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 	 Badiou's Equations--and Inequalities: A Response to Robert Hughes's 	 	  	 "Riven"

      *Arkady Plotnitsky*
      / Purdue University/
      plotnit@purdue.edu 

      (c) 2007 Arkady Plotnitsky.
      All rights reserved.

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   1. Robert Hughes's article offers an unexpected perspective on Alain
      Badiou's work and its impact on the current intellectual and
      academic scene, a clichÃ(c)-metaphor that (along with its avatars,
      such as performance or performative, also a pertinent term) may be
      especially fitting in this case, given that Badiou is not only a
      philosopher but also a playwright. What makes Hughes's perspective
      unexpected is its deployment of "trauma" as the main optics of
      this perspective. While the subject and language of trauma have
      been prominent in recent discussions, they are, as Hughes
      acknowledges, not found in Badiou's writings nor, one might add,
      in the (by now extensive) commentaries on Badiou. Hughes's reading
      of Badiou in terms of trauma rearranges the "syntax" of Badiou's
      concepts, as against other currently available readings of Badiou,
      even if not against Badiou's own thinking, concerning which this
      type of claim would be more difficult to make. In this respect
      Badiou's thought is no different from that of anyone else. One can
      only gauge it by a reading, at the very least a reading by Badiou
      himself, for example, in Briefings on Existence (which I shall
      primarily cite here for this reason and because it offers arguably
      the best introduction to his philosophy).

   2. Before proceeding to Hughes's argument, I sketch the conceptual
      architecture of Badiou's philosophy from a perspective somewhat
      different from but, I hope, complementing that offered by Hughes.
      The language of conceptual architecture follows Gilles Deleuze and
      FÃ(c)lix Guattari's view of philosophy, in What is Philosophy?, as
      the invention, construction of new concepts (5). This definition
      also entails a particular idea of the philosophical concept. Such
      a philosophical concept is not an entity established by a
      generalization from particulars or "any general or abstract idea"
      (What is Philosophy? 11-12, 24). Instead, it is a conglomerative
      phenomenon that has a complex architecture. As they state, "there
      are no simple concepts. Every concept has components and is
      defined by them . . . . It is a multiplicity" (16). Each concept
      is a conglomerate of concepts (in their conventional sense),
      figures, metaphors, particular elements, and so forth, that may or
      may not form a unity; as such, it forms a singular, unique
      configuration of thought. As a philosopher, Badiou is an inventor,
      a builder of new concepts, just as Deleuze and Guattari are, even
      when these concepts bear old names, as do some of Badiou's key
      concepts, such as event, being, thought, and truth.

   3. A distinctive, if not unique, feature of Badiou's philosophy, as
      against that of most other recently prominent figures, is the
      dominant role in it of mathematics, in particular of mathematical
      ontology. It is true that major engagements with mathematics are
      also found in Lacan and Deleuze, both of whom had a major
      philosophical impact on Badiou's work. There are, however, also
      significant differences among these thinkers in this respect, and
      it is worth briefly commenting on these differences in order to
      understand better Badiou's use of mathematics and mathematical
      ontology. For Badiou, to use his "equation,"
      "mathematics=ontology" (Briefings 59), and "ontology=mathematics."
      (Badiou's first identity is not mathematical, and hence these two
      identities are not automatically the same, but they appear to be
      in Badiou.) Reciprocally, Badiou wants to give mathematics a
      dimension of /thought/, specifically of ontological thought, which
      he distinguishes from other, most especially logical, aspects of
      mathematical thinking. "Mathematics is a thought," a thought
      concerning Being, he argues in Briefings on Existence (45-62). It
      is, accordingly, not surprising that Badiou is primarily
      interested in foundational mathematical theories, that is, those
      that aim at ontologically grounding and pre-comprehending all of
      mathematics, such as set theory introduced by Georg Cantor in the
      late nineteenth century, and in Badiou's more recent works, in
      category and topos theories, as developed by Alexandre
      Grothendieck in the 1960s. The latter offers a more fundamental
      mathematical ontology, encompassing and pre-comprehending the one
      defined by set theory. Indeed, it might be more accurate to
      rewrite Badiou's equations just stated as "mathematical
      ontology=ontology" and "ontology=mathematical ontology" (where
      mathematical ontology could be either set-theoretical or
      topos-theoretical). In other words, Badiou ultimately deals with
      mathematical ontology rather than with mathematics, and deals with
      it /philosophically/ and /not mathematically/, beginning with
      defining as irreducibly multiple "the multiple without-One" (the
      multiple minus One?), to be considered presently (Briefings 35).
      The equations just stated are still produced by philosophy, and
      not by mathematics, and the very argument that mathematics is a
      thought is philosophy's task, even though and because mathematics
      as ontology "functions as a [necessary] condition of philosophy"
      (54). Necessary, but not sufficient! For, as will be seen, while
      it is also "about identifying what real ontology is," philosophy,
      especially as thinking of "event" or "truth," exceeds ontology,
      since an event is always an event of "trans-Being," in part,
      against Heidegger, at least early Heidegger (59). Both "event" and
      "truth" are defined by Badiou in relation to what he calls
      "situation," as something from within which, but also against
      which or in discontinuously, an event emerges. It is this excess
      that defines Badiou's inequality, which may be symbolically
      written as "ontology=mathematical ontology <
      trans-Being=philosophy." Making ontology mathematical and thus
      also more Platonist is already a non-Heideggerian gesture,
      deliberate on Badiou's part. Heidegger prefers pre-Socratic
      thought, abandoned, albeit still concealed in Plato's philosophy
      as well. One may thus write another pair of
      equations--"philosophy=thinking the event" and "thinking the
      event=philosophy"--which may, moreover, be accompanied by those
      involving literature or poetry. This "thinking the event" might
      also be equal to literature, at least a certain type of literature
      or of literary thought. "Literature=philosophy," then, and, by the
      same token, a certain redux of Heidegger in Badiou? As I discuss
      below, and as Hughes's article suggests as well, to some degree
      this may be the case. This relation between literature and
      philosophy in Badiou's thinking the event may, however, also be
      undecidable, in Jacques Derrida's sense rather than in that of
      Kurt Gödel in mathematical logic. Derrida's undecidability refers
      to something that can "no longer be [unconditionally, once and for
      all] included within philosophical (binary) opposition," in this
      case, to our inability to decide unconditionally whether a given
      thinking, such as that of the event in Badiou's sense, is either
      literary or philosophical (Positions 43). It can be either, or
      sometimes both simultaneously, in different circumstances, even
      for the same thinker. Gödel's undecidability refers to the
      impossibility of proving certain propositions to be either true or
      false by means of the systems within which they are formulated, a
      concept that is crucial for Badiou in its own right.

