This edition of the Early Career Research SPotlight focuses on Becky Vartabedian. She is Assistant Professor in the Philosophy department at Regis University in Denver, and received her PhD from Duquesne University in 2015. Her primary area of research is contemporary Continental philosophy, focusing on its engagement with mathematics and mathematical logic and the implications of this engagement for social and political thought. Becky is completing work on the manuscript for Multiplicity and Ontology in Deleuze and Badiou, which will be published by Palgrave Macmillan sometime in 2018.
Your work focuses on the different ways Gilles Deleuze (alongside Felix Guattari) and Alain Badiou describe the relationship between “multiplicity” and “unity.” Can you explain the difference between these two camps, and why this is an important question?
Both Deleuze’s and Badiou’s work with multiplicity and unity are embedded in broader projects concerned with identifying conditions for transformation and novelty. They are interested in the “advent of the new” in philosophy, in politics, and our intellectual and interpersonal aspirations. Most readers come to Deleuze and/or Badiou through their respective and competing theories of the “event,” an idea indexing transformation in these areas. Readers then find that both thinkers claim the conditions for transformation are immanent, found in the structural features of the event itself. Events are linked to forms of unity or unification in both these systems: for Deleuze, the event is the expression of a consolidated multiplicity, occurring on both large and small scales (for example, in geological time or personal individuation); for Badiou, the event is linked to a type of ontological arrangement – a singular situation – determined using rules for organizing and reorganizing the contents of a closed set. Badiou’s event is identified in large-scale transformations in science, politics, and art, and in the intimate encounters of amorous love.
Attention to novelty and transformation is indeed significant, but my work is concerned with the conditions underwriting the presence of an event; this requires attention to the procedures by which any unity is consolidated, and the multiplicity on which these procedures operate. For Deleuze, unity is an emergent phenomenon, and multiplicity is the ground for its expression; Badiou, by contrast, claims that unity is the result of an axiomatic procedure and that pure multiplicity is the foundation from which it is built. Seeing their work in this context reveals their preoccupation with a very old philosophical question: Is being one or is it many? Both address this question directly (see, for example, Badiou’s Being and Event, p. 23/ff; Deleuze’s Difference and Repetition, p. 182/ff) and claim that neither of the traditional options are sufficient; as more precise alternatives, Deleuze posits multiplicity and Badiou posits multiple.
Deleuze’s multiplicity describes a set of ontological relations holding between component parts. More than emphasizing any single element in the network, it sees the transactions of this limited network as functioning to express or produce an individual or singular instance. For example, a Deleuzian analysis of personal individuation interprets the ‘event’ of one’s birth according to the conditions converging to express a particular instance; one’s parentage, the place and time of their gestation, the conditions under which this gestation occurred, the circumstances attending their birth, and so on, recognizing a series of conditions as constitutive of any singular instance. That the event is the birth of a human being is significant, but does not take any precedence in terms of the conditions governing existence. This sort of accounting is driven by Deleuze’s commitment – consistent through his work, whether individually or in collaboration with Félix Guattari – to prioritizing difference and challenging concepts of identity and conceptual application that would organize and thus minimize unique features of any singular instance. Attention to multiplicity in Deleuze’s work requires, then, an appreciation of the conditions for the possibility of any singular instance and a recognition of the relations holding among these conditions.
Badiou, by contrast, understands multiple as divided according to an inconsistent multiple, which can be articulated infinitely and is inconsistent insofar as its closure would yield a contradiction; a consistent multiple, which draws on elements of the inconsistent multiple to create ontological situations and describe that which exists; and a generic multiple, which offers the ontological framework for mapping the emergence of truths in any transformed situation. The only relations of significance for Badiou’s ontology are that of belonging and inclusion, relations that define parameters of membership in sets and subsets. This is immediately and necessarily embedded in a mathematical context, which I say more about below.
Differences in the articulation of the concept aside, focusing on a commitment in common to multiplicity situates Badiou and Deleuze in a conceptual lineage anchored by Kant, Hegel, and the late work of Merleau-Ponty. Approaching Badiou’s and Deleuze’s respective ontologies from this vantage liberates their work from parochialism or identifying their concerns as limited to materialist, post-structuralist, or other narrow frameworks of analysis. Emphasizing their use of mathematics, and particularly Badiou’s long engagement with mathematical logic, brings their respective work into alignment with traditionally analytic concerns. Though I’ve a long way to go on this score, my work is inspired by Paul Livingston and his skill in bridging the gaps between ‘Continental’ and ‘Analytic’ dispositions with Deleuze’s and Badiou’s programs (see e.g., Livingston’s The Politics of Logic [Routledge, 2011]).
