LAI Tsz Yuen
About the author
Lai Tsz Yuen, Ph.D. Candidate, Department of Humanities and Creative Writing, Hong Kong Baptist University, research topic: French mathematical structuralism (Bourbaki, Lautman, Deleuze, Badiou) and the realist/materialist turn of contemporary philosophy. Author of Topography: 12 Interviews with Contemporary Art Institutions in Hong Kong (Hong Kong: Exterior Culture, 2011).
Philosophy is prescribed by conditions that constitute types of truth or generic-procedure. These types are science (more precisely, the matheme), art (more precisely, the poem), politics (more precisely, politics in interiority, or a politics of emancipation) and love (more precisely, the procedure that makes truth of the disjunction of sexuated positions).
Alain Badiou, Conditions, (1992, 2008), p. 23
In Alain Badiou’s Manifesto for Philosophy (1989, 1999), the problem of the condition of philosophy has been raised afresh. In the particular context of contemporary philosophy ― from the end of the 20th century to present, confronting the ideology of ‘the end of philosophy’ and the current situation that Badiou calls ‘philosophy’s paralysis’ ― the re-examination of this problem, for Badiou, is to reaffirm the possibility and necessity of philosophy by providing it with proper restrictions: ‘Philosophy has begun; it does not exist within all historic configurations; its way of being is discontinuity in time as in space. It must thus be presupposed that it requires particular conditions’. Here, Badiou examines the possibility of philosophy in terms of its conditioned productive process, what he calls ‘generic procedure’, and announces the four generic procedures: the matheme, the poem, political invention and love, from which truth, the destination of philosophy, can be generated and seized by philosophy. In this sense, matheme, poem, politics and love, as truth procedures, are four conditions of philosophy. They can be qualified as conditions because they are the ‘evental origin’ of truth. In these four fields, event, something new and exceptional that supplements a situation or state of things, can take place, so that truth, which cannot be absorbed by the established system of knowledge relative to the situation but, rather, suspends and collapses the orderings of this system, is able (‘able’ here means ‘by chance’) to be generated in terms of the invention of new name (additional signifier) and the configuration of generic procedure corresponding to that particular event: ‘The origin of a truth is of the order of the event’. Thus it can be seen that it is an event happened in the field of matheme, poem, politics or love that defines and configures particular generic procedures. Through these generic procedures philosophy becomes possible and truth is able to be generated. Motivating by an event, philosophy within its conceptual space liberates the immanent movement of thought and relates those heterogeneous truth procedures to the singularity of time. Since philosophy is always ‘a reflecting torsion about that which conditions it’, it is the crises, the precarious conditions that sustains philosophy and makes a philosophy the great one: Philosophy pronounces the conjuncture of truth and its compounding function sets the generic procedures in the dimension of their joint historicity.
What does ‘condition’ mean in particular case? Here, I merely focus on the mathematical condition of Badiou’s thought for the sake of convenience in discussion. Concerning Badiou’s philosophy, or more precisely, his ontology presented in his first magnum opus, Being and Event (1988, 2006), the constitution of set theory of Georg Cantor (1845-1918), as an event happened in the history of the 19th century mathematics, is the mathematical condition of his thought. Cantor’s development of ‘transfinitude’ and his two theoretical inventions around this development, the first concerns the infinite multiplicity in positive sense by establishing the evaluation of different orders of infinity while the second concerns the consistency of the infinite in terms of the concept of ‘set’ in order to solve the traditional difficulty of the inconsistencies of the infinite, constitutes a critical turning point in the history of mathematics, a history that has been haunted by controversies on the problem of the one and the multiple since its beginning. From the first theoretical invention, Cantor finds that there must be orders of infinity in excess of the denumerable infinity or the ‘counted infinity’. From the second, he coins the term ‘transfinite’ which are numbers (cardinal numbers, ℵ) that are larger than all finite numbers yet not necessarily absolutely infinite. By developing such a ‘transfinite paradise’ (imitating David Hilbert’s expression), Cantor invents a new form of multiplicity, namely, a multiplicity without one. Based on Cantor’s invention, Badiou in Being and Event conceives and executes a subtraction of ontology from the metaphysics of the one and make his fundamental distinction between consistent multiplicity (multiplicity counted as ones) and inconsistent multiplicity (multiplicity qua multiplicity). This inconsistent multiplicity has been denied, excluded by the metaphysics of the one and considered as ‘nothing’, as the ‘impossible’. By subtraction or by overcoming the metaphysical constraint of thought that claims ‘what is not a being is not a being’ (Leibniz’s formulation), Badiou makes his decision: ‘the one is not’, which means that ‘nothing’ is, and dedicates his philosophical project towards the problem of that ‘impossible’: Can multiplicity be thought for the sake of the multiplicity rather than reducing multiplicity into any one? In the condition of this ‘Cantorian event’, which happened in mathematics yet contained great ontological significance, Badiou is able to deploy inconsistent multiplicity into his ontology and identify ontology with mathematics by announcing his famous statement: ‘Mathematics is ontology’ ― the ontological problem of ‘being’ (being qua being) can be ultimately grasped in terms of an ontology/mathematics of the ‘multiplicity’ (multiplicity qua multiplicity).