   4. In contrast to Badiou, Deleuze and Deleuze and Guattari define the
      role of mathematics, most centrally topology and geometry, less by
      mathematical ontology, especially in the foundational,
      set-theoretical sense dominant in Badiou. Deleuze's or Deleuze and
      Guattari's ontologies may be seen as conceptually /modeled/ on
      certain mathematical objects, such as dynamical systems or
      Riemannian spaces. (The actual definitions of these objects are
      not important at the moment.) This /modeling/, resulting in a kind
      of philosophical semblance or simulacrum of the mathematical
      concept used is, however, different from Badiou's ontological
      /equations./ In Lacan's case, it would be difficult to speak of
      any /specifiable/ ontology, mathematical or other, at the ultimate
      level, that of the Lacanian Real. In other words, in approaching
      the Real, Lacan is attempting to think that which cannot be given
      any /specifiable ontology./ The Real exists and has powerful
      effects upon either the Imaginary or the Symbolic, but cannot be
      represented or conceived of in specific terms. Lacan's use of
      mathematical, such as topological, objects or concepts is defined
      by this epistemology of the Real as irreducibly inaccessible, even
      while it has powerful effects upon what can be accessed or
      represented. For example, it may shape the topological
      configuration of unconscious thought, as defined by the Symbolic.
      But then this move beyond ontology is found in Badiou as well, and
      even defines thinking what is ultimately most decisive: thinking
      "thinking the event" and philosophy itself as nonontological, for
      "it is also important for [philosophy] to be released from
      ontology per se" (Briefings 59). Indeed, this "release" involves a
      version of Lacan's Real, a major inspiration for Badiou's thought.
      In Lacan and Badiou alike, the Real may be seen as /materially/
      existing, in a form of nonontological ontology, as it were,
      insofar as it cannot given a specifiable ontology, for example a
      mathematical one. It is worth stressing that, in general, the
      mathematical and infinitist grounding of his ontology
      notwithstanding, Badiou's philosophy is materialist, just as is
      that of Lacan, Deleuze, or Derrida. For all these thinkers
      thought, including mathematics, is a product of the material
      conditions and energies of our existence--from inanimate matter to
      living matter to our bodies to the cultural, including political,
      formations shaping our lives.

   5. Hughes does not miss the /significance/ of Badiou's "reengagement
      [as against the immediately preceding philosophical tradition,
      especially as manifest in Hegel, Nietzsche, and Heidegger] of
      philosophy with mathematics and set theory" ("Riven" ¶1). He does
      not, however, pursue, does not /engage/ with, this reengagement.
      Such an engagement would allow Hughes to offer a richer and deeper
      consideration of the problematics of Badiou's philosophy. On the
      other hand, this non-mathematical restaging of Badiou's thought is
      not altogether surprising and, to some degree, allows one to
      perceive and articulate aspects of this thought sometimes hidden
      behind the mathematical complexities of his argumentation.
      Besides, one might also argue that, while certain /mathematical/
      (set- or topos-theoretical) ontology essentially /grounds/
      Badiou's thought and is helpful in understanding it more deeply,
      his thought is ultimately not mathematical. It is fundamentally
      /philosophical/, even, again, as concerns ontology, since equating
      it with mathematical ontology is itself philosophical and not
      mathematical. His thinking the event or truth is, as just
      explained, philosophical on his own definition, by virtue of
      exceeding ontology=mathematical ontology, without, however,
      abandoning the latter. While justifiably attending to the
      questions of event and truth, Hughes does not consider this
      difference between ontology (as equal to mathematics or
      mathematical ontology) and philosophy (as equal to thinking the
      event). He is, however, right to place Badiou within a
      philosophical tradition of thinking about art, ethics, and
      politics defined, on the one hand, by the post-Heideggerian French
      thought of Lacan, Levinas, Blanchot, and Derrida, and, on the
      other by thinkers at the origin of Romantic thought ("Riven" ¶3).
      He is also right to relate this thinking to literature, at least
      implicitly, and again specifically to Romantic literature, as well
      as to Romantic philosophical thought. I return to these subjects
      later. My point at the moment is the essentially philosophical
      rather than mathematical nature of Badiou's thought (there is
      hardly any /mathematics/ in the sense of its technical,
      disciplinary practice in Badiou), and also the nature of
      philosophical thought itself, as /against mathematics/, but not
      /against mathematical thought/. If "mathematics is a thought,"
      mathematics is also not only mathematics (in the sense of its
      technical practice) but also a /philosophical/ thought, and hence
      reaches beyond ontology on the philosophical side. This
      philosophical dimension appears especially at the time of
      "crises," defined by Badiou as largely synonymous with "events."
      As Badiou writes, "mathematics thinks Being per se," or ontology,
      "save for the rare moments of crisis" (Briefings 59). At such
      moments it must move toward thinking the "event" which, according
      to Badiou's definition, would make it philosophy or at least
      philosophical. According to Badiou, "a 'crisis' in mathematics [as
      ontology] arises when it is compelled to think its thought /as the
      immanent multiplicity of its own unity/," and "it is at this
      point, and only at this point, that mathematics--that is,
      ontology--functions as a necessary [but, as I have said, not
      sufficient] condition of philosophy" (Briefings 54). This
      conjunction gives a crucial significance to the reciprocity
      between mathematics, /as ontology/, and philosophy as thinking the
      event or/as crisis, first, I argue, in mathematics itself,
      understood in broader (rather than only ontological) terms at the
      moment and, hence, beyond the purview of Badiou's argumentation
      concerning mathematics. Secondly, given that at stake in Badiou's
      statement is philosophy as such, this reciprocity between
      mathematics as ontology of the irreducible multiple and philosophy
      in thinking the event as crisis, and hence the discontinuity of
      the event, is according to Badiou irreducible in philosophy and,
      it follows, in Badiou's thought. This reciprocity between the
      multiple and the discontinuous in Badiou is my main point here and
      guides my argument from this point on.