You’ve also spent some time exploring how Deleuze’s/Guattari’s work is influenced by Riemann, and Badiou’s by Cantor. What influence did Riemann and Cantor have, and how did Deleuze and Badiou, respectively, adapt their ideas?
Concerning adaptation, both Badiou and Deleuze build their concepts of multiple and multiplicity from well-established mathematical ideas. Badiou, for example, cites the late 19th and early 20th century innovations concerning set theory and the foundations of mathematics – Cantor’s in/consistent multiplicity and theory of transfinite ordinals, Frege’s questions concerning comprehension and its result in Russell’s paradox, and the development of the Zermelo-Fraenkel axiom system – as a transformation (an event!) that makes possible a new way of thinking about multiples. These resources are brought to bear in the hypothesis that forms the “radical thesis” of Being and Event: “Insofar as being, qua being, is nothing other than pure multiplicity, it is legitimate to say that ontology, the science of being qua being, is nothing other than mathematics itself” (Badiou 2005, xiii). To establish the antecedent of this hypothesis – that being qua being is pure multiplicity – Badiou invokes Cantor’s inconsistent multiplicity, which is an infinite multiple that proceeds without closure. When Cantor introduces the concept in an 1899 letter to Richard Dedekind, he also identifies consistent multiplicity as a multiple that can be closed and remain consistent; consistent multiplicities are sets and, in Badiou’s work, are the ontological situations organized using the Zermelo-Fraenkel axiom system and the Axiom of Choice. In Cantor’s distinction of in/consistent multiples Badiou finds the basic components of his ontological system; Cantor’s theory of transfinite ordinality provides the framework for keeping the inconsistent multiple infinite.
Gestures to the work of Bernhard Riemann, and particularly the concepts developed in Riemann’s 1854 On the Hypotheses that Lay at the Bases of Geometry, are peppered across Deleuze’s work, both on his own and in collaboration with Guattari. Riemann’s insights concerning continuous magnitudes and their ability to be expanded in n-dimensions, offer a mathematical framework for organizing the virtual idea in Difference and Repetition, the concept in What is Philosophy?, and describes striated space in A Thousand Plateaus. Riemann’s work, as one in a series of non-Euclidean geometries, transforms the way continuous magnitudes are understood and manipulated. Continuous magnitudes traditionally describe spaces (lines, surfaces, and bodies) that are identified according to a common boundary; a line AB, bisected at point C allows me to describe segments AC and CB as parts joined at the boundary C. Riemann’s innovations are to read continuous magnitudes as either simply-extended or multiply-extended: line AB is simply extended when there is a single pathway between the two points (from A to B and back); it is multiply-extended with the addition of point C, which develops three pathways (from A to C, from C to B, and from A to B), and in this example the addition of points results in increased dimensionality. Above I indicate that Deleuze’s ontology situates singular instances as the expression of connected or networked conditions. Riemann’s insights allow Deleuze a framework for accommodating and connecting these contributing conditions, to degrees of increasing complexity. Pathway and dimension are Riemann’s concepts at work here, and these provide the conditions for expansion of a manifold to n dimensions such that connections between components may multiply. Riemann’s Hypotheses also presents the conditions for subtraction of a manifold, an analytical method marked by the n-1 figure appearing in Deleuze’s work, especially with Guattari in 1976 and forward.
The question of influence is trickier to nail down; it requires, I think, some attention to the way mathematics in general functions in Badiou’s and Deleuze’s respective oeuvres. Fortunately, Badiou has quite a lot to say about this.
In a recently-published interview with Gilles Haéri, Badiou attends to this question of influence, discussing the formative role mathematics had for him as a young high school student and its persistent shaping of his approaches to philosophical problems. This text, In Praise of Mathematics (translated by Susan Spitzer and published by Polity), shows Badiou accounting for this very question and doing so in an accessible and inviting way. His commitment to mathematics and the insistence that ontology is really a mathematical matter, follow from his avowed position as a type of mathematical Platonist. For example, when he describes it for a popular audience Badiou situates mathematics according to its place in the platonic doctrine of the Divided Line. It is the intermediary between that which is sensible and that which is conceptual; he takes seriously the way mathematics facilitates philosophical reflection and particularly thought concerning being qua being. From this point of view, then, when Badiou claims that the inconsistent multiple is properly no-thing (and, by extension, is no-where), this is in line with his Platonist commitment. Further, when he insists that his theory of the multiple is not identical to the atomist’s ‘many’ associated with bodies and void, it is because of this Platonism.