However, it cannot be ignored that Cantor’s set theory has its limitation, e.g., his intuitive definition of ‘set’, simply as an aggregation of separate objects of intuition or thought, leads to contradiction (which has been exposed by Russell’s paradox). In the subsequent development of set theory this definition is rejected by many mathematicians. Badiou is well aware of the distance between Cantor’s naïve set theory and the axiomatic set theory developed in the 20th century (Zermelo–Fraenkel set theory, in short, ZF, now becoming the standard of set theory) and must acknowledge that his ontology (concerning Being and Event) is deeply influenced by Ernst Zermelo and Abraham Fraenkel’s axiomatization of set theory, Nicolas Bourbaki’s naming of the empty set (∅), Paul Cohen’s forcing of the generic sets, etc. Then in what sense can we say that the constitution of Cantor’s set theory is the mathematical condition of Badiou’s philosophy? Here, a more definite meaning of ‘condition’ shall be explicated. The Cantorian event as a condition means that this event defines the problematics (the problem domain) of the post-Cantorian thought. It is equivalent to saying that what conditions Badiou’s thought is not merely those inventions of Cantor’s set theory but its difficulties. And, for Badiou, the latter is definitely more crucial to the post-Cantorian thought including his philosophy. In Cantor’s later period of research, when he considers ‘what sort of multiplicity would constitute a set’ and ‘can there be a set of all number’, he realizes that, concerning the cardinality (the size) of set, his conception of set leads to contradiction. In order to preserve the consistency of his idea of the well-ordered set, he cannot but separate the inconsistent multiplicities, the ‘untotalizable’ multiplicities what he calls the ‘absolutely infinite’, from any consistent multiplicity that would constitute a set, and leave this inconsistent multiplicities to the realm of the absolute (God). This ‘point of the impasse’ of Cantor that forces him to go through with his doctrine of the absolute opens up an evental site and thus prescribes the subsequent development, that is, the axiomatization of set theory in the following decades. It also grounds and limits Badiou’s ontology within the horizon of Cantor’s ‘absolutely infinite’. Paradoxically, it is this absolutely infinite that has been excluded by Cantor from his conception of set makes the conception possible. It reveals a topological relation, therein the inconsistent or excessive multiplicities grounds the establishment of the consistent multiplicities, the obstacle or ‘the point of impossibility’ grounds the consistent treatment of the inconsistency in mathematics, the ‘non-being’ grounds a presentation of being in ontology ― in a word, it reveals the position of the ‘not’, the exclusion that functions as the precondition of the mathematical ontology and its operation. Upon this ‘not’ Badiou develops his most important concept: the void. And this topological relation or the dialectic conditioned by topology manifests the profundity, the dynamic of Badiou’s entire philosophical project in Being and Event.