   6. As I see it, what defines Badiou's philosophy most essentially,
      what he is most essentially a philosopher of, is above all a
      philosophy of the multiple, specifically of the /ontologically/
      multiple: ontology=the set-theoretical ontology=the irreducibly
      multiple without-One. This is a particular view or interpretation
      of mathematical ontology that is not necessarily shared by
      mathematicians and philosophers working in foundations of
      mathematics, even if it is ultimately true (in the sense of being
      potentially irreducible). Indeed, Badiou would not speak of
      interpretation here. According to him, "mathematics has the virtue
      of not presenting any interpretations," and "the Real [understood
      close but not identically to Lacan's] does not show itself as if
      upon a relief of disparate interpretation." Instead, Badiou sees
      the situation in terms of different "decisions of thought"
      concerning what exists (e.g. made in the case of set-theory in
      terms of constructible sets, large cardinals, or generic sets),
      the decision through which thought "binds [one] to Being," "under
      the imperative of an orientation [of thought]" (Briefings 56-57).
      The concept itself of "orientation of thought" becomes an
      important part of Badiou's ontological thinking (53-54). That
      Badiou's ontology of mathematics (which, again, equals ontology in
      general) is that of the multiple without-One is, however, not in
      doubt: this is his ontological and political orientation and his
      decision of thought. He is a philosopher of the irreducibly
      multiple. I would also add, however, that he is equally a
      philosopher of the radical discontinuity, ultimately beyond
      ontology (although it enters at the level of ontology as well) by
      virtue of its connections, via the concept of event, to
      "trans-Being" and hence to /philosophy/. It is true that, as the
      title of Badiou's arguably most significant work, Being and Event
      (L'Ã(tm)tre et l'Ã(c)vÃ(c)nement), would suggest, he can more properly be
      defined as a philosopher of being and event, and of their
      conjunction. It would be difficult to argue against this view. But
      central as both of these concepts are to his thought, the
      architecture of both is essentially defined by the concepts of
      multiplicity and discontinuity. Indeed, we can describe these
      concepts in parallel terms, or again by way of two equations,
      being=the irreducibly multiple, the multiple-without One, and,
      defined by Badiou as trans-Being, the event=the radical
      discontinuity. In general in Badiou, as elsewhere in philosophy,
      the architecture of each concept is also defined by its relation
      to other concepts and, hence, by the entangled network of these
      concepts. Not unlike those of modern physics (such as Einstein's
      famous /E=mc^2 /), Badiou's equations encode the considerable
      architectural complexity of the concepts involved or of their
      relationships. Bringing the roles of multiplicity and
      discontinuity in Badiou into a sharper focus allows one to
      understand the architecture and mutual determination of his
      concepts more deeply, in part through the connections, along both
      lines (multiplicity and discontinuity), between Badiou's thought
      and that of other key contemporary figures. Thus, while these
      thinkers' thought is different, even as concerns multiplicity or
      discontinuity, as a philosopher of the multiple Badiou is close
      both to Deleuze and to Derrida, and as a philosopher of the
      discontinuous he is closer to Lacan, de Man, LÃ(c)vinas, and, again,
      Derrida--but not Deleuze. For even though Badiou draws inspiration
      from Deleuze as a thinker of the multiple, one of his discontents
      with Deleuze's "vitalist ontology," as he calls it, appears to be
      the insufficient role of discontinuity there, as against, for
      example, Immanuel Kant's "subtractive ontology." As a thinker of
      discontinuity, Kant is also a precursor of Levinas, Lacan,
      Derrida, and de Man.

   7. Hughes's article correctly stresses the role of discontinuity and,
      correlatively (they are not the same), singularity in Badiou's
      thinking of event, truth, and ethics, and the Lacanian genealogy
      (the Real) of this thinking, or its qualified connections to
      LÃ(c)vinas. (It seems to me that Hughes /equates/ "truth" and
      "event," too much ["Riven" ¶5], which, indissociable as they may
      be, they are not quite the same in Badiou.) Beginning with its
      title ("Riven"), Hughes's article centers primarily on the role of
      discontinuity in Badiou, especially that between "situation" and
      "event," via what Badiou calls "the nothing of its all" or the
      non-empty void linked to the Lacanian Real. Apart from a brief
      discussion of "a set of component elements or terms" involved in
      "the theatergoer's encounter with Hamlet" (¶9), the article gives
      little, if any, attention to the role of multiplicity in Badiou,
      at most mentioning it in passing, perhaps because the article's
      argument bypasses the mathematical-ontological aspects of Badiou's
      thought. Not coincidentally and, given its significance for
      Badiou, even remarkably, the term "ontology" is never mentioned in
      the article, except in a book title by Slavoj Zizek (who does not
      miss it!) in the bibliography. However, Badiou's thought is
      irreducibly defined by the ontology of the multiple and, again,
      the equally irreducible combination of the multiple and the
      discontinuous, in particular the trans-ontologically
      discontinuous. The singularity of the event and the truth always
      arises from and, through the non-empty void of the Real, grounds
      the multiple (mathematical or other) of the situation and give
      rise to a new multiple. This dynamics of the interplay between the
      Real and the multiple gives the structure and the history of a
      situation and an event (again, always exterior to the situation
      from within which it appears) the architecture of "the multiple of
      the multiple," a persistent locution in Badiou. According to
      Badiou, given that "philosophy will always be split between
      recognizing the /event/ as the One's supernumerary coming, and the
      thought of its /being/ as a simple extension of the manifold,"
      "the whole point is to contend, for as long as possible and under
      the most innovative conditions for philosophy, the notion that the
      truth itself is but a multiplicity: in the two senses of its
      coming (a truth makes a typical /multiple/ or generic
      /singularity/) and in the sense of its being (there is no /the/
      Truth, there are only disparate and untotalizable truths that
      cannot be totalized)" (Briefings 62; emphasis added). This
      statement clearly reflects a crucial significance of the
      relationships between the discontinuity of the event and the
      multiple of being in Badiou. One cannot totalize all truths, and
      each truth is itself an untotalizable multiple within the
      singularity of its event. This situation (in either sense)
      requires, for Badiou, "a radical gesture," which also manifests
      philosophy's faithfulness to Lucretius, in whose (physical)
      ontology of the multiple without-One "atoms, innumerable and
      boundless,/ flutter about in eternal movement" (/De rerum natura/
      II: 496; Briefings 62).

