Deleuze & Spinoza: What Can a Body Do?, Entry Directory

by Corry Shores
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Deleuze & Spinoza: What Can a Body Do?

Deleuze Cours Vincennes Spinoza 20-01-1981, selectively summarized

Deleuze Cours Vincennes 17/02/1981, summarized

"What Can a Body Do?" Power of Affection in Spinoza and Deleuze

Deleuze and Dance Part II: At the Limit of What Bodies Can Do: Michael Jackson’s Fullness of Death, Under Spinoza's Microscope

The DeComposition of Our Body's Functions. Review and philosophical application of Compound Functions in Edwards & Penney's Calculus (Section 1.4)

The DeComposition of Our Body's Functions. Review and philosophical application of Compound Functions in Edwards & Penney's Calculus (Section 1.4)

presentation of Edwards & Penney's work, by Corry Shores
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Edwards & Penney's Calculus is an incredibly-impressive, comprehensive, and understandable book. I highly recommend it.

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[I your author am not a mathematician; I am merely an admirer of Edwards & Penney's wonderful calculus book. Please consult the text or other references to be certain about anything in the summary below. I mean this emphatically.]

[Other Entries in the Edwards & Penney's Calculus Series]

The DeComposition of Our Body's Functions

Review and philosophical application of
Edwards & Penney's Calculus
Compound Functions
in
Section 1: Functions, Graphs, and Models
Subsection 4: Transcendental Functions

What Do Compound Functions Got to Do With You?

Consider if we are trying to lose weight. So we go on a diet. Over the course of a day, we begin to feel our appetite increase. So this would be one function: as time increases, our appetite increases. But then, as our appetite increases, there is a decrease in our willpower to hold strictly to the diet. So our decrease in willpower is like a function compounded on the first function. Our lives are filled with many such highly complex functional relations.

Brief Summary:

Functions can be compounded one-upon-another as if the output of one machine instantly becomes the input of another.

Points Relative to Deleuze
[Under Ongoing Revision]

We might find a composition of functions in Deleuze's account of sensation, building from his portrayal of Spinoza's affection. Deleuze's example is that we are looking for our glasses in a dark room. Someone enters and turns on the light. This causes us to make a transition from the way we are affected by the dark to the way we are affected by the light. Because we are searching for our glasses, this affection increases our power to act. Consider instead if we are meditating in the dark room. Then when someone turns on the light, this dazzles us and ruins our concentration, and we lose the power to act.

Affection for Spinoza is a matter of our body's composition. What gives our body its power is the differential relations between the speeds of its simple bodies. But its simple bodies are like calculus differentials, infinitely small parts that only obtain a finite value when put into a differential relation with other simple bodies. Consider if we take poison. This will disrupt the ways the simple bodies in our body differentially relate to one another. This is why we die. Our bodies no longer express the range of differential variations that define us. Instead, they eventually express for example dirt.

Now, Deleuze also places a value on our internal decomposition when it comes to the sensations that affect us. The discord of our faculties is what makes sensations more intense [see here and here.] Also consider Spinoza's Ethics Part IV, Proposition 39, Scholium. He writes:

It sometimes happens, that a man undergoes such changes, that I should hardly call him the same. As I have heard tell of a certain Spanish poet, who had been seized with sickness, and though he recovered therefrom yet remained so oblivious of his past life, that he would not believe the plays and tragedies he had written to be his own : indeed, he might have been taken for a grown-up child, if he had also forgotten his native tongue. If this instance seems incredible, what shall we say of infants? A man of ripe age deems their nature so unlike his own, that he can only be persuaded that he too has been an infant by the analogy of other men. (Elwes translation)

From what Spinoza says about the decomposition of the body, it would seem that to change from child to man, or from poet to someone different, would be a decomposition, and thus a loss of power. But could it be that Deleuze takes the opposite view? To change from child to man is not an expression of our body's frailty. It rather shows our body's power to become something new. Imagine we get a sickness like the Spanish poet, and we no longer recognize our past selves. This would seem to be a loss of power. But that would only be so when we take the perspective of the self whom our body no longer expresses. But our bodies are always as perfect as they can be, given the conditions affecting them at any given moment. So to become someone else is not really a deprivation. It could be a testament to the power of our bodies to become new things, to express new essences. The question for Deleuze might not so much be "What can a body do?" as much as it might be "What can a body become?"

So here would be the composition of functions in this case. A certain affection might for Deleuze increase the intensity of sensation. But that means a decrease in the organization of our faculties and our body's compositional relations. Yet this again would be an increase in our body's power to become new things, to express new relations and essences. So it ultimately is an increase in our body's expressive power.

Edwards & Penney's Calculus
Compound Functions
in
Section 1: Functions, Graphs, and Models
Subsection 4: Transcendental Functions

Recall the function machine.

We can think of functions like these 'black box' machines. The machine takes-in a number from one set of values, and it gives-out a value from another set. So consider the squaring function:

The machine takes-in a 2, for example, and then gives-out a 4.

We can also compound our functions. So we can take the result of one function, and then put it into another 'function machine', if you will.

So let's begin with the function g(x). We put in x, and it gives-out u. We then have another function f(u), which is the same as f(g(x)), and we read it as, 'f of g of x'. So we plug the u into the f function, and it gives out the value for f(u). We can then call f(u), or f(g(x)) a new name. We can call it h(x). So,

h(x) = f(g(x))

This requires that all the x values in g's domain correspond (by means of g) to values in f's domain. We call the g function here the 'inner function', and the f function would then be the 'outer function' in this case.

Edwards & Penney now give an example that will illustrate something about notation for composition of functions.

We will first find f(g(x)). First note the g(x). If our number for x is larger than 1, then we will have a negative number. But when we apply it to the f function, we will have the square root of a negative number. So instead we qualify it:

But let's instead consider if we first take f(x), and then after that apply it to the g function. To avoid having the square root of a negative number, we must first begin with a positive. Then after that, there are no restrictions for the g function. So

Edwards and Penney would like then to distinguish two notations:

f(g(x))

and

f ○ g

Our example above shows that the composition of functions f and g is not the same as g and f.

f ○ g ≠ g ○ f

So the notation f(g(x)) might remind us of multiplication notation. In the case of multiplication, it does not matter what order the functions are multiplied. But as we see in the composition of functions, the order does matter sometimes.

from Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002, pp. 36-37.

