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The Cone of Plotinus: Ontologies of Profusion and Particularization

I believe it is helpful when understanding how Plotinus viewed the degrees of Being, how the problem of how the production of the Many from the One is to be resolved (referred to here), it is helpful to picture to two, end-to-end comes often used to illustrate conic sections, above. For Plotinus uses two kinds of complimentary images. The first is that the Hen (The One, The Expressed) is comprehensive. It is the kind of totality which even transcends numericity, not even having Being predicated of it. It stands as a kind of outer limit, the widest circle which contains (gives birth to) all that is within it. In this way, most simply put:

1. The Hen is completely empty, so empty it overflows, producing something other.

2. This is the Nous (mind) which is born of looking at the Hen, in a kind of mirroring contemplation which constitutes its existence, producing a varigated Being.

3. And through this perfect mirroring gaze it achieves the productive capacity of the Hen, and produces the Soul.

4. The Soul is an activity which does not merely abide, but compelled to motion produces her opposite, sensation.

The movement is towards the particularized. The Hen has all things moving through it, perhaps in a Deleuzian vein we can call these intensities, though it is perfectly empty. From this are narrowings of hierarchies of existence, which can be viewed as if the upper mouth of the cone were heading towards it point. And the very end of this process is “matter” which may be said to have no-being, in the sense that it exists merely as a privation of the One, the absence of Being, something that Augustine took up in his analysis of Evil as a privation and that can be seen in Spinoza’s epistemology where falsity consists in privation.

A diagram to clarify these relations:

Plotinus’s heirarchy of Being is more famous than his thinking of any unity at all as a kind of profusion. In a wonderful analogy he compares the activity of the soul to that of a mirror. In this way we can say that the ultimate profusion of the One/Expressed (Hen), acts as something like both a great descending circle (the upper half of the diagram), but also as a kind of central point, that radiates out, growing weaker as it goes, as light would, until it reaches its outermost limit in a darkness (matter), which exists merely as a privation. In this sense anything that has being has it to the degree that it expresses/reflects the totality of the One, its activity consisting of what fills it. And in this way as well, matter serves as both an infintesmal point (the very nexus of the two cones), which does not exist, but also as an outer ring where the radiation of the Hen does not reach.

How did it come to be then, and what are we to think of as surrounding the One in its repose? It  must be a radiation from it while it abides unchanged, like the bright light of the sun which, so to speak, runs round it, springing from it continually while it abides unchanged. All things which exist, as long as they abide in being, necessarily produce from their own substances, in dependence on their present power, a surrounding reality directed to what is outside them, a kind of image of the archetypes from which it was produce; fire produces the heat which comes from it; snow does not only keep its cold inside itself. Perfumed things show this particularly clearly. As long as they exist, something is diffused from themselves around them, and what is near them enjoys their existence. (5.1 [10].6 27-37)

But one must consider light as altogether incorporeal, even if it belongs to a body. Therefore, “it has gone away” or “it is present” are not used of it in their proper sense, but in a different way, and its real existence is an activity. For the image in a mirror must also be called an activity: that which is reflected in it acts on what is capable of being affected without flowing into it; but if the object reflected is there, the reflection too appears in the mirror and it exists as an image of a colored surface shaped in a particular way; and if the object goes away, the mirror-surface no longer has what it had before, when the object seen in it offered itself to it for activity. (4.5 [29] 7.33-49)

These analogies of light and reflection, along with the hierarchies of Being risk becoming highly abstract, uninteresting, arcane structurings, if we take them as simply esoteric truths. But the hierarchies of Being are not just ontological strata, they are guideposts for how an investigating thinker should think of their own position in the world. They entail a phenomenology of projects that each person should engage in, the vision that oneself and one’s consciousness too is hierarchical. Part of this prescription is to the way that we “see” other objects, in particular how we binarize ourselves into subject/object relations. Plotinus’s analogies of light are more than analogies in that they invite us to see that any object that we orient ourselves toward is necessarily in existence through the same sharing of the field as we. Plotinus presses us to collapse the subject/object binary.

This is captured in his dichotomy of “looking at things” and “looking with light”. One might look at things in the world and never notice that light that illumines them, but if one learns to look “with” the medium, one participates in the very processes of illumination and is no longer captured by the illusions of particularization, the largely assumed cut-off nature of things.

One thing is an object of vision for it, the form of the sensible object, another is that by which [i.e. the light] it sees the form of it [the sensible object], which [the medium] is also an object of sensation for it, while being other than the form [of the sensible object] and the cause for the form of being seen and is concomitantly seen both in the form and with the form; for this reason the light does not yield a clear sensation of itself, because the eye is turned toward the illuminated object; but whever it [i.e. the light] is nothing but itself, it sees in an immediate intuition…This then is what the seeing of Intellect is like; this sees by another light the things illuminated by that first nature [i.e. the One or Good as the sun of the intelligible universe], and sees the light in them; when it turns attention to the nature of the things illuminated, it sees the light less; but if it abandons the things it sees and looks at the medium by which it sees them, it looks at pure light (5.5 [32]. 7.2-8; 16-21).