   8. The multiple is everywhere manifest in Badiou's thought and is
      expressly emphasized by Badiou as central to the ontology he aims
      to establish. This view is confirmed by the proposition, cited
      above, concerning mathematical thinking: at the time of a crisis,
      "its thought /as the immanent multiplicity of its own unity/"
      (Briefings 54). Given Badiou's view of mathematical ontology as
      multiple-/without-One/, this can only be read in terms of the
      ultimate /impossibility/ of this unity. (Otherwise the point would
      merely restate Leibniz, who is among Badiou's precursors here, as
      are Hegel and Kant [Briefings 141]). This multiplicity defines
      Badiou's ontology and always enters an "event," by definition
      always an event of crisis, "each time unique," or, in Derrida's
      title phrase, "each time unique, the end of the world" (Chaque
      fois unique, la fin du monde; published in English as The Work of
      Mourning). In the ethical plane, this emphasis on the irreducibly
      multiple serves both Badiou and Derrida (and in both cases, if
      differently, against Levinas) to think the /events/ (plural) of
      "evil," all evil. Some among such events are equally evil, but
      each nevertheless is unique, as well as irreducibly multiple as
      concerns the ontology involved, thus doubling the multiple.
      Indeed, as will be seen, as a multiple without-One, this
      ontological multiple is already doubled, is already the multiple
      of the multiple, which gives Badiou's overall situational ontology
      the form of the multiple of the multiple of the multiple. It
      follows that there is no single or absolute, absolutely radical
      evil, no matter how horrific or difficult to confront or even to
      imagine evil events may be and how much we try, as we must, to
      prevent their occurrence; there are other evil events and forms of
      evil that are comparable (in their evilness), but again each is
      different (Ethics 61-67). The (mathematical) ontological
      multiplicity found within an event or the situation that brings
      the event about always makes it political, as against Levinas's
      thinking of the ethical. Badiou elegantly reads certain specific
      actual political and mathematical "orientations" in terms of each
      other, in particular by mutually mapping the theory of generic
      sets and what he calls "generic politics" as "something groping
      forward to declare itself," both defined by the multiple
      without-One (Briefings 55-56). The same political complexity also
      defines other (more "positive") "events," political, cultural,
      mathematical, scientific, aesthetic, erotic, and so forth:

          the French revolution in 1792, the meeting of HÃ(c)loïse and
          AbÃ(c)lard, Galileo's creation of physics, Haydn's invention of
          the classical musical style [vis-vis the Baroque] . . . But
          also: the cultural revolution in China (1965-67), a personal
          amorous passion, the creation of Topos theory by the
          mathematician Grothendieck, the invention of the twelve-tone
          scale by Schoenberg." (Ethics 41) 

      Badiou's concept of the "situation," defined by the analogous
      complexity of the interaction between the singular and the
      multiple (e.g. Ethics 16, 129), always entails the possibility of
      an /eruptive/ event, such as those just mentioned, which,
      reciprocally, can only emerge in relation to a situation. This
      eruptive singularity of the event can, accordingly, only be
      comprehended philosophically, by the (trans-Being) thought of
      philosophy and not by (mathematically) ontological thought, but it
      cannot be considered apart from ontology and its irreducible
      multiple.

   9. The conceptual architecture just outlined makes Badiou a
      philosopher both of the irreducibly multiple and of the
      irreducibly discontinuous. Badiou rarely invokes the /term/
      "discontinuity" itself. The /concept/ is, however, clearly central
      to his thought, in particular as concerns "event," as each event
      is, again, always defined by the radical, unbridgeable,
      end-of-the-world-like discontinuity of a crisis (but is always an
      opening to the irreducibly multiple). Invocations of discontinuity
      are found throughout Badiou's writing, and Hughes lists quite a
      few of them, "riven, punctured, ruptured, severed, broken, and
      annulled," which he links to trauma ("Riven" ¶10). This is
      correct, because trauma always entails discontinuity. On the other
      hand, the latter is a more general concept, as is "event," and
      Badiou uses both concepts more generally as well, in part by
      linking them to multiplicity. In order to understand how the
      multiplicity of ontology and the discontinuity of event work
      together in Badiou, I turn to set theory, as opening "the very
      space of the mathematically thinkable" (Briefings 42).

  10. As we have seen, according to Badiou, "ontology" [including in its
      irreducible multiplicitous form] is nothing other than mathematics
      [of set theory or, later, topos theory] itself," or again,
      mathematical ontology=ontology, ontology=mathematical ontology
      (40). Given my limits here, I confine this discussion mostly to a
      /naïve/ concept of set, naïve" being an accepted term in
      mathematics in this context. A set is a collection of certain
      usually abstract objects called elements of the set, such as, say,
      the numbers between 1 and 10, which is a finite set, or of all
      natural numbers (1, 2, 3, 4, etc.), which is an infinite set, a
      countable infinite set, as it is called. There are also greater
      infinities, such as that of the continuum, represented by the
      numbers of points in the straight line. The resulting ontological
      multiplicity or manifold is, Badiou argues, unavailable to
      unification, to the One, and, as will be seen presently, this
      multiplicity is also inconsistent, while nonetheless enabling a
      set-theoretical ontology. While, on the one hand, "the /set/ has
      no other essence than to be a manifold" and while, with Cantor, we
      recognize "not only the existence of infinite sets, but also the
      existence of infinitely many such sets," that is, sets possessing
      different magnitudes of infinity, "this infinity itself is
      absolutely open ended" (41). In particular, it cannot itself ever
      be contained in a set. There is no "the One" of set theory,
      because the set of all sets does not exist or at least cannot be
      consistently defined, in view of the well-known paradox related to
      the question of whether this set does or does not contain itself
      as an element. (It is immediately shown not to be the set of all
      sets in either case.) Set-theoretical multiplicity is both
      ultimately uncontainable by a single entity or concept and is
      inconsistent, because of the impossibility of giving it the
      overall cohesion of a whole and because, as will be seen
      presently, it contains systems that are expressly inconsistent
      with each other in view of Gödel's incompleteness theorems.
      According to Badiou: "Ontology, if it exists has to be the figure
      of inconsistent multiplicities as such. This means that what lends
      itself to the thought of ontology is a manifold without a
      predicate other than its own multiplicity. It has no concept other
      than itself, and nothing ensures its consistency. . . . Ontology
      is the thought of the inconsistent manifold, that is, of what is
      reduced without an immanent unification to the sole predicate of
      multiplicity" (36, 40). Accordingly, "ontology, or the thinking of
      the inconsistent pure multiple, cannot be guaranteed by any
      principle" (39). In view of these considerations, Badiou's
      "initial [philosophical] decision was to contend that what can be
      thought of Being per se is found in the radical manifold or a
      multiple that is not under the power of the One, . . . [in] a
      'multiple without-One.' . . . The multiple is radically
      without-One in that it itself consists only of multiples. What
      there is, or the exposure to the thinkable of what there is under
      the sole requirement of the 'there is,' are multiples of
      multiples" (35, 40). Or via Plato's Parmenides, which already
      grapples with this situation and its "inconsistent multiplicity,"
      what we encounter here is "an absolutely pure manifold, a complete
      dissemination of itself" (46).