Spinoza. Ethics. Transl. Elwes. available online at:
http://ebooks.adelaide.edu.au/s/spinoza/benedict/ethics/index.html

Deleuze and Dance Part II: At the Limit of What Bodies Can Do: Michael Jackson’s Fullness of Death, Under Spinoza's Microscope

by Corry Shores
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Deleuze and Dance Part II

At the Limit of What Bodies Can Do:

Michael Jackson’s Fullness of Death,

Under Spinoza's Microscope

Kvond at Frames /sing has posted a thought-provoking entry on death and the body. He explains that our deaths are echoes that carry-on eternally throughout other living bodies. He writes,

Past events continue in their echoeous life in other taken-to-be-living bodies, how Mozart lives across us, and our instruments, our material etchings; but the body itself, as it once was, opens itself up to other confabulation, other involvements.

So consider if everything in the world around us is one (substance), and all the little parts of the world that we see, including ourselves, are just modifications of that underlying one thing. And these parts themselves have parts, just as we have internal organs, which are made of tissue, cells, atoms, and so on. Within each body-part are smaller bodies, and this can be said for any part of the physical world that extends before us.

Kvond has done extraordinary work already on Spinoza’s optics and lens craftsmanship. One topic he explores is Spinoza’s manufacture of microscope lenses. In one of kvond’s expansions of our exchange on Spinoza’s foci/infinity, he suggests that Spinoza’s notion of the infinite could be further explored in terms of the tiny worlds that his microscopes open-up.

In this other entry, kvond notes how Spinoza describes

the kind of knowledge that a worm in the blood of the body has, as it goes about bumping into something so vast it has no possibility of understanding. One has to keep mind that Spinoza was an early maker of microscope lenses (attested to be of rather high quality), and it is perhaps likely that he had stared into lenses, looking at blood and the what must have seemed infinitesimally small forms therein. (emphasis mine)

Kvond has even uncovered an account given by Theodore Kerckring, who used one of Spinoza’s microscopes:

Kerckring is in possession of a microscope made by Spinoza (the only record of it kind), and by virtue of its powers of clarity he is exploring the structure of ducts and lymph nodes. Yet he has skepticism for what is found in the still oft-clouded microscope glass leads him to muse about the very nature of perception and magnification, after he tells of the swarming of tiny animals he has seen covering the viscera of the cadaver, (what might be the first human sighting of bacteria). He writes of the way in which even if we see things clearly, unless we understand all the relationships between things, from the greatest breadth to the smallest, we simply cannot fully know what is happening, if it is destruction or preservation:

On this account by my wondrous instrument’s clear power I detected something seen that is even more wondrous: the intestines plainly, the liver, and other organs of the viscera to swarm with infinitely minute animalcules, which whether by their perpetual motion they corrupt or preserve one would be in doubt, for something is considered to flourish and shine as a home while it is lived in, just the same, a habitation is exhausted by continuous cultivation. Marvelous is nature in her arts, and more marvelous still is Nature’s Lord, how as he brought forth bodies, thus to the infinite itself one after another by magnitude they having withdrawn so that no intellect is able to follow whether it is, which it is, or where is the end of their magnitude; thus if in diminishments you would descend, never will you discover where you would be able to stand.

Spicilegium Anatomicum 1670. (emphasis mine)

Kvond then quotes from the 32 letter of Spinoza’s correspondences.

It is said by Colerus, his first biographer, than he would lift his magnifying glass and stare at mosquitoes and flies. All the vastness was opening itself up, and closing in.

Let us imagine, with your permission, a little worm, living in the blood¹, able to distinguish by sight the particles of blood, lymph, &c., and to reflect on the manner in which each particle, on meeting with another particle, either is repulsed, or communicates a portion of its own motion. This little worm would live in the blood, in the same way as we live in a part of the universe, and would consider each particle of blood, not as a part, but as a whole. He would be unable to determine, how all the parts are modified by the general nature of blood, and are compelled by it to adapt themselves, so as to stand in a fixed relation to one another. For, if we imagine that there are no causes external to the blood, which could communicate fresh movements to it, nor any space beyond the blood, nor any bodies whereto the particles of blood could communicate their motion, it is certain that the blood would always remain in the same state, and its particles would undergo no modifications, save those which may be conceived as arising from the relations of motion existing between the lymph, the chyle, &c. The blood would then always have to be considered as a whole, not as a part. But, as there exist, as a matter of fact, very many causes which modify, in a given manner, the nature of the blood, and are, in turn, modified thereby, it follows that other motions and other relations arise in the blood, springing not from the mutual relations of its parts only, but from the mutual relations between the blood as a whole and external causes. Thus the blood comes to be regarded as a part, not as a whole. So much for the whole and the part.

Letter 15 (32), 1662

Deleuze refers to this passage when talking about death, and the little bodies that constitute us, as well as our eternal essence, and his famous question, “what can a body do?’ I am reminded of an article about Michael Jackson, which describes his final days. In Michael’s honor, I would like to discuss the way his body danced and died, to illustrate certain Deleuzean ideas.

Deleuze’s treatment of our body’s simplest parts solves a problem in Spinoza’s philosophy: on the one hand, our body is finite; but our body’s essence is eternal.

Every one of us is an individual. And in fact, anything which holds together as something in the world around us is likewise an individual. Each thing extends in space. So we may infinitely divide that space to obtain smaller-and-smaller bodies. Or we might think of this in these terms: we use stronger-and-stronger microscope-lenses to see tinier-and-tinier parts.

If we think that our infinite magnifications or divisions will never reach a final part, then according to Deleuze we are considering the infinite as indefinite. However, when we conceive of the infinite as it actually is, then we will arrive upon final parts. So any one individual body is made-up of infinitely many simple bodies. None of these themselves alone are individuals, but all individuals are made-up of them. Deleuze says:

These are the ultimate terms, these are the terms which are last, which you can no longer divide. But, these terms are infinitely small. They are the infinitely small, and this is the actual infinite.