Following Badiou’s retrospect of this Cantorian event, we see the historicity of ‘condition’. The constitution of Cantor’s set theory in the late 19th century was singular in the history of mathematics. His invention of ‘set’ provided a language that could be used in the definitions of all kinds of mathematical objects. And its difficulties (paradoxes) forced set theory towards axiomatization in the 20th century, which is ‘an intrinsic necessity’ for the development of set theory itself. Between 1908 and 1940, the task of axiomatization was undertaken by Zermelo (among some other mathematicians), and accomplished by Fraenkel (i.e. the ZF system) as well as by Bourbaki (see ‘Summary of Results’, first published in 1939-1940, and then incorporated in Elements of Mathematics, Vol. 1: Theory of Sets). Thereafter, set theory became a foundational system of modern mathematics. For Badiou, the axiomatization of set theory manifests even more crucial significance in ontology ― based on the axiomatic set theory (the ZF system), there is only one type of presentation of being: the multiple. Such consideration of any multiple as intrinsically multiple of multiples, as the multiple without implying the being-of-the-one, formulates one fundamental proposition in contemporary research of ontology after the end of the metaphysics of the one or the ‘ontotheology’. This fundamental proposition only becomes conceivable in the condition of the establishment of the axiomatic set theory and its deployment of the multiplicity. To sum up in a general theory or with a ‘logical schema’ from the perspective of intellectual history, the Cantorian event, as an exception or ‘singularity’ happened in intellectual history, disturbs the inherent order of the knowledge system, engenders a transformation of its foundation and progression, and splits up a post-evental period from the pre-evental period. (Event is a caesura. Gilles Deleuze provided an excellent explication of this mechanism in Difference and Repetition (1968).) In the post-evental period, specified by its condition, a certain configuration of mathematics/ontology generates. It cannot be contained and legitimatized by the prevailing language and the dominant system of knowledge of the pre-evental period ― such configuration is totally unconceivable from a pre-evental perspective. In this sense these two periods must be divided and something ‘new’ (the post-Cantorian thought, the ontology of the multiplicities) has been invented ― this ‘new’ does not merely bring up a new form but also reconstitutes the foundation (the ‘past’) of the system. This configuration and its development would persist all through the post-evental period until the happening of a next event which is absolutely unpredictable at the moment. The happening of an event must give rise to the transition of conditions and thereafter the transformation of the configuration of thought. According to above logical schema we see that a historical process, namely, the happening of an event, the split, and the transition of the condition, is irreversible (as what ‘historicity’ means), while an event must be verified and articulated retroactively (as what Badiou’s retrospect and reconstitution of the Cantorian event has revealed). It also demonstrates that in any investigation of intellectual history the conventional schema of ‘foundation’ since Immanuel Kant that focuses on the research of the groundwork of knowledge without concerning the function of event and the transition of conditions from now on must be replaced by this schema of ‘condition’. The ‘foundation’ of a knowledge system in specific period is the effect or consequence of the (re-)configuration induced by an event and prescribed by particular conditions: ‘condition’ is primary while the establishment of ‘foundation’ is secondary. This schema introduces new horizon in studies of intellectual history.
In his Manifesto for Philosophy and Conditions Badiou has provided explication of how philosophy eclipses in specific period because of its ‘suture’ to only one condition. He defines ‘suture’ as a situation in intellectual history when philosophy ‘delegates its functions to one or other of its conditions, handing over the whole of thought to one generic procedure’, and result in its own suspension or suppression in favor of that procedure. For example, Badiou indicates, the positivist or scientistic suture as the main suture since the 19th century still dominates academic Anglo-Saxon philosophy. And in continental philosophy, after Hegel, philosophy in a period ‘is most often sutured either to the scientific condition or to the political one’, while after Nietzsche and Heidegger, poetry becomes another privileged condition that gives form to what Badiou calls ‘the age of poets’, a period in which ‘all philosophers claim to be poets’. With regard to contemporary philosophy, Badiou puts forth the completion of this situation by proposing a ‘de-suturation’, especially a de-suturation of philosophy from its poetic condition, and proclaims a renaissance of philosophy. This return of philosophy is only possible when the compounding function of philosophy is resumed, such that its four conditions can again be bonded together in their joint historicity. He affirms that crucial events have already taken place in the field of matheme, love, politics, and poem, and correspondingly, conditions of philosophy must be re-defined. Under these most recently defined conditions, reconfigurations of thought becomes possible and necessary in the contemporary era. This task for contemporary philosophy is very similar to the one that gave birth to the western philosophy in ancient Greece, in which philosophy must distinguish itself from ‘sophistry’ so as to draw itself out of the age of sutures. Badiou juxtaposes these two critical moments and declares that, for both cases, the philosophical gesture which is able to carry out the anti-sophistic configuration of thought must be a ‘Platonic gesture’. In the Greek era, it was Plato’s insistence in separating a distance between philosophy and the poem that foreclosed the ‘Parmenidian regime’ ― this regime of the relation between philosophy and the poem formed a pre-commencement of philosophy and produced ‘a fusion between the poem’s subjective authority and the validity of utterances deemed to be philosophical’, such that the authenticity of True was guaranteed by the sacred aura of utterance and the equivocity of language ― and executed, in terms of the order of matheme, the interruption of ‘the sacral exercise of validation by narrative’ or by ‘mytheme’: it was mathematics and its ‘literal univocity’ (for example, it could be found in apagogical argument and its ‘imperative of consistency’, which proved to be incompatible with any legitimation grounded in narrative) warranted this interruption, supported the ‘desacralization’ (‘to tear down mystery’s veil’) that ensured the commencement of philosophy, and finally established a regime of discourse grounding on its own inherent and earthly legitimation. Badiou thus concludes, ‘philosophy can only establish itself through the contrasting play of the poem and the matheme, which form its two primordial conditions (the poem, whose authority it must interrupt; and the matheme, whose dignity it must promote).’
