On the Place of the Negative in the Topological Real

The challenge is to conceptualize the position of the negative in the late Lacan. In an account of subjectivity that derives its ultimate ground from the topological Real [1] rather than the signifying chain, what is the status of lack, or negativity? 

Some of the key coordinates in the first paradigm would be the word as “the killing of the thing” [2], lack of being [3], and the hypothesis of the subject as a production of the signifying chain [2]. In fact, it would appear that in the early teaching, the Real finds its place only in relation to the Symbolic (i.e. as its point of impossibility, becoming something akin to the Kantian thing in itself).

The passage to the topological Real takes us from the word as the killing of the thing to: the word as another thing, another event in the Real. The topology of the knot simultaneously depicts the limits of symbolic and imaginary processes vis-a-vis the Real qua impossible and claims those very processes for the Real.[4] We behold the Real representing itself to itself, with a remainder of ineffability.

So while it is true to say that all representation—or, to expand this principle beyond the linguistic, beyond even the human, with a neurologically furnished concept like “modeling” [5]—is incomplete with respect to the modeled event, it does not follow that by representing or modeling that the referent is “killed.” Nor is it a given that the impulse to represent the Real implies some antecedent moment in which our access to it became barred. Rather, representation in all its forms can be thought of as a suprabundance, an effulgence, within and of the Real.

Which is to say that in addition to our relation to the thing—which endures—we also model, represent, and make our various renderings of the thing. Not to kill it, nor merely to memorialize it as dead, but to amplify our sustained relation to it. These renderings produce new effects, including the negativity of non-totalizability, of the elusiveness of the thing within the frameworks of representation, without nullifying our contact with the thing as such.

Or could we say that the problem comes from our use of words like “the Real” or “the Thing?” By speaking of a Thing in Itself, are we hoodwinked by a sly reification of that to which we will in the next moment have our access revoked?

What happens, then, if we refuse this first step? What if there's no “Real” in the singular, no reified Thing at all, but an infinite set of processes that only cohere as “things” within the order of representation, a set of processes in which we ourselves are embedded? What if even we aren’t “things” until we represent ourselves to ourselves in this way (which we may perhaps do much of the time, but not, it should be said, all of the time)? In this dereified Real, there are only processes in dynamic motion—with things, objects, and events taking shape as the molar crystallizations of an infinity of microscopic dynamics. 

A next step would be to employ the notion of relativity and to speak of specific points of view within this processual Real (a nice model for such a thing is famously given in Leibniz’s Monadology, in which the universe is reimagined as an infinite field of points, each of which bears its own particular vantage on the totality of creation).[6] In this account, negativity would arise as the limitation of one frame of reference or point of view vis-à-vis some other. Could we then assign to the hole within a topological space the signification of the limit of a particular vantage point within the infinity of relative monadic positions?

Between 1) subjects and world and 2) subsystems within a subject, the hole, and the unconscious, emerge as a fact of the multiplicity of forces in their non-alignability, their lack of perfect intelligibility to one another.

In order to refine our account of how negativity occurs in the topological/Leibnizian Real, we could perhaps borrow from Graham Harman's object-oriented ontology the notion of withdrawal, but put it to different use than Harman himself. Harman extracts the concept from Heidegger, who uses it to signify the manner in which the tool “withdraws” from the attention of the one who wields it. For Harman, withdrawal will mean something much more expansive: the ontological fact that all objects (and in Harman’s “flat” ontology, even human “subjects” are objects) are inexhaustible in relation to one another. That is, in my encounter with any conceivable thing, I will not encompass this thing in its totality, nor will it encompass me. Something escapes, something cannot be reached or comprehended.[7][8]

What if we ascribe this characteristic of withdrawal or inexhaustibility not to the “object,” but to the point in space (i. e. point of view) in the monadic sense? Now we are freed from the reification and closure that seems to plague Harman's objectal universe, and we can preserve the intricate dynamism of our processual Real. In this framework, we could say that each point in the process represents a potential point of view, or perspective, one that is actualized by various forms of life (and perhaps not only life). The requisite for the actualization of the point of view is some apparatus of receptivity, even a rudimentary one, that produces a schema or model of the surround, a discernible subset of the totality of the world. It is only when a point becomes a point of view that negativity enters the scene as the inexhaustibility of the other points, those that may be in view, but which are not identical with the point from which one views.