C’est bien des termes ultimes, c’est bien des termes qui sont les derniers, que vous ne pouvez plus diviser. Seulement, ces termes ce sont des infiniment petits. Ce sont des infiniment petits, et c’est ça, l’infini actuel. (Deleuze, Cours Vincennes: 10/03/1981)

Deleuze characterizes these smallest bodies as being inextensive; they are like calculus limits, or Newton’s "vanishing" ("évanouissants") quantities. So these infinitely small bodies are not themselves “things” but are more like the differential relations of calculus. (Deleuze, Cours Vincennes: 10/03/1981)

To better grasp what Deleuze will say about these differential relations, we should take his advice (Cours Vincennes - 22/04/1980) and briefly examine Leibniz’ simple triangle explanation of the differential ratios. [Click on images to enlarge].

We see lines x and y:

And we notice that the corresponding angles are the same in both triangles. Thus they are similar triangles; their proportions are the same, even if their sizes are different.

Now, we are to imagine the vertical line moving to the right.

So, we move line EY closer to point A, always maintaining the angle at C, and hence also at E

Eventually the smaller top triangle will vanish as the line passes through it.

Now, consider the moment right when the smaller triangle-sides e and c are just vanishing, but not yet vanished. They are at the limit of being magnitudes. So there is no extent between them and zero. However, they are not right on zero yet. So they do not have an extensive magnitude, because they extend to no distance away from zero. But they do have an intensive magnitude, which means a degree of difference. And the one vanishing line will have a relational difference to the other vanishing line. Together, they will make a ratio that has a finite value. We know what that is, because these lines maintained the same ratio-value as the larger triangle, even while the line moved.

So even though c and e are vanishing, and have no extensive measure, when we put them into a differential ratio relation at their limits, we obtain a finite value. This is the magic of differential calculus.

So the simple bodies do not exist on their own. They only exist when in relation to each other, just like the vanishing quantities of Leibniz’ triangle. Here Deleuze refers us to Spinoza's Letter on Blood. We saw that in this letter to Oldenburg (which we discussed above), Spinoza describes the constitution of our blood as being made of the relations between lymph and chyle. Deleuze says,

chyle is an infinite set of very simple bodies. Lymph is another infinite set of the very simple bodies. What distinguishes the two infinite sets? It is the differential relation! You have this time a dy/dx which is: the infinitely small parts of chyle over the infinitely small parts of lymph, and this differential relation tends towards a limit: the blood, that is to say: chyle and lymph compose blood.

le chyle c’est un ensemble infini de corps très simples. La lymphe, c’est un autre ensemble infini de corps très simples. Qu’est-ce qui distingue les deux ensembles infinis? C’est le rapport différentiel. Vous avez cette fois-ci un dy/dx qui est: les parties infiniment petites de chyle sur les parties infiniment petites de lymphe, et ce rapport différentiel tend vers une limite: le sang, à savoir: le chyle et la lymphe composent le sang. (Deleuze, "Cours Vincennes: 10/03/1981")

Such a limit is an infinity in the same way that a polygon tends towards its limit – being a circle – as its sides increase to infinity.

Deleuze explains:

The limit is precisely the moment when the angular line, by dint of multiplying its sides, tends towards infinity. (Deleuze, "Cours Vincennes: 17/02/1981")

Yet we are more than just blood. There are many such differential ratios that make-up our body, which is a cohering group of moving simple bodies in differential relations to each other. We are not the addition of all these differentials, but rather the integral sum:

this relation which characterises me, this differential relation or better, this summation, not an addition but this kind of integration of differential relations, since in fact there are an infinity of differential relations which compose me: my blood, my bones, my flesh, all this refers to all sorts of systems of differential relations.

ce rapport qui me caractérise, ce rapport différentiel ou bien plus, cette sommation, pas une addition mais cette espèce d’intégration de rapports différentiels, puisque en fait il y a une infinité de rapports différentiels qui me composent: mon sang, mes os, ma chair, tout ça renvoie à toutes sortes de systèmes de rapports différentiels. (Deleuze, "Cours Vincennes: 10/03/1981")

Now consider how our bodies are constantly in contact with other individual things. Good food increases our power or abilities. Toxins decrease our body’s capacities. This is because bad things disrupt the differential ratios that characterize us. They make them take-on different proportions. And this is our death. Deleuze says that if one of our own collections is

determined from the outside to take another relation than the one under which it belongs to me. What does this mean? It means that: I die! I die! In effect, the infinite set which belongs to me under such a relation which characterises me, under my characteristic relation, this infinite set will take another relation under the influence of external causes.

déterminée du dehors à prendre un autre rapport que celui sous lequel elle m’appartient. Qu’est-ce que ça veut dire? Ça veut dire: je meurs! Je meurs. En effet, l’ensemble infini qui m’appartenait sous tel rapport qui me caractérise, sous mon rapport caractéristique, cet ensemble infini va prendre un autre rapport sous l’influence de causes extérieures.

He gives the example

of poison which decomposes the blood: under the action of arsenic, the infinitely small particles which compose the blood, which compose my blood under such a relation, are going to be determined to enter under another relation. Because of this, this infinite set is going to enter in the composition of another body, it will no longer be mine: I die!

du poison qui décompose le sang: sous l’action de l’arsenic, les particules infiniment petites qui composent mon sang, qui composent mon sang sous tel rapport, vont être déterminées à entrer sous un autre rapport. Dès lors cet ensemble infini va entrer dans la composition d’un autre corps, ce ne sera plus le mien: je meurs!

. . .

I die when these parts which belong to me or which belonged to me are determined to enter under another relation which characterises another body: I would feed worms! "I would feed worms", which means: the parts of which I am composed enter under another relation — I am eaten by worms. My corpuscles, mine, which pass under the relation of the worms.