  11. While Badiou, thus, establishes his ontology on the basis of more
      general set-theoretical considerations, its crucial further
      dimensions are revealed by Gödel's famous discovery of the
      existence of undecidable propositions in mathematics and by Paul
      Cohen's findings (along the lines of undecidability) concerning
      the mathematical continuum. The latter is, as I said, defined by
      the order of the infinite larger than the countable infinity, 1,
      2, 3, . . . etc., of natural numbers, but in view of Cohen's
      theorem it is ultimately undecidable whether there is something in
      between. Gödel's concept of an undecidable proposition is arguably
      his greatest conceptual contribution. An undecidable proposition
      is a proposition whose truth or falsity cannot, in principle, be
      established by means of the system (defined by a given set of
      axioms and rules of procedure) in which it is formulated. The
      discovery of such propositions by Gödel (in 1931) was
      extraordinary. It undermined the thinking of the whole preceding
      history of mathematics (from the pre-Socratics on), defined by the
      reasonable idea that any given mathematical proposition can, at
      least in principle, be shown to be either true or false. We now
      know, thanks to Gödel, that such is not the case. For Gödel
      proved--rigorously, /mathematically/--that any system sufficiently
      rich to contain arithmetic (otherwise the theorem is not true)
      would contain at least one undecidable proposition. This is
      Gödel's "first incompleteness theorem." Gödel made the life of
      mathematics even more interesting with his "second incompleteness
      theorem" by proving that the proposition that such a system, say,
      classical arithmetic, is consistent, is itself undecidable. In
      other words, the consistency of the system and, hence, of most of
      the mathematics we use cannot be proven, although the possibility
      that the system and with it mathematics may be shown to be
      inconsistent remains open.

  12. Given the undecidablity of certain propositions inevitably found
      in any sufficiently rich axiomatic system, one can in principle
      extend the system in two incompatible ways by accepting /by a
      decision of thought/ such a proposition as either true or false.
      This allows one to have two different systems--incompatible with
      each other, but each perfectly consistent in itself. Since,
      however, Gödel's first theorem would still apply to each system,
      new undecidable propositions will inevitably be found in each.
      This makes the process in principle infinite, that is, potentially
      leading to the infinite multiplicity of mutually inconsistent
      systems, each of which, moreover, can never be proven to be
      consistent in view of Gödel's second theorem. This situation
      becomes especially dramatic in the case of Cantor's famous
      continuum hypothesis, which deals with the question: How many
      points are there in the straight line? It states, roughly, that
      there is no infinity larger than that of a countable set (such as
      that of natural numbers: 1, 2, 3, etc.) and smaller than that of
      the continuum (as represented by the number of points on the
      straight line). The answer to this question is crucial if one
      wants to maintain Cantor's hierarchical order of (different)
      infinities, and hence for the whole edifice of set theory. The
      hypothesis was, however, proven undecidable by Cohen in 1963.
      Accordingly, one can extend classical arithmetic in two ways by
      considering Cantor's hypothesis as either true or false, that is,
      by assuming either that there is no such intermediate infinity or
      that there is. This allows one, by decisions of thought, to extend
      the system of numbers, arithmetic, into mutually incompatible
      systems, in principle, infinitely many such systems--a difficult
      and for some an intolerable situation. The question of how many
      points are on the straight line cannot be determinately answered.

  13. Instead of seeing this situation as difficult and even
      intolerable, Badiou finds in it both a support for his program and
      a special appeal or even beauty. As he writes:

          As we have known since Paul Cohen's theorem, the Continuum
          [h]ypothesis is intrinsically undecidable. Many believe
          Cohen's discovery has driven the set-theoretic project into
          ruin. Or at least it has "pluralized" what was once presented
          as a unified construct. I have discussed this enough elsewhere
          for my point of view on this matter to be understood as the
          opposite. What the undecidability of the Continuum hypothesis
          does is complete Set Theory as a Platonist orientation [in
          Badiou's sense]. It indicates its line of flight, the aporia
          of immanent wandering in which thought experiences itself as
          an unfounded confrontation with the undecidable. Or, to use
          Gödel's lexicon: as a continuous recourse to intuition, that
          is, to decision. (99) 

      The appeal to Deleuze's concept of "line of flight" is worth
      noting. This view of the situation also shapes Badiou's
      understanding of Plato's thought, juxtaposed by him to
      conventional, especially conventional mathematical, Platonism.
      Plato's /thought/, Badiou argues, is interested primarily in "the
      movement of thought," and "the undecidable commands the perplexing
      aporetic style of the dialogues. This course leads to the point of
      the undecidable so as to show that thought precisely ought to
      decide upon the event of Being: that thought is not foremost a
      description or construction, but a break (with opinion and/or with
      experience) and, therefore, a decision" (90). For Plato, as for
      the /truly/ Platonist set-theoretical thinking, and for Badiou,
      "it is when you decide upon what exists that you bind your thought
      to being" (57). These statements bring together, in a firm
      conceptual architecture, Badiou's key concepts, invoked here, from
      the ontology of the multiple to thought to Being to event and
      through it, the interconnective discontinuity between ontology and
      philosophy.

  14. This conceptual and epistemological architecture is set up in
      Being and Event. Badiou retraces it (with some new inflections,
      especially along the lines of topos theory) in Briefings on
      Existence: A Short Treatise on Transitory Ontology (published in
      French in 1998). The book is not cited by Hughes, perhaps because
      it largely reprises Being and Event, apart from its discussion of
      topos theory. It is arguably the best available condensation of
      Badiou's philosophy, apart from the ethical problematic to which
      Badiou turns in Ethics, which also appeared in French in 1998.
      Briefings on Existence establishes the architecture just sketched
      by starting, in the "Prologue: God is Dead," with the radically
      materialist grounding of our being and thought, that of
      mathematics and set theory, or of the infinite, included. Chapter
      1, "The Question of Being Today," situates the question of Being
      in this framework of materiality and infinity, but now in relation
      to the ontology of the irreducible and inconsistent manifold or
      multiple, the multiple without-One, grounded in the axiomatics of
      set-theory, which is considered, as "a thought," in Chapter 2,
      "Mathematics as a Thought." With this argument in hand, Badiou is
      ready to define "the event as trans-Being" in Chapter 3. This
      definition establishes the crucial difference between mathematics
      as ontology (but again, their equation is stated and legitimated
      by philosophy), and philosophy as that which, while also "all
      about identifying what real ontology is," is ultimately released
      from ontology. Indeed, philosophy is a theory of what is "strictly
      impossible for mathematics" and "a theory of /event/ aimed at
      determining a trans-being." As I said, however, one might want to
      replace mathematics with mathematical ontology here, thus leading
      to an inequality defined earlier: "ontology=mathematical ontology
      < trans-Being=philosophy." According to Badiou, thus also defining
      "/event/" (as the concept is conceived in Being and Event):

