## 16 Dec 2008

### Deleuze Cours Vincennes 10/03/1981, summarized

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Gilles Deleuze

Cours Vincennes 10/03/1981

Confrontation with Gueroult's commentary
Confrontation avec le commentaire de Guéroult

All individuals are composed of an infinity of extensive parts. For Spinoza, there is no simple individual, because all are composite. However, individuals are composed of an infinity of "simplest bodies," which are neither finite atoms nor indefinites. To understand them, we must grasp the metaphysical, physical, and mathematical notion of the actual infinity, which is neither finite nor indefinite.

[for more on actual infinity, see Spinoza's 12th Letter and Gueroult's commentary,

It is not finite, because finite means that when analyzing something there will be a point where we must stop our analysis.

the analysis encounters a limit, this limit is the atom. The atom is subject to a finite analysis.

l’analyse rencontre une limite, cette limite c’est l’atome. L’atome est justiciable d’une analyse finie.

However,

The indefinite is as far as you can go, you can't stop yourself. That is to say: as far as you can take the analysis, the term at which you arrive will always be, in turn, divided and analysed. There will never be a last term.

L’indéfini, c’est si loin que vous alliez, vous ne pourrez pas vous arrêter. C’est à dire: si loin que vous portiez l’analyse, le terme auquel vous arriverez pourra toujours être, à son tour, divisé et analysé. Il n’y aura jamais de dernier terme.

Contrary to the indefinite, the actual infinite has last terms, but they are last ad infinitum, and thus are not atoms.

The infinite is actual, the infinite is in action. In effect, the indefinite is, if you like, infinite, but virtual, that is to say: you can always go further.

L’infini est actuel, l’infini est en acte. En effet, l’indéfini c’est, si vous voulez, de l’infini, mais virtuel, à savoir: vous pouvez toujours aller plus loin.

But the infinite has last terms, and these are Spinoza's simple bodies.

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.

These ultimate terms are not atoms, because they are infinitely small, or "vanishing" ("évanouissants") as Newton called them.

Infinitely small terms cannot be considered singularly;

they can only go by way of infinite collections. Therefore there are infinite collections of the infinitely small. The simple bodies of Spinoza don't exist one by one. They exist collectively and not distributively. They exist by way of infinite sets.

ça ne peut aller que parcollections infinies. Donc il y a des collections infinies d’infiniment petits. Les corps simples de Spinoza, ils n’existent pas uns par uns. Ils existent collectivement et non pas distributivement. Ils existent par ensembles infinis.

So there are no simple bodies in Spinoza, but instead only infinite sets of simple bodies. And thus

an individual is not a simple body, an individual, whatever it is, and however small it is, an individual has an infinity of simple bodies, an individual has an infinite collection of the infinitely small.

un individu n’est pas un corps simple, un individu, quel qu’il soit, et si petit soit-il, un individu a une infinité de corps simples, un individu a une collection infinie d’infiniment petits.

For this reason, Deleuze cannot understand why Gueroult wonders if Spinoza's simple bodies have a shape and magnitude (une figure et une grandeur). [See section V. of Gueroult's " Here he says that singular bodies have magnitude in extension.] If simple bodies are infinitely small and are thus vanishing, they could not possibly have shape or magnitude. However, what does have shape and magnitude are infinite collections of the infinitely small.

each individual corresponds an infinite collection of very simple bodies, each individual is composed of an infinity of very simple bodies.

à chaque individu correspond une collection infinie de corps très simples, chaque individu est composé d’une infinité de corps très simples.

Moreover, we must be able to know which collections of infinitely small bodies corresponds to which individual.

The infinitely small enter into infinite sets and these infinite sets are not the same. That is to say: there is a distinction between infinite sets.

Les infiniment petits entrent dans des ensembles infinis et ces ensembles infinis ne se valent pas. C’est à dire: il y a des distinctions entre ensembles infinis.

Infinitely small terms themselves cannot have an interiority, although the infinite sets they make up may have an interiority.

As such, the infinitely small simple bodies can only have exterior relations to each other:

The simple bodies have only strictly extrinsic relations, relations of exteriority with each other. They form a species of matter, using Spinoza's terminology: a modal matter, a modal matter of pure exteriority, which is to say: they react on one another, they have no interiority, they have only external relations with one another.