Je meurs lorsque les parties qui m’appartiennent ou qui m’appartenaient sont déterminées à rentrer sous un autre rapport qui caractérise un autre corps: je nourrirais les vers! "Je nourrirais les vers", cela veut dire: les parties qui me composent entrent sous un autre rapport — je suis mangé par les vers. Mes corpuscules, à moi, qui passent sous le rapport des vers. (Deleuze, "Cours Vincennes: 10/03/1981")

In death our simple bodies break-up and form into different ratios, for example, those of the worm feeding on our bodies. But what is important to note is that the proportional relations themselves do not disappear. “The formula” that makes us who we are always existed and always will exist, eternally, in the mind of God. But God’s mind is no different than the underlying substance of the whole world. It is merely another qualitative expression of the same thing. So we exist eternally. Only, substance expresses us for a finite duration as a modality. (And along the lines of Nietzsche’s eternal return, we could possibly come to be expressed again in exactly the same ratios, and perhaps we might come into existence over-and-over again infinitely many more times). But yet, we are always implicitly expressed in the world around us. This idea could be compatible with kvond’s description of our persistence after death as echoes through other bodies, which he says might be Spinoza’s God.

Depending on the variations of our internal ratio-relations, we might have more-or-less power or ability at any given time. These levels change throughout our lives. Yet, we remain who we are despite the changes we undergo. This is because our essence is really a continuum of power-variation. The essence variation-range itself is eternal, but its different levels express themselves as our current states at any given time. And again, that level of power is expressed as our internal simple-body ratios. When they lose their cohesion and consistency, we become something else, like soil and its small living organisms (our echoes, perhaps). While we are alive, our body is capable of certain actions. And we are affected by different things, like nutrients or toxins, which increase or decrease our capabilities. Our power swings up and down continuously, like a melody. But as kvond notes in his comments to this blog entry (at Michael Austin’s Complete Lies http://buymeout.wordpress.com), the stone is not imperfect on account of it being unable to see. For, conditions do not allow for stones to see. So we would not also consider a blind man as deficient either. Thus we do not become deficient as we near our deaths and our body decays on account of its composing-relations taking-on proportions that express other beings (like worms). Throughout the course of our whole lives, we will fully express our range of essence. But what is important for Deleuze is that we cannot predict if in the next instant we will have more capacities or less. This is because the way we are affected changes unpredictably, like a melody we hear for the first time. This is why Deleuze takes this question from Spinoza: “What can a body do?” For all we know, we could become much more powerful a moment from now. Or, we could suddenly die. We just never know what our body can do.

Someone who has shown us just how much a body can do, is Michael Jackson. His capacities in dance far exceeded what many consider humanly possible. Here are parts of Billy Jean, when first he introduces the moonwalk.

It seems that his body is right at the limit of what bodies can do. But his body also came to suffer harmful affections. He obtained addiction to pain medicines some think in the mid 80’s when a stage accident set his hair on fire. He also suffered chronic insomnia, and took heavy drugs to put himself down at night, then took others to get him up and through the next day. He suffered other ailments as well, and as he aged, his body came to be able to do less-and-less.

Even at the heights of his body’s ability to dance, he had a sense of its morbidity as well. In this scene during the Smooth Criminal song of his Moonwalker film, there is a breakdown where he and the other dancers evoke a voodoo underworld erotic dance of death.

Ian Halperin is a biographer who followed Michael during his final years. His superb article can be found here. He explains that Michael knew his body was incapable of handling the demanding 50 concert schedule he was contractually obligated to fulfill. In fact, Michael predicted that his attempt to go through with it would certainly kill him. But he did so anyway. He saw himself as being better if he were to die. Halperin writes:

Jackson told my contact that he wanted to die. He said that he didn’t have what it would take to perform any more because he had lost his voice and dance moves.

‘It’s not working out,’ Jackson said. ‘I’m better off dead. I don’t have anywhere left to turn. I’m done.’

Michael knew the concerts would kill him. But he did not quit. He instead took his body to the limit, where he would inevitably vanish. We can see from this final rehearsal video that he was not a frail old man. His body could still do amazing things. [Perhaps adjust the volume down for this one].

Our body will someday face its limit, when it ceases to be our body, and comes to compose something else. Right at that limit, no extent of time will stand between us and our deaths. We will not have vanished. But we will be vanishing.

I do not know what to say about us after we die. I think I agree with kvond’s characterization of us as echoing-away into eternity. But I would like to say more about what our bodies do while we are alive. When we reach the limit of our lives, we might also ask, what have our bodies done? If we would have died at a much younger age, we would have expressed a narrow range of variation. If we age and lose the parts of our youthful appearance and fitness, we are gaining a greater range of variation in how our essence is expressed. So the longer we live, the more we become. Even the “deficiencies” we develop in our later age are new notes in life’s melody. And when we reach the limit of our life’s duration, only then have we been as much as our bodies could be. To die a second earlier would mean to have undergone less expressive variation. However, this does not mean that those who die young have missed-out on more self-fulfillment. Circumstances did not allow for them to have a longer life, so they fully expressed the entire extent of their essence’s range of variation. Nonetheless, as we near death, we should look forward to it as the fulfillment of the expression of our selfhood.

Deleuze, Gilles. "Cours Vincennes: 10/03/1981".webdeleuze.com. English and French versions available here.

Deleuze, Gilles. "Cours Vincennes: 17/02/1981".webdeleuze.com. English and French versions available here.

Deleuze, Gilles. "Cours Vincennes: 20/01/1981".webdeleuze.com. The lecture is available here: French and English.

Deleuze, Gilles. "Cours Vincennes: 10/03/1981".webdeleuze.com. English and French versions available here.

Halperin, Ian. “I’m better off dead. I’m done. Michael Jackson’s fateful prediction just a week before his death.” Mail Online. 29-June-2009. http://www.dailymail.co.uk/news/article-1196009/Im-better-dead-Im-How-Michael-Jackson-predicted-death-months-ago.html

Leibniz, Gottfried. "Justification of the Infinitesimal Calculus by that of Ordinary Algebra." Philosophical Papers and Letters. Ed. & Transl. Leroy E. Loemker. Dordrecht: D. Reidel Publishing Company, 1956.