Such an investigative approach allows one to trace out the continuities which exist between oneself and what one investigates, something he compares to the radii of lines from the center of a circle, only apparently detached from one another:

[The One] is contemplated in many beings, in each and every one of those capable of receiving him as another self, just as the center of a circle exists by itself, but in every one of the radii in the circle has its point in the center and their lines bring their individuality to it. For it is with something of this sort in ourselves that we are in contact with god and are with him and depend upon him; and those of us who converge towards him are firmly established in him (5.1 [10]. 11. 9-15)

I do not really view this rather spiritual-sounding account to be spiritualized at all, but rather aimed at the concrete dynamics of power itself, the way in which things vividly express themselves in what for us is the most realized terms. If nothing else these metaphysics must prove themselves pragmatically, as means to find connections between parts which help us explain and read the world (and ourselves).

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Guattari’s Four Ontologies

For those who have never looked into the thought of Felix Guatarri, the nearly effaced thinker of the pair D & G, for which the name Deleuze can come to regularly stand, I post below a significant section from Gary Genosko’s admirable treatment of Guattari’s primary ideas, Felix Guattari: An Aberrant Introduction. The selection deals with the history of analytic concepts found in two cartographic, schematic grids, and their principle meanings. They are called the Four Functors, or functional domains, but I prefer to think of them, and call them The Four Ontologies, in part to indicate their necessary disjunction and modal differences, in part to necessitate their immanent reality. For those only familiar with the works of their joint authorship, you may find interesting familiar terms and concepts in new contexts. Enjoy. I read the book some time ago and the diagram still stays with me.

Guattari’s diagrams and tables of the four functors and the domains proper to each tell us a great deal about his attempts to overcome simple problems of doubling couplets (all sorts of reductive dualisms), of evoking logical or semiotic squares in a segmental quadrature of deterriotorialization (the four domains result from segmentation of the plane of consistency). In CS (cartographies schizoanalytiques, 41) Guattari wrote of the “two couples” that constituted the four categories – actual and virtual and possible and real -to which he added other couples – some familiar, like expression and content (Chs [Chaosmosis] 60) and some less familiar but with a broadly semiotic lineage. (See figures 5.1a and 5.1b.) By the time of Chs, Guattari saw the expression and content couple as a problem to be overcome because it was still too much stained by linguistics and automatic contraction that would restrict the openness of assemblages of enunciation (the detour became a dead end). His reference to the left and right hand sides of the figure further exacerbated the question of whether or not his Fourth term consituted an advance over the ingenious Threes discussed in the previous chapter since he kept adding couple upon couple. The Threes are still very much at work here. Guattari advanced by analogy with the important form-substance-matter distinction – which he profoundly modified to describe diagrammatic deterritorialization by means of sign-particles between form and matter (IM [L’Inconscient machinique] 224-5) – in relation to the Fours: just as substance is the manifestation of form in matter, existential Territories are the manifestation of incorporeal Universes and machinic Phylums in material Fluxes (CS 84, n. 1), given that substance is akin to Territory, Universes and Phylum are akin to form, and Fluxes are akin to matter (unformed). The abstract machines of the domain of Phylum are new coding of the a-signifying semiotics with a purchase on material fluxes (Flux), whereas the existential incarnation (Territory) of the incorporeal constellations (Universe) metamodel as virtual rather than actual the former relation.

However, Guattari use the example of two options of Freudian cartography as they concerned libido and the unconscious to demonstrate the core features of Figure 5.1a. On the left side, libido either pursues a deterritorialized option toward abstract matters of the possible (Phylum), or is reterritorialized into the psychogenetic stages and dualisms (Eros -Thanatos) of stratified Fluxes; on the right side, the unconscious explores deterritorialized lines of alterity that are both original and unheard-of (Universes) or takes refuge in the Territories of the repressed according to various reterritorializing maps of the mind that Freud developed over the course of his career, most pertinently, between the dream book and the “The Unconsious”, “Ego and the Id”, and “New Introductory Lecture 31”. (CS 44-7; Chs 62). Guattari was also, like Freud, mapping the unconscious. Without being reductionistic, Guattari’s cartography of the schizophrenic unconscious is situated against but in the tradition of  the Freudian metapsychology of diagramming the psychical topography and the two systems (Cs. [Pcs.] Ucs.), description of their characteristics, communications, conflicts, classifications (of instincts), and emergence of the Ego-Id-Superego – the three regions – or indeed, the Lacanian tripartite Real-Imaginary-Symbolic. Guattari took great pains to decentre his cartography from the linguistic signifier, from the many psychoanalytics dualisms (primary-secondary process); to render the domains contingent and evolutionary is relation to technology, art and science, and avoid reductive prototypes of subjectivity (CS 32ff). Whether or not he was successful will need to be carefully considered.
 
