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Tag Archives: Determination

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 private, 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 pinacle 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 millenia 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 infintesmal (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.


Spinoza’s Letter 21 to Blyenbergh: Negation and the Unseeing Stone

I reprint here part of a letter I wrote to a good friend, as part of our exchange over philosophy. It includes an explication of Spinoza’s influential January 28th letter to Blyenbergh, wherein Spinoza reveals his take towards negation, a passage which Hegel would focus on, as significant for what it asserts, but also what he would claim it does not grasp.

“omnis determinato est negatio”


I think that one of the most important ideas in Spinoza is the way that he treats “negation”, for he makes a distinction between the difference between negation and “privation”. It is rather in that Negation often is conflated with privation, making of it a kind of “lack”, upon which all desire is founded, that much of Modern Philosophy parts company with Spinoza. Instead Spinoza argues for the perfection and completeness of any particular state of the world, at any one point in time. His description of the capabilities of “seeing” (those missing in a blind man, and those missing from a stone), is one of the most illustrative examples of this thought. In his Letter 21 to Blyenbergh, he outlines fairly clearly the difference between negation and privation. It is an extraordinary thought, (not the first time said in history):

 I will proceed to explain further the words privation and negation, and briefly point out what is necessary for the elucidation of my former letter. I say then, first, that privation is not the act of depriving, but simply and merely a state of want, which is in itself nothing: it is a mere entity of the reason, a mode of thought framed in comparing one thing with another. We say, for example, that a blind man is deprived of sight, because we readily imagine him as seeing, or else because we compare him with others who can see, or compare his present condition with his past condition when he could see; when we regard the man in this way, comparing his nature either with the nature of others or with his own past nature, we affirm that sight belongs to his nature, and therefore assert that he has been deprived of it. But when we are considering the nature and decree of God, we cannot affirm privation of sight in the case of the aforesaid man any more than in the case of a stone; for at the actual time sight lies no more within the scope of the man than of the stone; since there belongs to man and forms part of his nature only that which is granted to him by the understanding and will of God. Hence it follows that God is no more the cause of a blind man not seeing, than he is of a stone not seeing. Not seeing is a pure negation.

January 28, 1665

What he means is that a blind man is not missing sightedness, just as the stone is not missing sightedness, only our imaginary comparison of one state of the world to another causes us to say so. Instead each thing (the blind man and the stone) is negated in a particular and determined way. That is to say, limited. The limitation is the nexus of causes that bring it into being, the bordering interactions with other modes of Reality which make it what it is. And what it is is exactly what it can do. Negation simply means having boundaries of the capacity to do.

The thing is, because Substance (or God or Nature) is by essence not limited at all, but infinite, all negation is a kind of illusion. That is, we might see the blind man as limited or determined in a certain fashion, but the blind man is actually a modal expression of Totality, and our drawing of a line around him, making of him a closed entity (which can or cannot see), is only a temporary perspective. If the blind man is standing on a plain of grass (or perhaps more thoroughly, living there) there is nothing that stops us from perceiving it as a blind-man-plain-of-grass assemblage, where “seeing” is only one sliver of any number of possible and complex interactions between parts, (one can glimpse the ecological consequences of such a flexibility, wherein dependence become expression, or inter-expression between environments). Moment by moment, each thing is perfect because it could be no other way; all is a full expression of God/Substance/Nature.

So when Spinoza talks of the non-being of something, that is, just as in the description of the perception of the basket in Joyce (perceiving through what something is not), this non-being is simply a perspective. It is, in a certain sense an imaginative illusion. There is no such thing as non-being, (it has no ultimate bearing on things), because all things derive their power from the fullness of Being itself. Any localized mode of Being (be it a stone or a man or a grassland) is a full expression of God, which is also dependent upon all the negations which constitute it. That is, the causal boundaries which compose any figure by limiting it, actually compose it, in the way perhaps how negative space around a statue might be said to “be” the statue.

So there is a double move in Spinoza. One is that any one particular moment of expression, of a man say (both of his body and his idea), is already perfect because it flows from the Infinite being of God, what we call Nature. The fullness and perfection of each thing is thus guaranteed. But the second move, one that Hegel misses [and I am following Gatens and Lloyd here, who are following Macherey] because he would like to wedge out the soul of a man to a place of importance, is that the negation of any one thing, that is, its actual boundaries which seem to limit it, are veritably the connective tissue to all that is, the assembled source of its power. (It is for this reason that Deleuze characterizes Spinoza’s Theory of Power as “the ability to be affected”. Through the fabric of these “negations” the assemblage of things shows itself to be an incredibly complex thing. Even the simplest thing, a water molecule, through its very limitations, connects to huge things, a tidal wave.


So to return to Joyce’s description of the basket, which is a beautiful one,

[quoted in a previous letter] In order to see that basket, said Stephen, your mind first of all separates the basket from the rest of the visible universe which is not the basket. The first phase of apprehension is a bounding line drawn about the object to be apprehended. An esthetic image is presented to us either in space or in time. What is audible is presented in time, what is visible is presented in spae. But temporal or spatial the esthetic image is first luminously apprehended as selfbounded and selfcontained upon the immeasurable background of space or time which is not it. You apprehend it as one thing. You see it as one whole. You apprehend its wholeness. That is integritas.