Spinoza. The Letters. Transl Samuel Shirley. Cambridge: Hackett Publishing Company, Inc., 1995.

Videos:

First Moonwalk:

http://www.youtube.com/watch?v=GRe2HfzDEGw

Smooth Criminal:

http://www.youtube.com/watch?v=PmN0dwDR1wo

Final rehersal:

http://www.youtube.com/watch?v=vbNNJXkxUhU&eurl=http://showstalker.net/2009/07/michael-jackson-last-rehearsal-video-they-dont-really-care-about-us/&feature=player_embedded

"What Can a Body Do?" Power of Affection in Spinoza and Deleuze

by Corry Shores
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[The following is quotation up to the Deleuze section, which is summary. My commentary is in brackets. The final quotation is the section where Deleuze obtains his famous question, "What can a body do?" (Qu'est-ce que peut un corps?) Preceding that are the sections that Spinoza cites in that final quotation.]

Baruch Spinoza

Ethics

Part II

Proposition 6

Prop. VI. The modes of any given attribute are caused by God, in so far as he is considered through the attribute of which they are modes, and not in so far as he is considered through any other attribute.

(Elwes)

((Other versions:

The modes of each attribute have God as a cause in so far as he is considered only under that attribute of which they are modes, and not in so far as he is considered under any other attribute.

(Parkinson 117)

PROPOSITIO VI

Cujuscunque attributi modi Deum, quatenus tantum sub illo attributo, cujus modi sunt, & non, quatenus sub ullo alio consideratur, pro causa habent.))

[For example, God considered in terms of extension cannot be thought to be the cause of an idea, only God conceived in terms of thought can be considered the cause of an idea.]

Part II

Definition 1

Definition I. By body I mean a mode which expresses in a certain determinate manner the essence of God, in so far as he is considered as an extended thing.

(Elwes)

((By body I understand a mode which expresses in a certain and determinate way the essence of God, in so far as he is considered as an extended thing.

(Parkinson 113)

I. Per corpus intelligo modum, qui Dei essentiam, quatenus, ut res extensa, consideratur, certo, & determinato modo exprimit.))

[The body is a mode of the attribute of extension, hence the body expresses the divine substance's extensivity, which is infinite because God is infinite, hence the body expresses God's infinity (also because the body implicates the infinity of all parallel attributes).]

Part II

Proposition 2

Prop. II. Extension is an attribute of God, or God is an extended thing.

(Elwes)

((Extension is an attribute of God, or, God is an extended thing.

(Parkinson 115)

PROPOSITIO II

Extensio attributum Dei est, sive Deus est res extensa.))

Part II

Proposition 12

Prop. XII. Whatsoever comes to pass in the object of the idea, which constitutes the human mind, must be perceived by the human mind, or there will necessarily be an idea in the human mind of the said occurrence. That is, if the object of the idea constituting the human mind be a body, nothing can take place in that body without being perceived by the mind.

(Elwes)

((Whatever happens in the object of the idea constituting the human mind must be perceived by the human mind, or, there will necessarily exist in the human mind an idea of this thing. That is, if the object of the idea constituting the human mind is a body, nothing can happen in that body which is not perceived by the mind.

(Parkinson 123-124)

PROPOSITIO XII

Quicquid in objecto ideæ, humanam Mentem constituentis, contingit, id ab humana Mente debet percipi, sive ejus rei dabitur in Mente necessario idea: Hoc est, si objectum ideæ, humanam Mentem constituentis, sit corpus, nihil in eo corpore poterit contingere, quod a Mente non percipiatur.))

[Here we are dealing with the mind of a human, which is a mode. Our bodies are our modalities in Extension, our mind's are our modalities in Thought. To every mode belongs parallel modes in the infinity of other attributes. The parallel to the body is our mind. Our mind is an idea of the body. So on account of this parallelism, whatever happens to the body must be perceived by the mind, because an affection of one would parallel a corresponding affection in the other attribute.]

Part II

Proposition 49

Prop. XLIX. There is in the mind no volition or affirmation and negation, save that which an idea, inasmuch as it is an idea, involves.

(Elwes)

((There is in the mind no volition, or, no affirmation and negation, apart from that which an idea involves in so far as it is an idea.

(Parkinson 156)

PROPOSITIO XLIX

In Mente nulla datur volitio, sive affirmatio, & negatio præter illam, quam idea, quatenus idea est, involvit.))

[For example, when we consider the idea of a triangle, we thereby affirm that its three angles equal two right angles, because we cannot conceive a triangle without also affirming this fact about it.]

What Can a Body Do?

[Following quotations from the Elwes translation only]

Part III

Proposition 2

Prop. II. Body cannot determine mind to think, neither can mind determine body to motion or rest or any state different from these, if such there be.

[There is no causation of a mode in one attribute to a mode in another attribute.]

Proof.-All modes of thinking have for their cause God, by virtue of his being a thinking thing, and not by virtue of his being displayed under any other attribute (II. vi.). That, therefore, which determines the mind to thought is a mode of thought, and not a mode of extension ; that is (II. Def. i.), it is not body. This was our first point. Again, the motion and rest of a body must arise from another body, which has also been determined to a state of motion or rest by a third body, and absolutely everything which takes place in a body must spring from God, in so far as he is regarded as affected by some mode of extension, and not by some mode of thought (II. vi.) ; that is, it cannot spring from the mind, which is a mode of thought. This was our second point. Therefore body cannot determine mind, &c. Q.E.D.

Note.-This is made more clear by what was said in the note to II. vii., namely, that mind and body are one and the same thing, conceived first under the attribute of thought, secondly, under the attribute of extension. Thus it follows that the order or concatenation of things is identical, whether nature be conceived under the one attribute or the other ; consequently the order of states of activity and passivity in our body is simultaneous in nature with the order of states of activity and passivity in the mind. The same conclusion is evident from the manner in which we proved II. xii.