          On the other hand [as against the ontological determination
          defined by set or topos theory], a vast question opens up
          regarding what is subtracted from ontological determination.
          This is the question of confronting what is not Being /qua/
          Being. For the subtractive law is implacable: if real ontology
          is set up as mathematics [mathematical ontology] by evading
          the norm of the One, unless this norm is reestablished
          globally there also ought to be a point wherein the
          ontological, hence mathematical, field is de-totalized or
          remains at a dead end. I have named [in Being and Event] this
          point the "/event/." While philosophy is all about identifying
          what real ontology is in an endlessly reviewed process [such
          as from set to topos theoretical ontology], it is also the
          general theory of the event--and it is no doubt the special
          theory, too. In other words, it is the theory of what is
          subtracted from ontological subtraction [such as that found in
          Kant's subtractive ontology]. Philosophy is the theory of what
          is strictly impossible for mathematics. (60) 

      This is a crucial point, a crucial /thought/. The distinction
      between the special and general theory of the event may be best
      understood, in part via Bataille (restricted vs. general economy),
      as that between the representational theory of the event and the
      theory that reveals something in the event, or the truth, that
      exceeds, irreducibly, any representation or any specific ontology.
      This thought governs the remainder of Badiou's argument in the
      book, developed via analyses of philosophical frameworks (Plato,
      Aristotle, Spinoza, Kant, and Deleuze), and set- and topos
      theoretical mathematics.

  15. It is also in this "space" of the relationships between Being and
      trans-Being, the space defined by the non-empty void of the Real
      (in Lacan's sense, extended by Badiou), that Badiou, in closing
      the book, also re-establishes the relationships between Being and
      appearing (153-68). In Lacan and Badiou alike, the trans-Being of
      the Real is conceived as the efficacity of both Being and
      appearing, or even of trans-Being of the event. Badiou, thus, also
      brings together his faithfulness to (the true) Platonism and his
      faithfulness to a reversal of Platonism, and thus to modern
      philosophy (163), in order to reveal "Being itself in its
      redoubtable and creative inconsistency. It is Being in its void,
      which is the non-place of every place" (169). Given this relation
      to appearing, Being comprises, from its two different sides, both
      the multiple without-One and the void, and in both of these
      aspects it is produced, as an effect or set of effects, by the
      efficacy of the Real. The /appearance/ of Being is traced through
      an important discussion of the relationships between mathematical
      ontology and mathematical logic, via topos theory. These
      relationships and Badiou's view of mathematics as a thought and
      ontology, as against logic, are important in this context and for
      Badiou's thought in general. Here suffice it to say that logic is
      linked to appearance, thus also giving the double genitive to the
      phrase "logic of appearance," and mathematical ontology is related
      to Being, /is/ Being. The configuration of Being and appearing,
      just defined, is that of "event," which Badiou's use of
      mathematical ontology helps him establish in order to move beyond
      ontology to philosophy. As Badiou writes:

          This [the configuration just described] is what I call an
          "event." All in all, it lies for thought at the inner juncture
          of mathematics [as ontology] and mathematical logic. The event
          occurs when the logic of appearing [the double genitive sense]
          is no longer apt to localize the manifold-being of which it is
          in possession. As MallarmÃ(c) would say, at that point one is
          then in the waters of the wave in which reality as a whole
          dissolves. Yet one also finds oneself where there is a chance
          for something to emerge, as far away as where a place might
          fuse with the beyond, that is, in the advent of another
          logical place, one both bright and cold, a Constellation. (168) 

  16. Badiou's appeal to MallarmÃ(c) signals that, along with being the
      space of philosophy (the space with which it is concerned and
      which it also occupies), this space also appears to be, in
      Blanchot's title phrase, the "space of literature" (the same
      parenthesis applies). It is the space from which, in a
      non-reversing reversal of Plato, mathematics, which only relates
      to Being or ontology, is exiled or rather into which it is only
      partially allowed as a tenant, as against poetry, which inhabits
      this space as a resident alongside philosophy. This orientation
      and decision of thought also brings Badiou closer to Heidegger,
      especially the later Heidegger, when the ontological projects of
      Being and Time (and several projects following it) are replaced
      with a certain conjunction of thinking and being, via Parmenides's
      fragment, "The Same is Both Thought and Being," which Badiou
      invokes (52). (The English translation is that of Badiou's French
      translation, different from Heidegger, and indeed the translation
      of this statement is itself a decision of thought.) At this stage
      of his thought, the true "thinking" [/denken/] is fundamentally
      linked by Heidegger to the thinking and language of poetry. The
      proximity between Badiou and Heidegger thus reemerging is tempered
      by differences (no equation here), most essentially because
      mathematical ontology and the equation "mathematical
      ontology=ontology=the multiple without-One" is retained by Badiou,
      as against Heidegger (on both counts: mathematics and
      multiplicity). This equation remains crucial, even if one can now
      add an inequality ontology< poetry=philosophy (as thinking
      "event"), or perhaps with poetry and philosophy in the undecidable
      relationships (in Derrida's sense) to each other. Either way,
      mathematics, poetry, and philosophy are brought together, in a
      Constellation.

  17. A reader of Badiou, or of Hughes's article, would not be surprised
      by the presence of literature in this space, any more than by the
      presence of this space in literature, by its becoming, in
      Blanchot's title phrase, the space of literature, defined by
      Blanchot along similar lines (of the discontinuity of the event).
      Hughes's article, to which I am now ready to return, deserves
      major credit for its exploration of the role of literature in
      Badiou's thinking of the event (ethical, aesthetic, or other), and
      additional credit for relating the situation and the event of
      Badiou's thought to the Romantic tradition, indeed to many
      Romantic traditions, which also form a multiple without-One.
      Hughes is also right to bring these aspects of Badiou's thought to
      bear on Badiou's thinking (of) subjectivity and the ethical, and
      the connections (proximities and differences) between this
      thinking (or Badiou's thought in general) and that of Lacan and
      Levinas. Hughes's "ventur[ing]" a (re)formulation of Badiou's
      ethical maxim as "/one must poeticize/" is compelling, especially
      given that the true ethical imperative (under the full force of
      which we come rarely, according to Badiou) is by event and truth.
      As Hughes says: "One might venture it as a new formulation of
      Badiou's ethical maxim: /One must poeticize/. That is, one must
      exceed one's situation and assume an ethical relation to the event
      by striving to name it through poetry. As the Romantic intuited
      and as Badiou's philosophy formulates much more precisely, poetry
      and ethics, like poetry and truth, are not to be disentangled"
      ("Riven" ¶21). This is, I think, quite true, as is the more
      general claim that Badiou "is suggesting a special role for poetry
      in the elaboration . . . of truth [in his sense]" (¶21).

