Sunday, January 11, 2009

Engendering Zero (Part 1)

The blog entry title refers to a reading of Alain Badiou, on Jacques Lacan' s psychoanalytic theory that was introduced in the last entry. As I said there, I am slowly making my way through Sam Gillespie's The Mathematics of Novelty (MON), as well as reading secondary sources on Lacan by Savoj Zizek and several others that were introduced. This is a long term project. I am sharing the journey and probably will make many wrong turns.

Zero gets defined as a mathematical element that when added to a number yields the same number. Historically, it took a long time before zero was even posited as a numeric element. It was hard to say zero should be in the company of that designating quantity. When we consider it is exactly zilch, zip,nada, nil and so on it gets a reputation for being at best a quantity of no importance. Indeed, the empty set signified as {} supplies not even a "0". Then to speak of engendering zero: to call forth or bring forth what? Precisely Nothing. The word implies generation and bringing into being in relation with the Void as it were. Yet these thinkers, (Badiou, Lacan, Zizek, and others al.) who I have come to appreciate from their political activism and historical analysis and/or other registers of thought, can, it seems to me, be conflated in their engendering of zero. That is to say there is plenty of scope for fusion and confusion. I need to understand. I thought this first post in the series should be mostly about what I have been reading on Lacan; but I will get to that in a later posting, first a bit on the beginning made in reading about Badiou's ontology=mathematics.

Alain Badiou: Being Qua Being and the Void

Badiou expresses ontology as "being qua being" and, as I see it, this is his engendering of the Void. When we consider the googled definition of ontology, we encounter reference to the nature, the meaning and the essence of being. One also finds the definition as having to do with presentation and representation of existence. I found it most helpful to look at the contrast of ontology with what it is often juxtaposed, that is in contrast to epistemology. Definitions from the net suggest epistemology generally means the study of how we know what we know - and the foundational sources of knowledge.

I may be wrong in expressing it this way, but whatI understand is that epistemology encompasses the whole domain of thought itself, knowledge as such. Ontology would encompass the domain of epistemology inasmuch as thought, knowledge would not be separate from being qua being; however, thought and new thought are always coming into being and do not encompass what is not known. Being qua being is where thought is situated, namely in the Void. I can try to trace support for my understandings from my reading of Gillespie in Mathematics of Novelty (MON); that is, as I work my way though the structure of the book I can't expect to convey adequately what is said there - but I can tell about what is said there and provide excerpts with commentary on my personal experience with the effects of the information on my thinking.

To be clear then, this series is a commentary on a learning process composed of studies on both Lacanian psychoanalysis and Badiouan ontology, finding the bridge from the Void. We are proceeding first on the latter for the time being. In telling you about what Sam Gillespie writes, the first section of the book "1. Conditions of the New" makes distinctions between the conditions of novelty for Badiou and those of Gilles Deleuze, one of the most influential and prolific French philosophers of the second half of the twentieth century. Why:

".. Badiou shares with Deleuze the fundamental convictions that philosophy as a project is far from over, that being is inherently multiple and is irreducible to the tenets of language, that philosophical novelty proceeds from an event, and that, despite its different manifestations in the world, being in and of itself is inherently univocal." (MON pg. 3)

Yet being qua being has unequivocal meaning in Badiou distinctly different than that in Deleuze, and the distinctions also extend to the shades of meaning for multiplicity and the event. This is what Gillespie's writing is about in this first section of his book. The essential distinction to put it in terms of my own thesis here is that unlike Deleuze, Badiou engenders the Void. This creativity, the emergence of the new or novelty, the conditions of this are the question. Both Badiou and Deleuze do not see philosophy as seeking discovery of the eternal unchanging One, rather they posit being as pure multiplicity, states of irreducible differences. Instead of a unifying unchanging abstraction of oneness, they see continuous change, the creation of the new. So from here we learn how they differ in the practice of philosophy.

Sam Gillespie explains that for Deleuze the concept of creativity is engendered from..