Badiou is thoroughly committed to ontology as a robust hypothesis; if anything can be said of being qua being, and given that being qua being is inconsistent multiplicity, then that which can be said must be mathematical. He is also committed to the exactitude of this model, which has tricky consequences – if mathematics is the science of being qua being, then the open questions go something like “What does ontology then offer us?”, and “What does philosophy have to do with ontology anyway?” At least in the continental tradition following Heidegger these sorts of questions are quite exciting, not because Badiou is asking his reader to abandon ontology, but to think of it in a register other than phenomenological or even philosophical. I appreciate that push to learn something new, or to put familiar questions to work in unfamiliar contexts.
This issue of influence is perhaps a bit clearer in Deleuze, because mathematics has a more didactic function in his work than in Badiou’s. As folks like Dan Smith (2003, 2012), Henry Somers-Hall (2010, 2013) and Simon Duffy (2013) have pointed out, Deleuze selects from minor traditions in mathematics (e.g., Bordas-Demoulin on the differential relation, the selection of Leibnizian infinitesimals over Newtonian integrals, etc.). He then uses innovations in these minor traditions as maps for discovering what Duffy has identified as “corresponding alternative lineages in the history of philosophy” (2013, 1). When a specific mathematical or scientific concept appears in Deleuze’s work, Duffy reminds his reader that these are deployed in service of “problems that are ‘essentially inexact yet completely rigorous’” (2013, 2; the interior quotation is from Deleuze’s Negotiations, 29). For Deleuze this means that his work with mathematics emphasizes relevant conceptual contributions as rigorously as possible while not diluting their technical or quantitative expression. I call this gesture didactic because rigorous scientific and mathematical frameworks are aids to thinking through equally difficult philosophical problems; Deleuze does not co-opt these as a replacement for the philosophical resources in place to engage the problem.
What applications do these ideas have to current philosophical debates?
Well, two ‘applications’ come to mind. First, is the recognition that a good deal of this reflection about multiplicity and unity occurred (and, in Badiou’s case, is occurring) in a live and fraught political context. As I discovered while doing research for my book, the question about the relation between multiplicity and unity arises for Deleuze, Guattari, and Badiou against the background of a ‘failed revolution’ (May ’68). As such, the multiplicity-unity relation offers a mechanism for assessing, basically, “what went wrong in May.” I think their insights and interchange over this issue – particularly in the conversation following the publication of Deleuze and Guattari’s “Rhizome: Introduction” in 1976 – offers a framework for reflecting on the structure(s) any mass movement needs to realize its aims. The composition of mass movements requires temporary – but common – catalysts to be legible (Deleuze and Guattari) and successful (Badiou). The lesson, particularly in reading Badiou’s early work and the Capitalism and Schizophrenia volumes of Deleuze and Guattari’s collaboration, is that these catalysts can only be temporary insofar as they don’t overwrite those interests signing on to the catalyst for the sake of change. This is an interesting prospect for understanding contemporary movements concerned with transformation.
This is also a reminder to keep abstract philosophical analysis ‘live,’ and in a way keeps those of us who work on ontological questions connected to the context in which we are engaging these. The historical and political location in which these questions become meaningful for Deleuze and Badiou should function as a kind of check: I ask myself, what does it mean to do ontology now and in the present context? I don’t know the answer to this (though I’m working on it), but it’s a valence of this reflection that I’m responsible to address. Take, for example, the ascendency of the Women’s March here in the United States as a benchmark. I’m not interested in asking whether it is a properly Deleuzian or Badiouian movement, but rather keen to understand the way that a sense of unity is expressed by the diverse and multiple interests signing on to the movement. What Deleuze, Guattari, and Badiou offer is a set of tools for understanding the relationship of structure to legibility (i.e., how a movement can be ‘seen’ against a background of diverse interests) and potentially the relationship of structure and legibility to success, whatever that means.
Second, I am interested in re-situating Deleuze and Badiou in a philosophical lineage by showing one of their central concerns to be with a uniquely philosophical question: what is meant when one claims being (qua being) is multiplicity or multiple? Because they are not only theorists but also systematic philosophers, I think it is necessary to see their ‘transposable’ concepts as founded in a stream of philosophical reflection as old as the western tradition of philosophical reflection itself, and to clarify this relationship. Seeing Deleuze and Badiou in a philosophical context is perhaps obvious to philosophers, but of course their work and concepts are attractive to thinkers in a variety of fields: communication, political theory, geography, education, and other fields in the humanities have taken up Deleuzian and Badiouian resources in their respective discourses. The result of this broad appeal is a complex, occasionally bewildering, and sometimes impenetrable secondary literature that obscures the origins of these transposable concepts like event or virtuality in a robust ontology or philosophy. Having a sense of the way these more accessible concepts are founded in (and dependent on, to some degree) an appreciation for ontological reflection is valuable. This is my teaching impulse coming through, I guess.
