The Fantasm of the Point: Vico, Plotinus, Campanella and even Badiou

(ca. 204-270 AD)

To return to the diagram of my last post on Plotinus I want to think along with a confluence of ideas that condense upon the very center of it, the infintesmal locus of “matter” which exists merely as a privation, yet also which alternately can be considered as a radiating center (under a different analogy).

The direction I want to go in this is a rumination that first starts from Badiouian notion that Being is not of the One, or “the One is not,” and that mathematics in a sense speaks Being,  pronouncing what is expressible of being-qua-being. The principle that the non-numerical One is beyond Being is of course one that Plotinus holds at the pinnacle of his Ontology, for Being starts with the varigated particularization of the Nous. It is there that the predication of Being takes hold. The way that Plotinus tells it, the Nous is produced by the plentitude/emptiness of The One, and necessarily breaks it apart into a kind of representation which divides it into parts. The reason that Plotinus gives for this division into likenesses is interesting. It is that the Nous struggles with the fact that it has no control over that upon which it ultimately depends, a control which expresses itself in the desire to preserve:

The hypostasis of the Intellect [Nous] cannot maintain its vision of the One in primal unity, but “being being unable to preserve the power which it was procuring, it broke it up and made the one [power] that it might bear it part by part [katà méros]” (6.7 [38] 15.20-22). In so doing, Intellect constitutes itself as an imitation of the Good, as a many-hued and varigated Good (agathòn poíkilon).

F.M. Schroeder, citing Plotinus in Form and Transformation

Now there is a great and dissatisfying danger of simply reading these particularizations as mere abstractions of an esoteric philosophy, the most gripless of metaphysics, but Plotinus’s reasoning as to why the Nous indeed breaks up the One has strong affective, phenomenological correlates. It is the very dependency of the unity of the Nous upon what lies beyond it, and inclusive of it, that generates a corresponding particularization. In drawing power from what is outside, the inside distinguishes itself. If we turn to the simple figure of a circle (for millennia a favorite of philosophers, and think in terms of systems theory, we understand that whatever system there is, it necessarily is less complex than its environment. This is to say, as all systems (the inside) depends upon a more complex outside, the very inside/outside boundary issue of dependency drives the very divisions of the inside in regard to what lies beyond it. If we allow the observations of evolutary theory, life has moved from less to more complex, and with this increase of internal divisions (differences that make differences) it has relatively gained a greater role in the preservation of the power upon which it depends (and, notably, which it is also an expression). Plotinus’s story of the Nous serves as a metaphysical directionality which prescribes how any person (organism) might orient themselves to conditions which are beyond it, like the Nous with totalizes these relations, the move is towards a complexification of differences that make differences.

For Plotinus, this process of particularization comes from what he calls “beholding” or “witnessing”. Whereas the first particularization beholds the One/the Expressed, those of Soul and Sensation are even more narrow in what they behold, all the way down to matter, which simply exists as a non-existent privation. A speck of darkness.

A Retreat to Vico’s Conception of Mathematics: the ficta of points (1668 – 1744)

I find this speck of nothingness interesting because its very non-divisibilty division reflects something of mathematics, the way in which points or numbers are non-existent distinctions that operate as a kind of limit. What I have in mind is Giambattista Vico’s interpretation of mathematics as the most divine of human acts, because in the invention of the point and the unit human beings act just a God did, creating something out of nothing in imitation of divinity, scientia humana divinae sit imitatrix. For Vico, a forerunner to some themes found in Kant, human beings cannot truly know things that they have not created. Only God truly knows what is created. The reason why human beings can have perfect knowledge of mathematics is that its creation is wholely their own. In a sense, mathematics operates “within” the circle of human articulation.

To quote some Vico, and then a commentator, to give perspective on his position:

…man defines the names themselves, and on the model of God with no underlying thing he creates (creat) the point, line and surface as if from nothing, as if they were things…to establish (condidit) for himself a certain world of forms and numbers, which he embraces within himself: and by producing, shortening, or composing lines, by adding, substracting, or reckoning numbers, he effects infinite works because he knows infinite truths within himself

But the point of the human imagination is not the point we draw with a pencil: “the point, when you draw it, is not a point: the one, when you multiply it, is no longer fully one.”

“man, containing within himself an imaginary world of lines and numbers, operates in it with his abstractions, just as God does in the universe with reality.”

With something of Plotinus’s reasoning, the very imaginary abstraction that human beings creates is a coping mechanism for that which lies beyond them and upon which they depend. Here Robert Miner provides a good overview of Vico’s approach to the knowing of human understanding:

Abstraction is the mind’s way of coping with its estrangement from things. Because he cannot possess ‘the elementa rerum by which things themselves exist with certainty,’ he resorts to the fabrication (confingere) of elementa verborum, elements which, despite their unreality, are able to ‘stimulate ideas with no controversy.'”

Vico has described human truth as a factum that is arrived at through a synthesis of elements that are only partially grasped, because they exist outside the mind which grasps them. If the human mind is essentially outside the elementa rerum, how does it manage to grasp even their outside edges? Vico proceeds to answer this question: “God knows everything, because he contains within himself the elements from which all things are composed; man seeks to know these elements by a process of dividing (dividendo).”