".. a free act of the philosopher that operates alongside the concept's self-positing.."

and in this correspondence, the philosopher's..

".. subjective capacity to generate concepts is the concept's objective potential to exist.." (MON pg. 2)

The text the goes on to quote Deleuze on this ".. auto-poetic characteristic.." whereby ".. the most subjective will be the most objective..". What is most significant here for my thesis, congruent with that of Gillespie, is that though Deleuze departs from the point of multiplicity, this multiplicity has this auto-poetic characteristic; while Badiou does not assume the creative power of being..

".. but rather that to think being, we need nothing more than a formal assertion that nothing - that is the empty-set or zero - exists.. having in itself no descriptive properties or content.. then the being it formalizes is simply nothing, void. As Badiou puts it.. 'the sole term from which ontology's compositions without concept are woven is inevitably the void'.." (MON pg. 3)

The impasse between the two thinkers of the multiplicity, then, is precisely on the issue of the conditions of the new. Deleuze posits the multiplicity in its entirety and conceives novelty as its creative capacity of difference in repetition of the whole of the past. Problematic is the question of there being a novelty, a creation, if what is posited as new is repetition. Still, it would be something emerging from something - as opposed to Badiou's conception of something new from nothing. The beginning of resolution of this impasse, for me, came with the first line of the second part of the first section (1. Conditions of the New, II. Badiou's Novelty - following I. Deleuzian Novelty):

"On the basis of the above, Badiou is led to conclude that for Deleuze, 'the thought of the new plunges the latter into that part of it which is its virtual past'." (MON pg. 7)

The emphasis here is on the nature of thought itself. I am going to discuss what I anticipate based on what I think I know. Later we will see how Badiou will utilize the axioms of set theory launched from the axiom of the empty set, but for now I focus on the issue of temporality to which set-theory will return. What I think I know is, if thought is the virtual past, what Badiou may mean in the above statement is that thought of the new is not the new. I might venture to say that part of thought which he suggests exists, not the past, has particular significance. I would not attribute it to Badiou, but I am predisposed to think any part of thought would be based on memory and therefore the past. Furthermore, would not the thought of the Void, which is not, be essentially a virtual past? I take this thought forward in learning what Badiou says about being qua being and the Void. The next key sentences from Gillespie (for me) are a page later:

".. Badiou divides the domain of experience into two distinct categories.. there is the situation.. unified presentation (the 'count as one'); consistency (an order to the multiple terms that appear within it); and [secondly] representation."

I would relate this to what I said earlier about epistemology and thought. The "count as one" is a reference to Badiou's application of set theory; the terms or elements of a situation form the set, are included in the set. One knows them as such, it is knowledge, it is thought in the domain of epistemological order. It is unified or consistent presentation. The empty set {} is axiomatically said to exist. Presentation of a situation is symbolized in set theory as the order of the situation's elements {A.B,C,..}. As for representation:

".. can be said to supplement the situation.. to render the gap between consistency.. and inconsistency (the void that escapes, or exceeds, the count for one).." (MON pg.8)

These two categories of experience can be distinguished in set-theory by the axiom of the power set. The elements belonging to set are simultaneously terms of subsets included in the set - the power set is the set of all subsets of a given set. I provided a somewhat more detailed discussion of Badiou's application of set theory last month in the entry entitled The Stupid Christ (Part 2) wherein the following was quoted from an entry at the blog The Parallel Campaign:

“.. the Void as Badiou sometimes calls it, cannot be presented, but it founds all possible presentation. The empty set is therefore what Badiou calls a pure, or empty name, it is not the presentation of the Void but its name. Therefore inconsistent and consistent multiplicity are linked through this axiomatic naming through the application of the count for one, the empty set sutures the presentation of consistent multiplicities, which are not, to inconsistent multiplicity, which is: Æ, the empty set, is the proper name of being. It also has a strange universal property; it is included in every set but never belongs. Therefore every set represents the void, but it is never presented and its universal property does not amount to much, it is simply the representation of nothing..”