What is the Fourth Term anyway?  How many is an open Three? The diagramming of the transversal relations between heterogenous domains: material and energetic Fluxes (F); an abstract machinic Phylum (P); existential Territories (T); leaves incorporeal Universes (U) that escape the coordinates of F, P, and T (CS 74). The  Fourth term is the virtual possible and, together with the actual possible, these envelop the actual real and virtual real. Guattari linked both powerlessness and unreachable foundations with Twos; pyramidal dialectical trees with Threes, and the generation of non-prioritized, proliferating trans-entity interactions that respected the principle of autopoesis with Fours…
 
…Guattari’s model of the unconscious had three types of energetico-semiotic quantic configurations describing interentity relationship: non-separability, or synchronic compossibility (intrinsic reference); separability or diachronic complementarity involving time and becoming (extrinsic reference); and quanitification operating between non-separability and separability, but not subordinate to them (non-separability being the semiotic superstructure of separability; quantification being the pragmatic superstructure of separability). Each had their own tensors (although Lyotard used this concept to describe a singular point of libidnal intensity such as Dora’s throat against the semoitic nihilism that a sign stands for something for someone, this extra-semiotic element produced libidnal intensity through force and singularity, like a proper name, as opposed to signifying meaning through differentiation; 1993: 54-6) and because Guattari was concerned with describing inter-entity relations by means of this mathematically derived concept, it may be thought of as a generalized vector of such relations. These relations, about which more will be shortly, are constrained by those between the levels of the unconscious that Guattari presented (it is evident from Figure 5.1a that there are NOT, for example, direct connections between Fluxes and Universes and Territories and Phylums, but Guattari invented indirect links by means of synapses). So, in the first instance, one of the tensors of non-separability is Expression and Content (extrinsic reference of deterriotorialization) and the other is System and Structure (intrinsic reference of deterritorialization). Both concern deterritorialization and this axis occupies the place of both possible and real in Figure 5.1a (where possible was, infinite, irreversible, deterritorialization, far from equalibrium, shall be; and where the real was finite, reversible deterritorialization close to equalibrium shall be (CS 86)). The tensors of separation are semiotic (engendering laterally, from their point of origin, sites of entities of meaning – hence largely Territorial functions functions) and the surplus value of possibility, which  relays the site of entities of meaning and transfers them, via synapes of effect – situated  between Fluxes and Phylums – and affect – situated between Territories and Universes – to pragmatic effects and subjective affects. The tensors of quantification are synaptic: they are, as suggested, relays for the transfer of the surplus value of possibility toward the sites of entities polarized as either systematic or structural. As I indicated in Figure 5.1a, each domain has a figure in which entities are situated: Fluxes=Complexions; Phylums=Rhizomes; Territories=Cut outs; Universes=Constellations. Although Guattari preferred to diagram the domains as four parallel sub-ensembles in a topological space in order to give some depth to an otherwise two-dimensional diagram such as Figure 5.1a and its variations, the latter were commonly used.
 
As for the metamodel’s contraints, there are restrictions on direct tensorial relations that I have already mentioned (but which the synaptics mediate); tensorial relations are subject to dyssynchrony;and the levels, corresponding to the three configurations governing inter-entity relations but based upon order of presupposition: Level 1 has no presuppositions; Level 2 presupposes Level 1 (semiotic); Level 3 presupposes Levels 1 and 2 (pragmatic and subjective). Guattari’s work is not very far removed in spirit from what Freud and Lacan did in their diagnosis and algorithms. Freud even went so far as to compensate for weakness in his diagrams, asking his audiences to make mental corrections. Constraints include how the id relates to the external world only via the ego, the specification of certain types of entities (cathetic intensities that are mobile or not), and topographic relations of semiological algorithms defined by two cumbersome structures (metaphor and metonymy), etc. Despite Guattari’s warnings abou the profound modification of psychoanalysis, he continually introduced codings that suggested precisely the diminishment of such modifications. For example, the fourfold segmentation of domains on the plane of consistency is based on two arguments:
 