Les corps simples n’ont les uns avec les autres que des rapports strictement extrinsèques, des rapports d’extériorité. Ils forment une espèce de matière, en suivant la terminologie de Spinoza: une matière modale, une matière modale de pure extériorité, c’est à dire: ils réagissent les uns sur les autres, ils n’ont pas d’intériorité, ils n’ont que des rapports extérieurs les uns avec les autres.

Deleuze asks the question, "what allows us to distinguish one infinite set from another" (that is, one individual from another), by reforming it as

under what aspect does an infinite set of very simple bodies belong to either this or that individual? Under what aspect?

sous quel aspect un ensemble infini de corps très simples appartiennent à tel ou tel individu? Sous quel aspect?

For Spinoza, a set of infinite parts belongs to me when they form a certain relation, and when they form some other relation, they belong to another individuality. And, it is according to their relations of movement and rest that one infinite set belongs to a certain individual.

Gueroult's interesting hypothesis is that Spinoza's relation of movement and rest is one of vibration, because 17th century physics had begun studying the simple and compound pendulums.

Individuals for Spinoza would be kinds of compound pendulums, each composed of an infinity of simple pendulums. And what defines an individual is a vibration.

individus pour Spinoza, ce serait des espèces de pendules composés, composés chacun d’une infinité de pendules simples. Et ce qui définira un individu, c’est une vibration.

[Tentative explanation: A compound pendulum may be considered a pendulum on a pendulum. Because physical pendulums have infinitely many mass points, they can be thought of as being made up of infinitely many simple pendulums, which explains the wave-like arc in the string's swing. See links below for more.]

But, Deleuze counters, if the individual is like a compound pendulum made up of infinitely small simple pendulums, then these simple pendulums would have to have magnitude, but we know that as infinitely small they do not have magnitude. The relations between infinitely small parts cannot be vibrational, rather

between infinitely small terms, if we understand what is meant in the 17th century by the infinitely small, that is: which have no distributive existence, but which necessarily enter into an infinite collection, between infinitely small terms, there can only be one type of relation: differential relations.

entre des termes infiniment petits, si on comprend ce que veut dire au XVIIe siècle l’infiniment petit, c’est à dire: qui n’a pas d’existence distributive, mais qui entre nécessairement dans une collection infinie, et bien entre termes infiniment petits, il ne peut y avoir qu’un type de rapport: des rapports différentiels.

Differential relations subsist when the terms vanish [see Deleuze's explanation from the previous lecture.]
There were three types of relation known in the 17th century:
1) Fractional relations (known for a long time); e.g. 2/3
2) Algebraic relations (receiving firm status with Descartes); e.g. ax +by = etc, from which we obtain x/y.
3) Differential relations; e.g. dy/dx = z.

Fractions are irreducibly relations. 2/3 is not a number, because no number times three yields 2.
So a fraction is not a number but rather is a complex of numbers, although by convention we treat them as numbers when we use fractional symbolism for what are normally numbers, for example 4/2 for 2. Thus the fraction already presents a sort of relation that is independent of its terms.

However, in a fraction, the terms must be specified, we must still say "2" over "3." But in an algebraic relation we may use variables instead of specific terms; we may say "x" over "y." Here we have an even greater independence of the relation to its terms. However, even though x and y have variable values, they must still have a value:

it is again necessary that my variables have a determinable value. In other words, x and y can have all sorts of singular values, but they must have one.

the relation is quite independent of every particular value of the variable, but it is not independent of a determinable value of the variable.

il faut encore que mes variables aient une valeur déterminable. En d’autres termes x et y peuvent avoir toutes sortes de valeurs singulières, mais ils doivent en avoir une.

et le rapport est bien indépendant de toute valeur particulière de la variable, mais il n’est pas indépendant d’une valeur déterminable de la variable.

[Hegel makes the same point in Science of Logic

The differential relation takes a third step. Deleuze reviews from his last lecture that:

dy in relation to y = 0; it is an infinitely small quantity. Dx in relation to x equals zero; therefore I can write, and they wrote constantly in the 17th century, in this form: dy over dx = 0 over 0: dy/dx=0/0.

dy par rapport à y égal zéro; c’est une quantité infiniment petite. Dx par rapport à x égal zéro; donc je peux écrire, et ils écrivent constamment au dix-septième siècle, sous cette forme: dy sur dx = O sur O.

