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.