In the contemporary era, philosophy is sutured with the poetic condition, dominant by Heideggerian nostalgia (recourse to pre-Platonic, poetic language; ‘only a God can save us’) and Wittgensteinian sophistry (‘whereof one cannot speak, thereof one must be silent’; ‘language game’), and caught in a situation of ‘paralysis’, ‘a completion of philosophy’, as well as a ‘nihilism’ that declares ‘the access to being and truth is impossible’ (the ‘postmodern’). For the (re-)turn of philosophy, Badiou proposes a desacralization (or anti-sophistry), a de-suturation of philosophy from its poetic condition, and a contrast between the poem and the matheme. The ‘sovereignty of language’ claims the limits of thinking: ‘of what is subtracted from language, there can be no concept, no thought’. This ‘contemporary conviction’ or ‘general dogma’ has excluded that ‘unnamable’ (by language) from thinking and sentenced it as ‘the indiscernible’. For Badiou, the philosophical gesture that is able to break through such ‘prison of language’ must again be a Platonic one, although it has to be conditioned by that event happened in modern mathematics. After the Cantorian event, the problematics of the post-Cantorian thought revolves around the inconsistent multiplicities, the unnamable and the indiscernible that is totally unthinkable for the philosophy sutured with the poetic/linguistic condition. And Cohen’s forcing of the generic sets and ‘generic’ multiplicities makes it possible to produce a concept of the indiscernible and thus opens the access to that ‘impossible-real’. Badiou proclaims, what a contemporary philosopher counterattacks ‘Great Modern Sophistry’ is the following point: ‘Being is essentially multiple’, and therefore ‘our century will have been the century of protest against the One’ ― ‘God is truly dead, as are all the categories that used to depend on it in the order of the thinking of being’. Retroactively, Badiou affirms that ‘the multiple’ had already been contained in Plato’s thinking. Although, inevitably limited by his time, he still reserved the rights to the One (also see Deleuze’s inversion of Platonic philosophy in his two magnum opuses published in 1968, 1969), Plato’s attempt was to ‘ruin the linguistic and rhetorical variance of sophistry from the aporia of an ontology of the multiple’. Conditioned by modern mathematics after Cantor, the Platonic gesture in contemporary philosophy must be a ‘Platonism of the multiple’. Actually this position had already been undertaken by Albert Lautman (1908–1944) in 1930-40s. Lautman’s thought, commented by Badiou as ‘the only great openly Platonic as well as modern thinking’, had constituted a modern Platonism. Badiou concludes, ‘The century and Europe must imperatively be cured of anti-Platonism. Philosophy shall only exist insofar as it proposes, to match the needs of our times, a new step in the history of the category of truth. It is truth which is a new idea in Europe today. And as with Plato, as with Lautman, the novelty of this idea is illuminated in the frequenting of mathematics’.
 The problem of the condition of philosophy or of knowledge is critical for other philosophers, for example, Immanuel Kant and Michel Foucault. See Michel Foucault, ‘What Is Enlightenment?’ in Essential Works of Michel Foucault, 1954-1984, Volume I: Ethics: Subjectivity and Truth, ed. Paul Rabinow and Nikolas Rose, (New York: New Press, 2003), p. 43-57.
