Engendering Zero (Part 2)

As stated at the beginning of Part 1, the title of this entry refers to a reading of Alain Badiou's mathematics and Jacques Lacan's psychoanalytic theory - and specifically my reading Sam Gillespie's The Mathematics of Novelty; as well as reading secondary sources on Lacan, notibably Savoj Zizek and several others. How is it that these thinkers can speak of engendering zero: calling forth or bringing forth what? Precisely Nothing. Engendering zero implies generation and bringing into being in relation with the Void as it were. Why and how the Void? That has been my question.

Part I restricted the exploration to Badiou's ontology=mathematics. I think we made a minimal beginning (perhaps discussing about the first 13 pages of Gillespie's book). I will recap what was my personal concern, my learning as it were, keeping in mind this should not be conclusive - in fact there is a self-questioning going on:

(a) 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.

(b) What I think I know is, if thought is the virtual past, thought of the new is not the new. 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?

(c) 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.

(d) The term "Situation" is used to signify a set of consistent presentation. The thought of the Void as in (b) above is not the Void, it is part of consistent presentation. The unthinkable Void in nonetheless experienced as that which escapes the "count as one" - multiplicity within the situation plus inconsistent multiplicity are signified by the term "State".

(e) Applying the language of set-theory: 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.

(f) Novelty 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 (which by chance occurs because it is possible). The situation in any State has its presented truth, the Truth of the Event (emerging by virtue of inconsistent multiplicity) engenders transformation of the situation, engenders a novel situation and a novel State.

(g) 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.

(h) 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.

(i) 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. In terms of this blog and its thesis, the process of allegiance to Truth is a revolution of the mind.

(j) This idea of allegiance or fidelity in Badiou is a matter of atheistic faith. If indeed an Event occurs it manifests as a rupture in the situation, and the mind of the individual(s) subject in that situation, who for a period of time are directly acting in response to that rupture until the novel situation is established. That an Event has occurred is thus known in an anterior sense to have taken place. In the interim, the transforming individual is functioning in relation to inconsistent multiplicity.

The above is a very sketchy schematic of what I think I know about Badiou's ontology=mathematics. This was discussed in greater detail in Part 1 of this series. Important to add is that in Badiou's theory the truth (small t) in situations is categorized as existing in basically four quadrants: love, science, art and politics. The latter is obviously the primary domain of revolutionary practice. Important to Badiou and the thinkers featured in this blog is that the current political situation in the world at this time is established in the authority of capitalist power - and that the Event which is rupture in this situation is the advent of the communist hypothesis.

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 - and so we turn to the content for Part 2:

I spoke a couple of posts ago, in leading in to this current series, that the original work of Lacan is not easily accessible to those of us who do not know French and who are not professionally schooled and experienced psychoanalysts. Badiou was deeply influenced by Lacan as is well known and he has been a secondary source on Lacan's system for me. Even more so I have read Savoj Zizek on Lacan and I will get to that soon enough. There are some other good writers I have been reading, also secondary sources on Lacan whose thoughts I want to reference - but also writings about Zizek on Lacan, which will be my starting point.

A very good introduction to Zizek is Zizek: A Primer by Glyn Daly. Having established Zizek's background and getting to his psychoanalytic stance rooted in the idea of Death Drive (itself rooted in Zizek's reading of Hegel), the article then says:

"It is neither a cancellation nor any kind of physical death but is rather a certain excessive impulse that persists beyond mere existence or biological life. As Zizek argues: 'Human life is never just life, it is always sustained by an excess of life' (Zizek, 2001b: 104). The human being is precisely that entity that is sustained by a "more than human". It is this "inhuman" excess - born of a fundamental alienation - which is the death drive and which is constitutive of humanity as such. Death drive is a constant impulse to resolve the gap, or heal the wound, in the order of Being; to overcome dislocation and establish the full presence of subjectivity by finding its ultimate name/place in the world."

So let me anticipate already where I am going in my thesis conflating Badiou and Zizek on Lacan: order of Being (ontology, being qua being) exists not just as our mere biological life (our situation), but is sustained by an excess of life (inconsistent multiplicity); the fundamental alienation / death drive (the fundamental Event) is a constant impulse to heal the wound (establish a novel situation).

The questioning going on in me has to do with the perhaps repetitive and therefore non-novel resolution characteristic of thought itself in the thought of subjectivity as an ultimate name/place in the world. As I understand it, Lacan as per Zizek, posits this very impossibility of thought encompassing all of experience - that the subject as the thought of one's place in relation to the world is not the Subject. Glyn Daly does not provide this gloss on Zizek with application of the capital "S", but otherwise what she says lends to my thesis:

"Zizek insists on the validity of the notion of [S]ubject (Zizek, 1999: 158-59). The [S]ubject is neither a positive entity nor an identifiable locus but is thoroughly de-substantialised - it is precisely 'this empty nothing' of which Hegel speaks. This is why the Lacanian mark for the subject is $ (S-barred, the empty place or void that cannot be filled out in an ultimate sense)."

So we begin Lacanian algebra with $ (S-barred). What follows in the article text is a continuation of the Hegelian theme:

"Subjectivity [small s I say] will be more or less stable according to context. Under the impact of a traumatic experience, however, we experience a certain 'night of the world'[Hegel] where coherence and cohesion become radically undermined: that is, the condition of subject."Here it is hard to say small s because we are speaking I believe of the situation under assault of the Subject whose domain is inconsistent multiplicity.