  18. It appears to me, however, that Hughes disentangles too much both
      from mathematics and from mathematical ontology, as the ontology
      of the multiple and the political without-One, and from ontology
      in general in Badiou. Hughes's invocation of Poe's "The Purloined
      Letter" on his way to his conclusion just cited is apposite here:
      "We might think of this [this special role of poetry] as somewhat
      akin to the insight of Poe's Dupin, who says, referring to the
      Minister [a poet and a mathematician] who has purloined the royal
      letter, that "as a poet and mathematician, he would reason well;
      as mere mathematician, he could not have reasoned at all" (¶22).
      We might recall that Poe's "The Purloined Letter" and Lacan's
      reading of it in his "Seminar on 'The Purloined Letter'" engage
      the question of the relationships between poetry and mathematics.
      However, could the Minister think as a mere poet, at least as
      sharply as Dupin, who out-thinks him? Perhaps he could not, at
      least if we read the story through Badiou's optics, where the
      thinking of the Real is at stake, and Poe does not say that the
      Minister could either. In fact, both Lacan's and Derrida's
      readings (in "Le Facteur de la VÃ(c)ritÃ(c)," in The Post Card) place
      Dupin in a position that is more akin to that of a philosopher in
      Badiou, as both a poet and a mathematician. Part of Derrida's
      critique of Lacan is that, unlike Dupin/Poe, Lacan does not think
      the multiplicity and dissemination of writing in his reading. One
      might add that Lacan also places the whole case too much in the
      Symbolic register, thus both reducing the multiple to the Oedipal
      and, as it were, forgetting the Real. In any event, in my view
      Badiou's ontology of the multiple without-One and its political
      underpinnings and implications could have sharpened and enriched
      Hughes's analysis of the ethical and/as literary problematics in
      Badiou. Hughes invokes the multiple only briefly in his discussion
      of a theatergoer's encounter with Hamlet in Being and Event
      ("Riven" ¶12).

  19. Consider, for example, how the connections between Badiou and
      Levinas appear from the perspective of Badiou's mathematical
      ontology of the multiple. Hughes does note the potential role of
      the mathematical considerations for Badiou, including as concerns
      the difference between him and Levinas. Thus, he says:

          Badiou's mathematical grounding and conceptualization of
          alterity, his "numericalities" of solipsism and the Infinite,
          /his set-theoretical elaboration of the event/, and his
          insistent recourse to the category of /truth/ as the grounds
          for the specifically /ethical/ force of alterity and the
          infinite--all this is quite foreign to Levinas's sensibility .
          . . This [along with other factors that I omit for the moment,
          given my context] also gives Badiou a broader scope for
          thinking the ethical in places--art, science,
          /politics/--where Levinas's writings do not often venture.
          (¶22; some emphasis added) 

      Hughes, however, does not take advantage of the mathematical
      aspects of Badiou's thought, in particular "/his set-theoretical
      elaboration of the event/," which entails and enacts the multiple
      without-One and, within it, the political, as considered here. As
      a result, Hughes's analysis ultimately leaves Badiou's thought
      within the domain of rupture, discontinuity, inscribed "through
      tropes of /trauma/" (¶23). The Levinasian ethical /situation/ (the
      term can be given Badiou's sense as well) is defined by an
      encounter with the radical, irreducible alterity of the Other
      (/Autrui/), which should not be simply identified with a person or
      a subject. (This alterity is not unlike that of Lacan's Real in
      epistemological terms, but is different in ethical terms, is
      ethical.) It may be noted that Badiou, and some of his followers,
      tend to over-theologize Levinas's thinking on this point. Contrary
      to Badiou's argument in Ethics, while Levinas's thought has
      significant theological dimensions, the Other as /Autrui/ is not
      theological, even if it is /modeled/ on theology, and as such may
      be better termed, via Heidegger and Derrida, "ontotheological."
      For the moment, the appearance of the Other is the /event/ that
      transforms the /situation/ (again, in Badiou's sense) in which
      each of us finds oneself when the Other appears. This appearance
      (including in the sense of phenomenon) redefines our world, or
      home, since, according to Levinas, we must welcome the Other with
      hospitality (Totality and Infinity 27). Levinas's conception is
      more complex because the event of the appearance of the Other has
      always already occurred, thus making /ethics/ and its /infinity/
      precede /totality/, which Levinas often sees as defining
      /philosophical/ thought. These complexities do not, however,
      affect my argument here.

  20. In contrast to Levinas, for Badiou any ethical event, good or
      evil, or beyond good and evil, while it may involve an encounter
      with the other (no capital), cannot be defined by the alterity of
      the Other as /Autrui/ (with capital O or A) in Levinas's sense.
      Any situation or any event is defined by and defines (but cannot
      be contained by) the mathematical and, correlatively, political
      ontology of the multiple without-One, by /Badiou's infinite./ As
      such, it is not only without totality, but also without /Levinas's
      infinity/, which appears as a form of totality from where Badiou
      stands, since it is defined by the One (as the Other), rather than
      by an infinitely multiple without-One. Accordingly, in an ethical
      event, as in any other event, we always confront the Real and its
      alterity through the manifold or the multiple, whether we do it
      together with others or/as in encountering an other (and hence, as
      against Levinas, still always together and never apart within the
      multiple). Subjectivity, it follows, is this political
      multiplicity as well, and hence every subject is a multiple
      without-One. By the same token, "the truth itself is but a
      multiplicity: in the two senses of its coming (a truth makes a
      typical /multiple/ or generic /singularity/) and in the sense of
      its being (there is no /the/ Truth, there are only disparate and
      untotalizable truths that cannot be totalized)" (Briefings 62;
      emphasis added). An ethical or any other situation or any event is
      always political, infinite yet multiple, multiple without0 One,
      without any possibility of unity or totality. Because of the role
      of the political multiple-without One of Being, always involved in
      an event, the multiple is irreducible in the trans-Being of the
      event as well. There is no event, no encounter, ethical or other,
      that can ever be ontologically single; it can only be singular in
      the sense of its uniqueness or discontinuity relative to its
      situation, on the one hand, and to other situations and events, on
      the other. Hence the political is irreducible in and defines the
      ethical, rather than being grounded in the Levinasian ethical
      Other. In his Adieu to Emmanuel Levinas, Derrida offers a
      respectful and subtle, but firm, critique of Levinas along similar
      lines, although there are also differences between Badiou and
      Derrida, specifically insofar as there is no ontological infinite
      (in Badiou's sense) in Derrida. It also follows that, while Hughes
      is right to stress the singularity of the event and its alterity
      or exteriority to the situation, it is not possible to speak as
      Hughes does along more Leibnizean lines of the Oneness of the
      situation in Badiou or to read "its /all/" "as the Oneness of
      one's multifarious elements" ("Riven" ¶12).