 Alain Badiou, Manifesto for Philosophy: Followed by Two Essays: “The (Re)turn of Philosophy Itself” and “Definition of Philosophy”, trans. & ed. Norman Madarasz, (Albany, N.Y.: State University of New York Press, 1999), p. 33.
 Ibid., p. 35. Here, concerning the relation between four conditions and philosophy, Badiou indicates: ‘the lack of a single one (condition) gives rise to its (philosophy’s) dissipation, just as the emergence of all four conditioned its apparition’.
 Truth is not produced by philosophy but by the generic procedures. Philosophy ‘does not establish any truth but it sets a locus of truths. It configurates the generic procedures, through a welcoming, a sheltering, built up with reference to their disparate simultaneity.’ See ibid., p. 37. The philosophical category of Truth is empty/void. Truth is a hole in sense. See Alain Badiou, Conditions, trans. Steven Corcoran, (London; New York: Continuum, 2008), p. 11, 43.
 Alain Badiou, Manifesto for Philosophy: Followed by Two Essays: “The (Re)turn of Philosophy Itself” and “Definition of Philosophy”, p. 36-37.
 Ibid., p. 38-39.
 See Tzuchien Tho, “What is Post-Cantorian Thought? Transfinitude and the Condition of Philosophy”, in Badiou and Philosophy, ed. Sean Bowden and Simon Duffy, (Edinburgh University Press, 2012), p. 19-38.
 Alain Badiou, Being and Event, trans. Oliver Feltham, (London; New York: Continuum, 2005), p. 23.
 Alain Badiou, Conditions, p. 111.
 See Georg Cantor, ‘Letter to Dedekind’, in From Frege to Gödel, ed. Jean Van Heijenoort, (Cambridge, MA: Harvard University Press, 1967), p. 114. Based on this standard version, Tzuchien Tho corrects the mistakes in English translation of Cantor’s text quoted by Badiou in Being and Event. See Tzuchien Tho, “What is Post-Cantorian Thought? Transfinitude and the Condition of Philosophy”, in Badiou and Philosophy, p. 31.
 Alain Badiou, Being and Event, p. 41.
 Ibid., p. 42.
 Ibid., p. 43.
 Ibid., p. 44-45.
 Gerrit Jan van der Heiden, Ontology after Ontotheology: Plurality, Event, and Contingency in Contemporary Philosophy, (Pittsburgh, Pennsylvania: Duquesne University Press, 2014).
 Alain Badiou, Manifesto for Philosophy: Followed by Two Essays: “The (Re)turn of Philosophy Itself” and “Definition of Philosophy”, p. 61. Badiou’s conclusive thesis is: ‘if philosophy is threatened by suspension, and this perhaps since Hegel, it is because it is captive of a network of sutures to its conditions, especially to its scientific and political conditions, which forbade it from configurating their general compossibility.’ See, ibid., p. 64.
 Ibid., p. 62.
 Ibid., p. 69-71.
 Ibid., p. 67.
 They are: set theory (from Cantor to Cohen), Lacanian psychoanalysis, May 68, and Paul Celan’s poems. See Ibid., p. 80-88.
 Sophist is the double of philosopher. ‘The ethics of philosophy essentially inheres in retaining the sophist as adversary, in conserving the polemos, or dialectical conflict. The disastrous moment occurs when philosophy declares that the sophist ought not be, the moment when it decrees the annihilation of its Other.’ See Alain Badiou, Conditions, p. 18-20.
 Alain Badiou, Manifesto for Philosophy: Followed by Two Essays: “The (Re)turn of Philosophy Itself” and “Definition of Philosophy”, p. 97-98.
 Alain Badiou, Conditions, p. 36-38.
 Ibid., p. 38. Badiou also indicates: ‘We can also say that the Platonic relation to the poem is a (negative) relation of condition, one that presupposes other conditions (the matheme, politics, love).’
 Alain Badiou, Manifesto for Philosophy: Followed by Two Essays: “The (Re)turn of Philosophy Itself” and “Definition of Philosophy”, p. 50-52.
 Ibid., p. 94-95, 97-98.
 Ibid., p. 56.
 Ibid., p. 94.
 Ibid., p. 95.
 Ibid., p. 103.
 Ibid., p. 100.
 Ibid., p. 101.
 Alain Badiou, ‘Chapter Seven: Philosophy and Mathematics’, in Conditions, p. 93-112.