What is the relation of “dividing” to making? Is dividendo creative or destructive? Vico’s answer is “both.” De antiquissima 1.2 begins with an homage to the fecundity of dissection. The “anatomy of nature’s works” gives birth to a range of human scientiae. It does so by inventing their objects. One can divide man into body and spirit. From body, human science has “picked out (excerpsit) or, as men say, abstracted figure and motion, and from these, as well as from all other things, it has extracted (extulit) being and unity.” The objects obtained through abstraction give rise to the human scientiae metaphysics (whose proper object is ens), arithmetic (unum), geometry (figura), mechanics (motus from the edge), physics (motion from the center), medicine (corpus), logic (ratio), and ethics (voluntas).

The fecundity of dissection comes at a cost. Man creates the human scientiae by fragmenting, and therefore destroying, the whole…The entities created by abstraction – being, unity, figure, motion, shape, intellect, will – are “one thing in God, in whom they are one, and another thing in man, in whom they are divided.” Ripped from the whole in which they have life, humanly obtained elements are disiecta membra. “In God they live, in man they perish.” Our efforts to understand nature by cutting it up supplies us with theories rather than works: “in nobis sunt ratiocina, in Deo sunt opera.” All that man acquires through dividing the whole, is like man himself, nihil prae Deo; all finite and created beings are nothing but disposita entis infiniti ac aeterni. Etymology confirms the connection between division and diminution: Vico asserts that minuere means both “to lessen” and “to separate.”

The limitations of abstraction ensure that we have access only to the extrema of the elementa rerum. In what is likely to be an illusion to Lucretius, Vico declares that when man starts to investigate the nature of things (naturam rerum vestigabundus), he finds that “he does not have within himself the elements from which composite things exist.” This lack (brevitas) is not a morally neutral feature of the human condition, but a “vice of the mind” (mentis vicium). It is an effect of fallenness, a decline from a primordeal state in which mind and nature where integrated. (Vico uses nefas to characterize physicists who think they can provide real defintions of things.) Man responds to this condition by turning the mentis vicium to good use, by performing an operation that relies solely upon the mind and bypasses, as it were, the material world. “By abstraction, as they say, he fabricates (configit) two things for himself: the point that can be drawn and the unit that can be multiplied.” The association of abstractio and configere suggests that abstraction is creative. The suggestion is confirmed in the Prima Riposta, where Vico writes that mathematics [move to quotes on mathematics].

Truth in Making, Robert Miner

The Terminus Point of Nonbeing: Campanella (1568 – 1639 )

There is another evocative figure of radiating being, that which Campanella uses to characterize how each thing is but a point from which non-Being radiates, a kind of photographic negative of Plotinus’s conception:

 What we are concerned with is something that has an actual bearing on the existential order [not “relative nothingnesss” (nihilum secundum quid), the essence of a thing prior to existence], i.e., the composition of an infinite nonbeing with a finite being in existing realities. This is the point at issue, and this Campanella tries to illustrate by means of an analogy. Just as we can conceive a line stretching from the center of the earth beyond the circumfrence of the sky in infinitum, so, he says, man, like any other creature, is but a little dot where infinite nonbeing is terminated. Man is in effect the negation of an infinite number of other things and of God himself, being surrounded, as he is, by an infinite nonbeing (Bonansea, Tommaso Campanella, citing Met, II, 6, 3, 7)

In this Campanella presents something very close to Spinoza’s letter 21 claim that “all determination is negation,” something that Hegel made quite a bit of. Only in Spinoza any particular determination/negation is not a negation of God/Substance, but rather its Substance (Campanella always heretically veering towards collapsing God and Creation into one panpsychic whole, like Spinoza, but careful to walk the line).

What I am inspired to say about these circular analogies for Being and coherence of action, with their distinct and performative inside/outside designations, is that somehow mathematics in coming out of the pure fictiveness of human creation, in inventing the Non-Being of the immaterial point, somehow grasps whole the entire matrix of radiating conceptions, and is able to map out with great fecundity the very Oneness which is beyond Being (in a Plotinian sense). Weaving out the very absence, the infinitesimal (as my wife tells me, what is the decimal point which divides the infinitely large from the infinitely small, made of?), we get a glimpse of the very varigatedness that Plotinus attributes to Nous likeness taking.  The whole thing is sutured closed, or at least remotely closed, for one imagines that there are many kinds of mappings that can be woven from the nothingness of the point.

Further though, even in its appropriation of the infinite nothingness, mathematics owes Alfred Korzybski’s adage “The map is not the territory,” while keeping in mind that mapping, and map-following is itself part of the territory (one hunts through the map, as one hunts through the territory). All organisms seem to in some form follow Plotinus’s thoughts on why the Nous mirrored the One, being unable to preserve that upon which they depend. The semiotic relations that make up an organisms internal relations, and then thus relations to other organisms, are not only performances, but also are duplications (not necessarily representations), “picking out” (intelligere, to choose out) certain aspects of the world, and it is always a tension between picking out the most important, valued features, and sheer numericity, since these two are intimately related. In a certain sense, mathematics too needs to be seen as a vast material organism/organization, as material as any map, appendage to the human species.

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).