Nevertheless, though such is the case, and though there be no further room for doubt, I can scarcely believe, until the fact is proved by experience, that men can be induced to consider the question calmly and fairly, so firmly are they convinced that it is merely at the bidding of the mind, that the body is set in motion or at rest, or performs a variety of actions depending solely on the mind’s will or the exercise of thought. However, no one has hitherto laid down the limits to the powers of the body, that is, no one has as yet been taught by experience what the body can accomplish solely by the laws of nature, in so far as she is regarded as extension. No one hitherto has gained such an accurate knowledge of the bodily mechanism, that he can explain all its functions ; nor need I call attention to the fact that many actions are observed in the lower animals, which far transcend human sagacity, and that somnambulists do many things in their sleep, which they would not venture to do when awake : these instances are enough to show, that the body can by the sole laws of its nature do many things which the mind wonders at.

Again, no one knows how or by what means the mind moves the body, nor how many various degrees of motion it can impart to the body, nor how quickly it can move it. Thus, when men say that this or that physical action has its origin in the mind, which latter has dominion over the body, they are using words without meaning, or are confessing in specious phraseology that they are ignorant of the cause of the said action, and do not wonder at it.

But, they will say, whether we know or do not know the means whereby the mind acts on the body, we have, at any rate, experience of the fact that unless the human mind is in a fit state to think, the body remains inert. Moreover, we have experience, that the mind alone can determine whether we speak or are silent, and a variety of similar states which, accordingly, we say depend on the mind’s decree. But, as to the first point, I ask such objectors, whether experience does not also teach, that if the body be inactive the mind is simultaneously unfitted for thinking? For when the body is at rest in sleep, the mind simultaneously is in a state of torpor also, and has no power of thinking, such as it possesses when the body is awake. Again, I think everyone’s experience will confirm the statement, that the mind is not at all times equally fit for thinking on a given subject, but according as the body is more or less fitted for being stimulated by the image of this or that object, so also is the mind more or less fitted for contemplating the said object.

But, it will be urged, it is impossible that solely from the laws of nature considered as extended substance, we should be able to deduce the causes of buildings, pictures, and things of that kind, which are produced only by human art ; nor would the human body, unless it were determined and led by the mind, be capable of building a single temple. However, I have just pointed out that the objectors cannot fix the limits of the body’s power, or say what can be concluded from a consideration of its sole nature, whereas they have experience of many things being accomplished solely by the laws of nature, which they would never have believed possible except under the direction of mind : such are the actions performed by somnambulists while asleep, and wondered at by their performers when awake. I would further call attention to the mechanism of the human body, which far surpasses in complexity all that has been put together by human art, not to repeat what I have already shown, namely, that from nature, under whatever attribute she be considered, infinite results follow. As for the second objection, I submit that the world would be much happier, if men were as fully able to keep silence as they are to speak. Experience abundantly shows that men can govern anything more easily than their tongues, and restrain anything more easily than their appetites ; when it comes about that many believe, that we are only free in respect to objects which we moderately desire, because our desire for such can easily be controlled by the thought of something else frequently remembered, but that we are by no means free in respect to what we seek with violent emotion, for our desire cannot then be allayed with the remembrance of anything else. However, unless such persons had proved by experience that we do many things which we afterwards repent of, and again that we often, when assailed by contrary emotions, see the better and follow the worse, there would be nothing to prevent their believing that we are free in all things. Thus an infant believes that of its own free will it desires milk, an angry child believes that it freely desires vengeance, a timid child believes that it freely desires to run away ; further, a drunken man believes that he utters from the free decision of his mind words which, when he is sober, he would willingly have withheld : thus, too, a delirious man, a garrulous woman, a child, and others of like complexion, believe that they speak from the free decision of their mind, when they are in reality unable to restrain their impulse to talk. Experience teaches us no less clearly than reason, that men believe themselves to be free, simply because they are conscious of their actions, and unconscious of the causes whereby those actions are determined ; and, further, it is plain that the dictates of the mind are but another name for the appetites, and therefore vary according to the varying state of the body. Everyone shapes his actions according to his emotion, those who are assailed by conflicting emotions know not what they wish ; those who are not attacked by any emotion are readily swayed this way or that. All these considerations clearly show that a mental decision and a bodily appetite, or determined state, are simultaneous, or rather are one and the same thing, which we call decision, when it is regarded under and explained through the attribute of thought, and a conditioned state, when it is regarded under the attribute of extension, and deduced from the laws of motion and rest. This will appear yet more plainly in the sequel. For the present I wish to call attention to another point, namely, that we cannot act by the decision of the mind, unless we have a remembrance of having done so. For instance, we cannot say a word without remembering that we have done so. Again, it is not within the free power of the mind to remember or forget a thing at will. Therefore the freedom of the mind must in any case be limited to the power of uttering or not uttering something which it remembers. But when we dream that we speak, we believe that we speak from a free decision of the mind, yet we do not speak, or, if we do, it is by a spontaneous motion of the body. Again, we dream that we are concealing something, and we seem to act from the same decision of the mind as that, whereby we keep silence when awake concerning something we know. Lastly, we dream that from the free decision of our mind we do something, which we should not dare to do when awake.

Now I should like to know whether there be in the mind two sorts of decisions, one sort illusive, and the other sort free? If our folly does not carry us so far as this, we must necessarily admit, that the decision of the mind, which is believed to be free, is not distinguishable from the imagination or memory, and is nothing more than the affirmation, which an idea, by virtue of being an idea, necessarily involves (II. xlix.). Wherefore these decisions of the mind arise in the mind by the same necessity, as the ideas of things actually existing. Therefore those who believe, that they speak or keep silence or act in any way from the free decision of their mind, do but dream with their eyes open.

Gilles Deleuze

Expressionism in Philosophy

Ch.14

"What Can a Body Do?"

The first expressive triad of modality is:

1) an essence as a degree of power

2) a characteristic relation in which that degree of power expresses itself

3) the extensive parts subsumed under this characteristic relation

In the Ethics there is system of equivalences producing a second expressive triad:

1) the essence as a degree of power

2) a certain capacity to be affected in which it expresses itself

3) the affection that, each moment, exercises that capacity

(196b/217b) [Citations give French version first, followed by English.]