You’ve developed your work and interests into a novel set of courses that you’ve taught or soon will teach (such as “Philosophy and Social Issues: Precarious Bodies” and “Hospitality, Justice and the Common Good”). What led you to develop courses on these topics, and how have your interests influenced them?
In part, this is a practical matter! I work in a small and mighty Philosophy department that serves our growing number of majors and functions as a utility player for many programs across our College. My colleagues and I offer courses for the Peace and Justice studies department, Women’s and Gender Studies, our first-year foundational writing program, and the Integrative Core. When we’re working this widely, we balance our interests and expertise with the diverse groups of students participating in our courses and work with an awareness of the diverse preparation they bring to engaging philosophical and theoretical texts.
For example, the “Hospitality, Justice, and the Common Good” course is part of our Integrative Core, which is required for all third- and fourth-year students in Regis College. I built the first version of this course when I learned that Regis was interested in becoming an Anchor Institution, which means it is pursuing ways to put its diverse resources to work in supporting the community immediate to Regis. I wanted to ask my students to consider how – and how well – Regis treats its neighbors, which is a question of hospitality. To address this issue, students identify areas of need in the communities surrounding Regis and identify ways Regis’s resources can be put to work for this community. This is work of qualitative research, so students are engaged in community walk activities, are speaking with community leaders and engaged with community organizations, and develop proposals for extending Regis’s resources based on this work. They conclude the semester by presenting their proposals to university stakeholders and members of the community with whom they’ve connected.
I supplement the qualitative research with reflection on human connection, reading Camus’ The Stranger alongside Kamel Daoud’s The Meursault Investigation and portions of Frantz Fanon’s Black Skin, White Masks; students read Iris Marion Young’s 2006 Responsibility for Justice to examine and reflect on models of responsibility that serve an institution’s commitment to promoting justice and the common good. In this context, my expertise is brought to bear in the reflective and theoretical portions of the course, but its majority is devoted to students developing and demonstrating their own expertise on issues of significance to our lives together. This course, then, is originally a response to an institutional imperative; theory serves, but is not the center, of the course. In its second and third iterations, I team-teach with a colleague from the Biology department, so the center of the classroom is even more distributed. This is a great challenge to my sense of what it means to teach, and I’m grateful for this opportunity.
My upcoming “Philosophy and Social Issues: Precarious Bodies” is a course designed for our majors, students in the Peace and Justice program, and the Women and Gender Studies program; it is designed to fill a gap in our curriculum that has emerged around critical race theory and associated forms of reflection, and coincides with a surge of anti-racist activism on our campus. In this case, I use my training in Phenomenology (especially that of Merleau-Ponty and his inheritors) to make situated, embodied agency the theoretical and evaluative point of departure in this course. I hope to help my students recognize the power and efficacy of structural limitations on situated embodied agency, to help them determine the way racism, sexism, heterosexism, and ableism are each impingements and variations on Iris Marion Young’s “I Cannot.” It is in this “I cannot” that I see an expression of precarity. I then hope to use work in Judith Butler’s Giving an Account of Oneself (2003) and insights from Patricia Hill Collins and Sirma Bilge concerning intersectionality as affirmation of agency and critical tool to offer students ways and means toward transformative agency and ethical interpersonal encounters. I look forward to teaching this for the first time in spring 2018.
The diverse needs and preparation our students bring to the classroom have allowed me to re-situate myself and my expertise as aids to student learning. As such, I’m interested in pedagogy that de-centers the classroom in the student’s favor; I provide a framework, and students are empowered to flesh it out, whether with critical reading and reflection, service learning, or their hard-earned experience. This raises all kinds of issues about practical matters associated with teaching: what grading looks like in a de-centered context, what the stakes of learning are (e.g., must students get the right answer? Is there a right answer?), and what teaching itself means. Because I’m able to teach courses that include or overlap with my AOS (and are not solely focused there), I’m less worried about whether students are “getting it right,” and am enabled to help my students “get it” (whatever it is) in the first place. Regis has given me both the space and the opportunities to develop novel pedagogical approaches, and though it might occasionally be a disaster, this freedom is a great gift.
You can ask Becky questions about her work in the comments section below.
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