      1. for discursivity, an ontological argument: if there is a given (donne/), there is a giving (donnant);
            – unity, discontinuous divisions of Territories and constellations of Universes (giving);
            – plural, continuous, fusional complexions of Fluxes and rhizomes of Phylums (given);
      2. for deterritorialization, a cosmological argument: two domains of intrinsic reference without immediate intersection yield a GIVEN corresponding to an intrinsic, systematic reference and a GIVING corresponding to an intrinsic structural reference;
            -finite, reversable, deterritorialization referenced around a point of equilibrium;
            -infinite, irreversable deterritorialization referenced far from a point of equilibrium
 
The problem is that giving-given corresponds to expression-content as does structure-system, on top of which Guattari develops his division of the unconscious into three levels reflecting the later topography of Freud’s ego-id-super-ego model, a primary, secondary, and tertiary unconsciousness, each with their own tensors. Remember the pairings that pile up in the two-dimensional Figures 5.1a and 5.1b, with their expansions, are worked by processual cycles (Figure 5.2 [not included here]) which seem to lack real depth. Guattari struggled with representing the four domains (CS 80).
 
      Level 1. Primary Unconscious
      Level of Intrinsic Reference: Systems and Structures
      Reversible Tensors:
      (a)   systematic referent, on the side of the given between sites of entities of Flux and those of Phylums (left side of Figure 5.1a) (i.e., systems that articulate material and energetic Fluxes on abstract machinic rhizomes);
      (b)   structural referent, on the side of giving, between between sites of Territorial entities and incorporeal Universes (right side of Figure 5.1a) (i.e., a musical structure that crystalizes rhythms, melodies of incorporeal Universes; a biscuit that conjures an incorporeal Universe of another time and place but, through globalization, becomes available everywhere, leads to the Universe’s implosion, and the existential Territories of subjectivity become ambivalent about their own taste)
 
SUMMARY: F=complexion; P=rhizome; T=cut out; U=constellation.
 
      Level 2. Secondary Unconscious
      Level of Extrinsic Reference: Semiotic Tensors
      Irreversible Tensors of:
      (a) persistence, vectorized from Systems to Structures (from given to giving):
            – sensible tensors virtualizing sensible contents within existential Territories (i.e., cutting out from diverse Fluxes a refrain of territorialization in an ethological assemblage, as in the Stagemaker’s upturned leaves on its display ground selected from the Flux of leaves);
            – noematic tensors virtualizing the noematic contents within Universes (i.e., smile of the Cheshire cat, unlocalizable as a point in space);
      (b) tensors of transistency, vectorized from structures to systems (giving to given):
            – diagrammatic tensors actualizing diagrams in Fluxes (i.e., a machine-readable magnetic strip of a bank card that, in conjunction with a personal identification number, provides access to an account);
            – machinic tensors actualizing abstract propositional expressions of rhizomic Phylums (i.e., the incorporeal faciality of Christ projected on machinic capitalist Phylums, already traversing spaces before being deployed; already always there).
 
SUMMARY: F-T=sensible; T-F=Diagrammatic; P-U-noematic; U-P-machinic.
 
      Level 3. Tertiary Unconscious
      Persistence and Transistency: Pragmatic (between F and P) and Subjective (between T and U) Synapes
      (adjusting the three configurations of non-separation, separation and quantification in different ways on earlier Levels: on L1, in the presentifcation of the backwards-looking potentialities of Systems and Structures; on L2, forward looking surplus value of possibility of semiotic concatenations)
      (a) Bivalent synapes result from the conjunction of two afferent tensors of consistency – F and P – effect of extrinsic coding (i.e., perception without foundation, hallucination) and T and U – affect of extrinsic ordination (i.e., a “real impression” of a dream).
      
      (b) Trivalent synapes result from the conjunction of two afferent tensors and one efferent tensor resulting in:
            — Consistency F – closed systems effect (i.e., closed cybernetic loop);
            — Consistency P – open systemic effect (i.e., micro-social systems upon which family therapy strives to intervene);
            — Consistency T – closed structural affect (i.e., function of the mature Freudian topography);
            — Consistency U – open structural affect (i.e., becoming vegetable, child, animal).
 
      (c) Tetravalent synapes either associate effects of extrinsic coding (consistency F and P) with open and closed systemic synapes or affects of extrinsic ordination (consistency T and U) with open and closed structural synapes:
            – pragmatic synapse (between F and P): an affect is virtualized when an assemblage is polarized by a relation of persistence emanating from pragmatic to subjective;
            – subjective synapse (between T and U): an effect is actualized when an assemblage is polarized by a relation of transistence emanating from subjective to pragmatic (hence, a play of virtual persistence implosion and actual transistence expansion without destroying the two poles of effect and affect).
 
SUMMARY: F-P=open systemic effect; P-Fclosed system effect; T-U-open structural affect; U-T=closed stuctural affect. (Note: summary based on correction to Table 3, CS 91); see also the tensors and entities mapped in CS 83.)