Novelty then, for Badiou, is engendered from the Void (a name for that in excess of presentation). We are to understand this with reference to his conception of the Event. In the above quotation there is depicted the action of suturing: new situations (consistent multiplicities) which are not, that which are possible because of inconsistent multiplicity, are possible being sutured in the power set of that situation because it includes the empty set as well as all subsets generated by its presented elements. The aphorism from Badiou:

"All radical transformative action originates in a point which, from the interior of a situation, is an evental site." (Being and Event pg. 197)

This procedure, which Badiou terms a "Truth" procedure results in a novel situation. Prior to the Event (unpredictable except as a possibility, arising by chance - aleatory) being qua being consists in the situation (which should be understood to be the power set of all situations or any presented number of elements known as a set), which is consistent multiplicity, which is the count as one; and in addition to the situation is the empty set . This is the "State" of the situation in Badiou's lexicon, the actual existing of the situation and the Void naming inconsistent multiplicity. The situation in any State has its truth, the Truth of the Event engenders transformation of the situation, engenders a novel situation and a novel State.

The Event then must be pure operation. The situation can be seen as a "subtraction" from the State. In the condition for the new is a "subtraction from the subtraction" - or a "plus-one", a novel situation and its truth. The Truth procedure inaugurated by the Event is an operation from the Void. This operation occurs in the experience of the Subject - the subtraction and the subtraction from subtraction are related to the two categories of human experience. The consistency of the situation and the State is one register of human experience, another register is inaugurated by the Event.

We are all individuals. As such we participate in a given State as an individual Subject in that State. A novel State then, would logically require a transformation of the situation of at least one individual. As Gillespie writes, it is from the ..

".. appearance of an event that something anterior to the presentative immediacy of the known or discerned [the epistemological paradigm I want to say] can appear.. events do not signal the advent of a truth; rather they inaugurate subjects who intervene in a situation to the extent that these unique individuals remain faithful to an event by seeing its consequences through to a restructuring of the situation.." (MON pg. 9)

Novelty then, is expressed in the anterior future tense as it is known to have taken place. In terms of this blog and its thesis, the process of allegiance to Truth is a revolution of the mind. This revolution, from its overarching register of Truth may also be taken to pertain to different types of situations while remaining inconsistent Void in being qua being:

".. there is the empty category of Truth (with a capital T), and there are local truths (plural, small t) produced in the situations that are unique to the conditions.. where these truths are effected. There are four such conditions for Badiou: art, science, politics and love.. No single condition can be determining for philosophical truth [Truth] in itself." (MON pg. 9)

Sam Gillespie's The Mathematics of Novelty develops its theses from this beginning. Much of what I read from and about Badiou concerns issues of art, science, politics and love; the energy from this attention derives from a revolutionary practice that confronts the coordinates of power in these four domains of human experience. It is a revolution of the mind as it gains insight inaugurated by Events that are to transform the coordinates of power in given situations. As Badiou writes in St.Paul: The Foundation of Universalism:

".. where the name of a truth procedure should obtain, another which represses it holds sway. The name 'culture' comes to obliterate that of 'art'. The word 'technology' obliterates the word 'science'. The word 'management' obliterates the word 'politics'. The word 'sexuality' obliterates 'love'. The 'culture-technology-management-sexuality' system, which has the emmense merit of being homogeneous to the market, and all of whose terms [elements of that situation's set] designate a category of commercial presentation, constitutes the modern nominal occlusion [occlusion by the existing coordinates of power] of the 'art-science-politics-love' system, which identifies [T]ruth procedures typologically." (SP pg. 12)

So as I say, this concerns revolutionary practice - and obviously from the above quote the questioning of capitalist power and its authority. It is enough in this beginning to have established Badiou's philosophy in the context of engendering zero. I think it is clear that this topic focus is on the nature of subjectivity, our personal relationship to the Void - which is also the focus in reading Lacan's engendering of zero in psychoanalysis, as we shall see in a later part of this discussion.

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