Each extensive mode is made up of a great number of extensive parts, and all parts from every mode affect one another ad infinitum, hence all existing modes are affected in many diverse ways.

Modes have affections in accordance with their "certain capacity of being affected" (un certain pouvoir d'être affecté). Different creatures -- horses, fish, even different individual humans -- are each affected by different things and in different ways.

Modes cease existing when they no longer are capable of maintaining their characteristic relations, which occurs when the mode is no longer able to be affected in many ways. Thus, modal relations go hand-in-hand with the capacity to be affected, so the questions What is the structure of a body? and What can a body do? are equivalent questions, because "what a body can do corresponds to the nature and limits of its capacity to be affected (ce que peut un corps, c'est la nature et les limites de son pouvoir d'être affecté).

On account of God's infinite power (potentia), he has the capacity (potestas) to be affected in an infinity of ways.

The mode's capacity to be affected in many ways is "always exercised under the action of external modes" (toujours nécessairement rempli sous l'action des modes extérieurs.) (198c/218c)

Although the very great number of ways that a finite mode may be affected is an infinity, it is a greater or lesser infinity relating to something finite. The infinity of ways that God is affected (on account of his affections being self-caused and not externally conditioned) is an unlimited infinity comprising all the essences of modal existences. (198c/218c.d)

Affections are not sufferings or passions.

Affections that can be completely explained by the nature of the affected body are active affections, and themselves actions.

Si nous supposons des affections qui s'expliquent entièrement par la nature du corps affecté, ces affections sont actives, sont elles-mêmes des actions.

(219a/198d)

So because there are no causes external to God, he then is the cause of all his affections, thus all his affections are explained by his own nature, and for this reason all of God's affections are active.

Not so with existing modes, which do not exist by virtue of their own nature, because "their existence is composed of extensive parts that are determined and affected from outside, ad infinitum" (leur existence est composée de parties extensives qui sont déterminées et affectées du dehors, à l'infini) (199a/219b). So because the sources of modal affections are exterior, they tend to be passions.

Spinoza's ethical question is, can finite modes such as ourselves attain to active affections, and if so, how do they do so?

When God is affected, a mode is produced. But when a mode is affected, there is a second degree of affection, an affection of an affection. When some body has an effect on us, there is a passive affection. The idea of such an affection does not express its cause, but instead indicates our body's present condition, thereby exercising our capacity to be affected. The bodily affection is a corporeal image, and the idea of the affection in our mind is an inadequate idea, an imagining.

What flows from the ideas of affections are another sort of affections: affects (affectus) or feelings. (199bc-200a/219c-220ab) Our body undergoes duration, hence its present state is inseparable from its previous state, both linked together in continuous duration. Because the ideas we have indicate the present state of our body's constitution, every idea is linked to another idea indicating an earlier state of the body. Our feelings are ideas that concretely relate present and past in a continual duration. (200a.b/220b.c)

There are thus two sorts of modal affections:

1) states of a body or ideas indicating these states, and

2) changes in the body or ideas indicating these changes.

(200bc/220c)

When we begin existence, we have passive feelings (passions) and thus inadequate ideas.

When we have an idea that cannot be formally explained as a product of our power of understanding, then we are not the cause of the idea, and the idea is inadequate. This inadequate idea causes a feeling, then, that we did not cause and is thus a passion. (200d/220-221)

Our capacity to be affected is thus exercised, from the beginning of our existence, by inadequate ideas and passive feelings.

Notre pouvoir d'être affecté se trouve donc rempli, dès le début de notre existence, par des idées inadéquates et des sentiments passifs.

(201a/221ab)

Moreover, adequate ideas and active feelings are likewise linked. When we are the cause of an idea, it is adequate, thus we are also the cause of the idea's corresponding feeling. Such a feeling that we cause is an action. So when our mind has adequate ideas, we do certain things; and when we have inadequate ideas, we undergo certain things. The ethical question is a methodological question of how we are to become active, which is to ask, "how can we produce adequate ideas?" (201b/221c)

As the mode undergoes passive affections, its capacity to be affected appears as a force or power of suffering (force ou puissance de pâtir). The mental equivalent of the body's power of suffering is power of imagining and of experiencing passive feelings. (201d/212-222)

But regardless of how much one is being passively or actively affected, one's capacity to be affected remains constant. And active and passive affections are in an inversely proportional relationship: when we produce active affections, our passive ones decrease. (202a/222b.c)

And yet, our capacities to be affected vary as well, because a mode's composition and decomposition passes through many stages, so we might even say that when we grow out of childhood, we change our body or relation. Is who we are as an infant the same as when we are a full adult, and also the same when we are at our eldest age? As we undergo these changes, so too changes our capacities to be affected. Let's consider the example from Deleuze's footnote 15:

Ethics Part IV, 39, scholium:

I would here remark that I consider that a body undergoes death, when the proportion of motion and rest which obtained mutually among its several parts is changed. For I do not venture to deny that a human body, while keeping the circulation of the blood and other properties, wherein the life of a body is thought to consist, may none the less be changed into another nature totally different from its own. There is no reason, which compels me to maintain that a body does not die, unless it becomes a corpse ; nay, experience would seem to point to the opposite conclusion. It sometimes happens, that a man undergoes such changes, that I should hardly call him the same. As I have heard tell of a certain Spanish poet, who had been seized with sickness, and though he recovered therefrom yet remained so oblivious of his past life, that he would not believe the plays and tragedies he had written to be his own : indeed, he might have been taken for a grown-up child, if he had also forgotten his native tongue. If this instance seems incredible, what shall we say of infants? A man of ripe age deems their nature so unlike his own, that he can only be persuaded that he too has been an infant by the analogy of other men. However, I prefer to leave such questions undiscussed, lest I should give ground to the superstitious for raising new issues.