Stephen Dedalus, in The Portrait of The Artist as a Young Man

If we keep in mind the way that Spinoza sees the body and the nature of perception, we see how even this description of the basket is superseded by the notion of the perceptive Body itself. Recall, Spinoza says that all perception of “things” (those things outside of us), are actually our perception of our body. All ideas are of our body being in a certain state. A neurophysiologist can describe the brain as being our sixth sense, that which perceives the Body. So, while it may very well seem that we are perceiving a “basket” and doing so by also perceiving its non-being, all that is not-basket outside of it, Spinoza would say that all the while we are only holding ideas about our own body being in a particular state (a state that due to the causal relations between out body and all else, which allows us with clear ideas to act powerfully in the world). The being and non-being of things cloaks the actual changes in power of our own body, as we form ideas of that body in particular states.

This conception of the body as a closed arena of perception, forming ideas only about its own state, leads Spinoza to articulate a theory about the passions and being a passive state. Affects, that is emotional reaction to the world, is part of the imaginary and confused ideas of the world that necessarily make up human perception. In a sense, it is part of our experience of living in time, the way that we compare the world and ourselves to past and future states of being. This is a very subtle and strange thought for me, and one which it took me a long time to understand, and then possibly to accept. The core expression of it is found at the end of part 3 of the Ethics, in “The General Definition of the Affects”:

E3: DOA. Emotion, which is called a passivity of the soul, is a confused idea, whereby the mind affirms concerning its body, or any part thereof, a force for existence (existendi vis) greater or less than before, and by the presence of which the mind is determined to think of one thing rather than another.

Explanation.–I say, first, that emotion or passion of the soul is a confused idea. For we have shown that the mind is only passive, in so far as it has inadequate or confused ideas (E3P3). 

I say, further, whereby the mind affirms concerning its body or any part thereof a force for existence greater [or less] than before. For all the ideas of bodies, which we possess, denote rather the actual disposition of our own body (E2P16C2) than the nature of an external body. But the idea which constitutes the reality of an emotion must denote or express the disposition of the body, or of some part thereof, which is possessed by the body, or some part thereof, because its power of action or force for existence is increased or diminished, helped or hindered. 

But it must be noted that, when I say a greater or less force for existence than before, I do not mean that the mind compares the present with the past disposition of the body, but that the idea which constitutes the reality of an emotion affirms something of the body, which, in fact, involves more or less of reality than before.

Note, central here is that the Mind, as it moves through pleasures and pains and appears to do so by comparing its current state to other states, past and future, but Spinoza claims that it really is not doing so at all. Instead, the Mind as it thinks is rather affirming in more or less clear ways the force of particular parts of the body, such that that actual affirmation gives those parts, that expression, more reality. This is an amazing thought. We conceive of ourselves having one reality, a fixed baseline of reality, as all things do, passing into various characteristic states. But here Spinoza, because there is only One Reality, that is the reality of Substance, the things which partake of that reality more (that is, express themselves with a greater capacity to act, a greater capacity to be affected), actually are more Real. The coming and going of Pleasure and Pain is the coming and going of the Reality of a thing, even though each state is perfect, because from the point of view of the Totality even the smallest part is a fully real expression of the Whole. Our entire lives are fluctuations of becoming more or less real as persons, as we pass into more or less active states of being, all the while expressing a perfection.

I thoroughly agree with you that our departures over Nietzsche, insofar as we have disagreements, are in the degree of credit that I offer him. There are a few reasons for this for me, the largest of which is that I am, or have been quite Nietzschean in nature, and thus have found Spinoza to be a kind of relief or antidote for this nature-a way of directing it, making its impulses more powerful and more at ease. In this sense Nietzsche gets my razored critique as part of my own self-critique. I also believe that Nietzsche himself requires that I be ungenerous, as this is the way that he conducted his own thought, savagely attacking those he thought close to himself. He would not want to be “given” anything. Thus for me reading Nietzsche generously is somewhat unNietzschean. And lastly I suppose, I am hardest on those that achieve the broadest degree of cultural acceptance, and Nietzsche has been rather thoroughly embraced by an academic heritage, at least on the Continental side, and by culture as a whole. I can think of no other modern philosopher, in spirit, who is so well esteemed (if mis-understood) by non-philosophers; and also not one so credited. Thus my stand against Nietzsche operates as both a stand against myself, and a stand against various instutionalizations of thought, a pronged critique I cannot resist. Spinoza then operates as something new, radical and liberating, in the most pragmatic of senses. I certainly would not to think to have you agree with me in approach, because this is individual, but it is good that you know the motivations of my arguments, and take them for what they are worth for you. Yes Nietzsche can be read as reacting to the “moral climate of his time” (but this makes him a bit reactive and not as active as he might be); and the same can be said of Spinoza, but his tone and method more quiet (perhaps more powerful?). The question of the influence of his own thought, and his pre-mediation of those difficulties is an excellent one. Considering that he was a near-forgotten writer until reanimated after the two world wars, this either reflects his own inflated sense of grandiosity, or his incredible prescience. Probably both.

As to my thought that there is no “negation” in biology, I mean that only in the sense that there is no “non-being” in biological explanations. In genetics in particular, and statistical and population analysis, the idea of “lack” has no place at all. Instead we only have ways of combining, molecular and algorithmic capacities to act, and an inter-relationship between environment, populations and genetic properties which only display what can be done. The genetic material and the conditions which unfold are shown to be expressions of each other, by most accounts that I have read. Specifically I have in mind the work of Maturana and Varela and their biological theory of Life, Autopoiesis, but also general Neo-Darwinian accounts. I have yet to hear any theory of biology which would support a Hegelian view of the world. This is not to say that it is not possible, but only that I have not heard it.