  21. To some degree, the argument just given also applies to Lacan's
      use of the Real, in part in juxtaposition to Badiou's concept of
      the Real or how this concept can be used and developed, and has
      been used and developed by Badiou. That is, Lacan's use of the
      Real may also be seen as to some degree bypassing the multiple and
      the political, and centering primarily on individual subjectivity
      or intersubjectivity and on the ethical, as innovative and radical
      a move as the introduction of ethics into psychoanalysis might
      have been. Apart from other key differences (such as those those
      having to do with the role and architecture of language,
      signification, desire, the Imaginary and the Symbolic), Lacan's
      claims concerning the ethical are not as strong as those of
      Levinas. Indeed, by being placed within the triangularity of the
      Oedipal (transformed, as against, Freud, via the economy of the
      signifier) and hence within a certain Oedipal politics, Lacan's
      ethical order or subjectivity is at least implicitly political.
      Nevertheless, one can speak of a certain curtailment of the
      multiple and/as the political, and Deleuze and Guattari have
      criticized Lacan along these lines in Anti-Oedipus. It appears to
      me that on this point, too, Hughes's analysis can be deepened and
      must, to some degree, be adjusted. Let me reiterate that, even
      apart from being an extraordinarily powerful concept in its own
      right, Lacan's Real is crucial for Badiou and even irreducible in
      his philosophy (including in his sense, as discussed above).
      Hughes, accordingly, is correct to give major attention to this
      significance, specifically in the context of Badiou's ethical
      thinking, and to link Lacan's Real and its connection to language
      to the problematics of literature and Romanticism, and to the way
      both think "the void of the real" ("Riven" ¶13). The concept is
      indeed especially significant, as Hughes argues, for Badiou's
      concept of event, as always the event of trans-Being: the "trans"
      of this "trans-Being" is essentially linked to the Real in Lacan's
      sense, or rather--and this is my point here--in Badiou's sense.
      For it seems to me that Badiou's deployment of Lacan's Real is
      assimilated into his thinking though the multiple and the
      political without-One, or it follows without-Three (the Oedipal
      three), as much as without-Two, the ethical Two of Levinas, which
      is still ultimately the One (Lacan's Three is three). The Real
      cannot by definition be reduced to ontology--any ontology but
      especially Badiou's mathematical ontology--any more than can an
      event and its trans-being, grounded in (as arising from) the Real.
      I would argue, however, that this disruptive work of the Real, as
      understood by Badiou, cannot be dissociated from the multiple
      without-One. The Real acts upon this ontology and disruptively
      transforms its multiplicity by giving rise to events, but only
      into another multiplicity.

  22. Now, is this transformation /traumatic/? Or, more generally and
      more pertinently to Hughes's argument, how does Badiou's concept
      of event relate to that of trauma, especially as considered by
      Lacan, via the Real? As Hughes says, Badiou does not appeal to and
      does not primarily, if at all, think the event as trauma. As
      Hughes states, "to be clear, 'trauma' is not a word Badiou himself
      employs . . . he uses an array of others to describe his
      subjects--riven, punctured, ruptured, severed, broken, annulled,
      and so forth" (¶10). Hughes gives his reasons for his appeal to
      trauma. One might ask, however (and this question appears to be
      missing in Hughes's article): Why does Badiou not appeal to
      trauma? Although Badiou's ontology of the multiple could be
      brought to bear on this question as well, the main reason for
      Badiou's avoidance of trauma, I contend, lies in the nature of
      trauma as being primarily, fundamentally about the past event and
      its primarily negative, traumatic impact on the (post-event)
      future. By contrast, even though he grounds his concept of event
      in a Lacanian concept of the Real, Badiou appears to be primarily
      concerned with the future, and moreover with the positive,
      transformative future of events (which may of course have occurred
      in the past). This futurity is part of the architecture of
      Badiou's concept of event, and defines actual events--of whatever
      kind and whenever they occur--as futural events. Let us revisit
      Badiou's list of events cited earlier: "The French revolution in
      1792, the meeting of HÃ(c)loïse and AbÃ(c)lard, Galileo's creation of
      physics, Haydn's invention of the classical musical style, . . .
      the cultural revolution in China (1965-67), a personal amorous
      passion, the creation of Topos theory by the mathematician
      Grothendieck, the invention of the twelve-tone scale by
      Schoenberg" (Ethics 41). These events may have been traumatic and
      may have left their traumatic effects or traces, but it is their
      futural impact, as creating new situations, that is above all at
      stake for Badiou, even in the case of a personal amorous passion,
      or love. Indeed, there is no need to say "even," for passion and
      love are about the present and future, even though they can and
      sometimes do have traumatic effects. Lacan's concept of the Real
      easily allows Badiou to give it this futural dimension because,
      apart from Badiou's mathematical (ontological) and political
      extension of the Real, it is indeed a more general concept rather
      than something that isirreducibly connected to trauma. It is true
      that, according to Lacan, "the function . . . of the real as
      encounter . . . first presented itself in the history of
      psycho-analysis in a form that was in itself already enough to
      arouse our attention, that of trauma" (Four Fundamental 55). That,
      however, need not mean and, I would argue, does not mean that the
      function of the Real is limited to trauma, even in Lacan or in
      psychoanalysis; quite the contrary, and Badiou is right to take
      advantage of the broader sense of Lacan's extraordinary concept in
      defining his conception of the event.

  23. The futural orientation (also in Badiou's sense) of his thought of
      the event is, however, a more complex matter. For this orientation
      not only poses a question for Hughes about his reading of this
      concept in terms of or via tropes of trauma, it also poses a
      question for Badiou from the traumatic side of the Real. The
      significance of this futural orientation of thinking the event is
      undeniable, including in our understanding of history, and hence
      the past, as shaping our present and future. But the past, the
      ghosts of the past inevitably haunt us, many ghosts of many pasts,
      for this ontology is multiple without-One, too--that of the
      multitudes of the living and the dead, each with its own end of
      the world, unique each time, both multiple and unique, like the
      ontology of snowflakes. It is, yet again, literature that brings
      together both these multiples without-One, that of the living and
      the dead and that of the falling snow. It does so in Joyce's
      thinking an event of trans-Being, human (the passion of love),
      literary, and political, in ending, /uniquely and multiply
      ending/, "The Dead" and Dubliners: "the snow falling and faintly
      falling, like the descent of their last end, upon all the living
      and the dead," of Ireland and of the world. "/All/ the living and
      the dead," each unique and multiple, as snowflakes in a
      snowfall--past, present, and future.

      / Theory and Cultural Studies Program
      Department of English
      Purdue University
      plotnit@purdue.edu /


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