(Elwes)

Deleuze says that both our capacity to be affected as well as our characteristic relation "enjoy a margin, a limit, within which they take form and are deformed" (jouissaient d'une marge, d'une limite dans laquelle ils se forment et se déforment) (202d/222-223). Hence we see, says Deleuze, the significance of Spinoza's letter to Meyer where he describes infinities of differential variation within maxima and minima [see entries on Spinoza's Letter on Infinity, Hegel's commentary, Gueroult's commentary, and Deleuze's commentary] [Also note Deleuze's term "deformed:" we will see in his aesthetics that the intensity of sensation results from deformation, in subtle contrast to transformation.]

But powers to act and to suffer are only inversely related when we conceive of affection abstractly. Leibniz was influenced by Spinoza's theory of affection, and wonders if passive force should be considered distinct from active force. What distinguishes them is that active forces are real, positive, and affirmative; whereas passive forces assert and express nothing except the imperfection of the finite. Active force is autonomous, passive ones are not, because passive forces are merely the limitations of active forces; hence there would be no passive force were it not for the active force that it limits. Passive forces are limitations as well of an even deeper force, which is the essence asserting and expressing itself solely inactive forces. (203a.d/223a-224)

So the power of suffering does not express anything that is positive, because there is always something imaginary in passive affections which prevents them from being real.

We are passive and impassioned only by virtue of our imperfection, in our imperfection itself.

Nous ne sommes passifs et passionnés qu'en raison de notre imperfection, par notre imperfection même.

(204b/224b)

The agent of the action acts through what he is in possession-of, and the patient of an action suffers through what he lacks. But our passive force is merely the limitation of our active force, and hence it asserts nothing, because it expresses nothing. It merely "involves" (enveloppe) our impotence (impuissance), which is the limitation on our power of action; it is the lowest degree of our power of acting (le plus bas degré de notre puissance d'agir). (204c.d/224c.d)

Only active affections are really able to positively exercise our capacity to be affected. Our power of action, which is our capacity to be affected, expresses our essence, which is the same as our power of action. (205a/225b)

Spinoza reconciles two fundamental principles:

1) From the physical view: An essence's capacity to be affected remains fixed, regardless of whether active or passive affections exercise that capacity. So because the essence's capacity remains fixed, no matter the affection, modes are always as perfect as they can be.

2) From the ethical view: An essence's power of being affected is fixed, but fixed within minimum and maximum limits. When passive affections exercise their power of being affected, then that power is reduced to the minimum. This leaves the mode imperfect and impotent, and cut-off from its essence or degree of power, that is to say, it cuts us off from what we can do.

So a mode is always as perfect as it can be, but its perfection is relative to those affections that actually belong to the modal essence. [So given certain circumstances, our essence's capacity to be affected decreases, thus it cannot be expected to have more power at that moment. The stone cannot be expected to see.]

So the mode undergoes expressive changes, because its changes in power are changes in the mode of substance's self-expression of its infinite power. There is a vast network of modes acting on each other, that is, affecting each other; these are the mechanical changes the mode undergoes. Also, the essence itself changes. As we grew from child to adult, our essence changed as well. What changed was our capacity to be affected; these are "metaphysical" changes of the essence itself, stemming from whatever affections belong to the mode while it exists. So while we exist, our essence itself varies with us, which should be expected, because essences lie along an indivisible continuum of variation of degrees of power. Thus our essences vary, but between a maximum and minimum of variation. So two things are eternal or fixed in regard to essences: their limits of variation, and their perfection at any given time of existence. (205b.d/225b-226)

So we see then the importance of Spinoza's ethical question, the point of which can be formulated two ways:

1) We do not even know of what a body is capable,

2) We do not even know of what affections we are capable, nor the extent of our power.

So during our existence, our essence's power of affection will reach both its minimum and maximum. But we are finite beings with limited knowledge even of ourselves. So at any given time, we cannot know whether or not we are at our maximum, because we cannot know if other modes might affect us in such a way as to increase our power later.

But Deleuze suggests that we can try to become concretely active, so that we can know our maximum of power.

(205-206/226a.b)

[Yet Spinoza is still a determinist. If we endeavor to become more active, we were determined exteriorly to do so. But so what? If while I am striving to become more active, (which would mean more rational), it should not matter to me if there are forces acting on me compelling me to do so. And is this not our experience anyway? Are we not the most driven to action when some extraordinary force compels us, almost as though we had no choice? Hence Deleuze does not say that we should try to become concretely active so that we can become our maximum. Again, we are finite modes who cannot know what our essence's capacities are; we can only know it once we reach it, and even then we cannot know it for sure.

Herman De Dijn offers the example of his daughter returning home past curfew. He stays-up waiting and worrying, increasingly becoming angry. When she arrives, he begins yelling and scolding, but his daughter explains that she blew her bicycle tire on her way home. De Dijn was passively affected to have passions of anger, but even knowing the cause of his daughter's lateness does not make him stop being angry all at once.

He could also think rationally about his affections. He might think to himself, "when I am forced to worry about my daughter's well being, I become passionate." Knowing the cause of his anger, that is, thinking rationally about his anger also will not make it go away, but it makes it better, because he knows that the cause is exterior, and he better knows what that exterior cause is. His very knowing the cause is an active affection, he knows more his own ways of being affected. This does not change the way things are affecting him at that time, but it maximizes his essence's power (of being affected).

So our striving for active affection should be a rational affair; we should strive to be active by learning and reasoning what affections cause our essence's power to increase (similarly to how De Dijn learned which affections cause them to decrease). So by knowing rationally the ways we are affected, we are thereby striving to be more active, which allows us to experience a higher degree of power.]

Deleuze, Gilles. Spinoza et le problème de l'expression. Paris: Les Éditions de Minuit, 1968.

Deleuze, Gilles. Expressionism in Philosophy: Spinoza. Trans. Martin Joughin. New York: Zone Books, 1990.

Spinoza. Ethics. Ed. & Transl. G.H.R. Parkinson. Oxford: Oxford University Press, 2000.

Spinoza. Ethics. Transl. Elwes. available online at:

http://ebooks.adelaide.edu.au/s/spinoza/benedict/ethics/index.html

Spinoza. Ethica. available online at:

http://www.hs-augsburg.de/~harsch/Chronologia/Lspost17/Spinoza/spi_eth0.html

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