wittgenstein alonewho opened the path to postmodernity. Also Nietzsche’s death of God points to the same direction.   
[5] The multiplicity of the names of truth—theorems, principles, declarations, imperatives, beauty, and laws—becomes restricted to one single eternal, genuine name, i.e.,
[6].- With regard to that, Badiou says: “As being is multiple, and truth must be, a truth shall be a multiple, thus a multiple-part of the situation of which it is the truth, it cannot be an “already” given or present part. It shall stem from a singular procedure.” (1999: 106)
[7].- Indeed, for Badiou “Prior to philosophy, a “prior to” that is not temporal, there are truths. These truths are heterogeneous, and proceed within the real independently of philosophy [… These truths are related to four possible registers, systematically explored by Plato. The four plural loci, where a few truths “insist”, are mathematic art, the political, and the amorous encounter. Such are the factual, historic, or pre-reflexive conditions of philosophy.” (1999: 123)
[8].- In that sense, it is worth pointing that “el vacío de la categoría de Verdad, con V mayúscula, no es el vacío del ser, puesto que es un vacío operatorio, y no presentado. El único vacío que es presentado al pensamiento es el vacío del conjunto vacío de los matemáticos. El vacío de la Verdad . . . no es pues ontológico; es puramente lógico” (Badiou, 1992: 59).
[9].- Concerning that, Badiou says the following: “The most frequent cause of such a blockage is that instead of constructing a space of compossibility through which the thinking of time is practiced, philosophy delegates its functions to one or another of its conditions, handing over the whole of thought to one generic procedure. Philosophy is then carried out in the element of its own suppression to that great benefit of that procedure.” (1991 : 61) 

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