Glyn Daly then states the Lacanian idea $ (S-barred), having traced Zizek's evolution on the same concept:

"We might say that the subject gets caught in an impossible attempt to produce a framework of [S]ubjectivity (to find its name/place), but from which it is already ontologically excluded. In this sense, the subject marks the site where an irresolvable economy of lack and excess are played out."

I want to put it this way: I know I exist and I know the world exists - isn't this our common experience as human beings? I mean this is the framework of daily existence. We can actually for a period observe this duality - and then experience that we forget to observe this fragmentation in the field of thought. Nonetheless, such observation provides an insight that the knower is the known in that the subject and its objects in the world are in the field of thought. We then say this is "my insight" so continue subjectivity (small s). We continue to experience ourselves as a subject with external objects as comprising the total unity of life. But the fact is that however we experience the subject there is some excess to the subject from which this experience is occurring - this would be the Subject (a name for no thing of thought - of Nothing, of the Void).

My point is that the subject itself in the field of thought along with thought of that separate from the subject comprise a situation which is a subtraction from the State which would include the excess, the Subject. These are my ideas and I may learn that I am not seeing this clearly.. I want to find out. Returning to the text of the article we have the introduction of another Lacanian algabraic symbol "a" as she continues on "an irresolvable economy of lack and excess":

"This economy is perhaps best illustrated by the relationship between subject and its 'objects a'(objets petit a - objects small Other). Lacan's object a refers to the object-cause of desire: that which is in the object more than the object and which makes us desire it in the first place. It alludes to the originally lost object (the missing element that would resolve drive and 'restore' fulfilment) and, at the same time, functions as an embodiment of lack; as a loss positivised (Zizek, 1997: 81; Zizek, 1999: 107).. Object a bears witness to an empty structure of desire - a structure that can never be filled out. Desire is always elsewhere and alludes to an absence whose central reference is a fundamental void around which drive constantly circulates and constantly misses its target. Zizek refers to object a in terms of a Kantian 'negative magnitude': something that acts as a stand-in for Nothingness (Zizek, 1999: 107). There exists a metonymy of lack whereby any empirical object can act as this stand-in. Object a is doubly paradoxical in that it refers to an original "lost" object (of completion/unity) that never existed, and also in that its own existence depends on its very unattainability."

In Badiou we saw how what I have called "engendering zero" consisted in production of a novel State composed of a new relationship of consistent multiplicity, the situation, with inconsistent multiplicity, being qua being. The situation, with its modalities of love, art, science and politics exists as a consistent multiplicity, but always in relation to the possibility of the Event. It can be said I think that inconsistent multiplicity is that excess in relation to which the situation always lacks. Lacanian psychoanalysis appears to approach analysis by positing the human psyche as a situation, its consistency maintained by the subject $ in relation to object a. The death drive arises with desire for the excess which is unattainable, the from which it is subtracted. I am speculating and questioning, but this is what I make of the statement later in the text:

"The 'manyi identifications and forms of collective objective life are made possible through the persistence of the "one" of radical negativity. The infinitude of signification is the result ultimately of the one true signified...void.

Glyn Daly's article is indeed a comprehensive primer on Zizek. She goes on to discuss much more of Zizek's Lacan, then how that is foundation to his political philosophy. This effort begins with a sketch of Lacan's psychoanalysis:

"The persistence of radical negativity is what the later Lacan generically characterised as the Real: the ultimate 'signified' around which all signification is constituted and simultaneously finds its limitation and inexorable failure. As is well documented elsewhere (e.g. Fink, 1995), the Real is inextricably linked with the registers of the Symbolic and the Imaginary and together these form a basic triadic structure for all (human) Being. In general terms, both the Symbolic and the Imaginary may be said to belong to the order of signification. While the Symbolic refers to the (potentially) infinite uses of signification through language and symbols, the Imaginary refers to the particular ways in which signification becomes arrested around certain fundamental images of ourselves that offer a sense of coherence and place in the world. It is through the Imaginary that we achieve particular forms of identification and which enable us to resolve the basic question(s) of who we are for the Other; we "narrate" ourselves around certain basic images with which we identify and/or wish to project."

I have to leave it at that for now. I barely scratched the surface of Badiou in Part 1, and I fear I did even less in beginning to explore Lacan in Part 2. Its a long process.. I rather think I can spend the rest of my life adding parts now and then. My intention is to continue working through Gillespie's book while also going back to further study of Zizek's How to Read Lacan. Its really hard to clearly express how this study is affecting me. I can just say certain insight seems to be growing from it about both life and death. I closing I want to relate a story I heard from someone very wise I was lucky enough to know - the story has come to mind lately while writing these posts and maybe it will be obvious why.

The story is one about Abraham Lincoln. I don't know if I have all the facts straight but the point will be made anyway. Lincoln it seems was always fascinated by the question of whether there was such a thing as immortality. As he often had the chance to meet and speak with many great intellects, it was known that he would sometimes chose to pose a question such as "Do you believe in immortality and if so why? It seems he never got a satisfactory reply. One day however he put the question to a famous Shakespearean actor (I forget his name). The actor replied "Yes I am sure of it!" Of course Lincoln pressed him as to why. "Because I cannot conceive of nothing without myself as witness of that nothing." Lincoln leaps to his feet exclaiming "That's the philosophy for me!".

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