That is, in the infinite processual becoming that is the Real at its most radical, it is when an entity is localized as a point of view from which some metabolization of the world occurs that a cut transpires, a hole. We might say that these holes, defined as sites wherein loops are irreducible to a point, are structural, essential [9]—they are fundamental to the Real as realized from that particular point of view. Every point, each perspective, constitutes a distinct structure (one that is dynamic, to be sure) with its unique dialectic of surface and hole(s).

Therefore, it's not that language produces the negative. The negative arises well before the development of language, in the more fundamental adoption of a point of view, which will carry the ramifications of differentiation, distinguishability, separation, alterity, withdrawal, inexhaustibility, unknowability. 

Furthermore, there is a specific class of entities, beings, inhabitants of points of view that model not only the surround but also their own being—to some degree. The negativity and withdrawal that we already attributed to points other than the point from which one views is also at play in the reflexive relation of self-modelization, or depicting to oneself one's own position or apparatus of receptivity. When we endeavor to look at our looking, view our view, we entify or objectify our monadic position and experience the same phenomena of inexhaustibility, etc. We are riddled with holes when we apprehend ourselves. The "we" here is not necessarily a linguistic being, not necessarily a human being, but any entity capable of self-modelization as a subset of the more general function of modelization of the Real.

We may indeed experience the inexhaustibility and withdrawal of our own being differently than we do the same phenomena in what we call "other," as a consequence of our situatedness, our adopting of a location. Yet essentially, a hole outside and one inside (that is, outside and inside the territory of the self, of what is "mine") are equivalent.

The human subjectivization of the hole in the self entity has taken uncountable forms, and is often depicted in myth. One thinks of original sin, the fall from grace, etc. Castration, including its Lacanian variation—symbolic castration [2]—is one such rendering. We would argue that just as the emphasis on the "symbolic” as constitutive of the negative is insufficient, castration in the key of Freud [10] also confuses the universality with one of its particular subgenres. The fact of a limit to power, capacity, knowledge, or function is more fundamental than speaking, but also more widespread and various than the sexual and familial connotations of castration anxiety allow for. To be limited, to experience oneself lacking, may or may not imply the perception that one wasn't always lacking and therefore suffered a primordial loss. Similarly, not all losses need be experienced as perpetrated by some other, and further still, not all perpetrators need be fathers or father substitutes. Finally, not all losses, if they are losses, include a sexual valence.

Castration, Freudian and Lacanian alike, each fail as universal conditions of subjectivity by mistaking the particular for the universal, the concrete for the abstract.

Over and against these, we would posit a universal condition in which lack emerges as a consequence of the point of view upon the Real being incapable of totality, a result of its particular situatedness, which implies finitude, difference, and the inexhaustibility of the other qua other points, be they points that appear to us to possess their own view (i.e. a similar capacity of world-modeling) or if they appear to us lifeless, without subjective potentiality, utterly objectal. In either event, the structure that is our situatedness will produce sites of withdrawal, formalizable as holes.

Notes:

1. Lacan, J. (1972). L'Etourdit (J. Stone, Trans.). Retrieved from http://www.freud2lacan.com.

2. Lacan, J. (2006). Écrits: The first complete edition in English (B. Fink, Trans.). W. W. Norton & Company.

3. Lacan, J. (1988). The seminar of Jacques Lacan: Book II: The ego in Freud's theory and in the technique of psychoanalysis, 1954–1955 (J.-A. Miller, Ed.; S. Tomaselli, Trans.). W. W. Norton & Company.

4. Lacan, J. (1974-1975). Seminar XXII: RSI (Gallagher, Trans.). Retrieved from http://www.lacaninireland.com.

5. Graziano, M. S. A. (2019). Rethinking consciousness: A scientific theory of subjective experience. W. W. Norton & Company.

6. Leibniz, G. W. (1989). Philosophical essays (R. Ariew & D. Garber, Eds. & Trans.). Hackett Publishing Company.

7. Harman, G. (2002). Tool-being: Heidegger and the metaphysics of objects. Open Court.

8. Harman, G. (2018). Object-oriented ontology: A new theory of everything. Pelican Books.

9. Hatcher, A. (2002). Algebraic topology. Cambridge University Press.

10. Freud, S. (1905). Three essays on the theory of sexuality (J. Strachey, Trans.). Basic Books. (Original work published 1905)