But this relation of zero over zero does not equal zero, because the relation between dy and dx subsists even as the terms vanish.

This time, the terms between which the relation is established are neither determined, nor determinable. Only the relation between its terms is determined.

Cette fois-ci les termes entre lesquels le rapport s’établit ne sont ni déterminés, ni même déterminables.

[See Hegel's description, Science of Logic
dx/dy = z tells us nothing about dx or dy themselves, but it does tell us something about their relation, which is z, a third term; for example, it tells us something about the "trigonometric tangent."

Hence the logic of relations.

We will say of z‚ that it is the limit of the differential relation. In other words, the differential relation tends towards a limit. When the terms of the relation vanish, x‚ and y, and become dy and dx, when the terms of the relation vanish, the relation subsists because it tends towards a limit, z‚. When the relation is established between infinitely small terms, it does not cancel itself out at the same time as its terms, but tends towards a limit.

On dira de z que c’est la limite du rapport différentiel. En d’autres termes le rapport différentiel tend vers une limite. Lorsque les termes du rapport s’évanouissent, x et y, et deviennent dy et dx, lorsque les termes du rapport s’évanouissent, le rapport subsiste parce que il tend vers une limite: z. Lorsque le rapport s’établit entre termes infiniment petits, il ne s’annule pas en même temps que ses termes, il tend vers une limite.

So unlike Gueroult, Deleuze says that relation of proportions of movement and rest in the collection of infinitely small parts is not like the vibration of pendulum movement, but rather it is a differential relation: "It is a differential relation such that it is manifested in the infinite sets, in the infinite sets of the infinitely small." (C’est un rapport différentiel tel qu’il se dégage dans les ensembles infinis, dans les ensembles infinis d’infiniment petits).

Deleuze offers his example from Spinoza's Letter on Blood:

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.

[What makes the blood is not its contents, but their differential proportion, their pure relation of difference.]

The infinite sets of simple bodies do not exist by themselves: they are what they are only through their differential relations, hence they are already related and grouped together by those proportions defining their differential relations. Just like dx and dy each alone is nothing in comparison to x and y, because they are infinitesimal, but only exist through their differential relations, so too the infinitely small simple bodies of Spinoza's individual.

Power is what distinguishes one infinite set from another.

the infinite sets have different powers [puissances], and that which appears quite obviously in this thought of the actual infinite is the idea of the power [puissance] of an set.

les ensembles infinis ont des puissances différentes, et ce qui apparaît de toute évidence dans cette pensée de l’infini actuel, c’est l’idée de puissance d’un ensemble.

We cannot say that one infinite set is different from another on account of the number of terms in their sets, because it is infinite in both cases.

infinite sets are defined as infinite under such and such a differential relation. Between other terms the differential relations can be considered as the power [puissance] of an infinite set. Because of this an infinite set will be able to be of a higher power [puissance] than another infinite set.

les ensembles infinis se définissant comme infinis sous tel ou tel rapports différentiels. Entre d’autres termes les rapports différentiels pourront être considérés comme la puissance d’un ensemble infini. Dès lors un ensemble infini pourra être à une plus haute puissance qu’un autre ensemble infini.

We know that our collections of infinitely small parts interact with exterior such collections, and 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.

Deleuze offers 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!

The infinitely small parts that belong to us are composed under a certain relation that characterizes us, but they are not added but summed by integration:

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.

What makes our characteristic set of relations of movement and rest our own is that they express our singular essence.

each individual is a singular essence, each singular essence expresses itself in the characteristic relations of the differential relation type, and under these differential relations, the infinite collections of the infinitely small belong to the individual.

chaque individu est une essence singulière, laquelle essence singulière s’exprime dans des rapports caractéristiques de types rapports différentiels, et sous ces rapports différentiels des collections infinies d’infiniment petits appartiennent à l’individu.

When dealing with essence, we are no longer in the domain of existence.

to exist is to have an infinity of extensive parts, of extrinsic parts, to have an infinity of infinitely small extrinsic parts, which belong to me under a certain relation. Insofar as I have, in effect, extensive parts which belong to me under a certain relation, infinitely small parts which belong to me, I can say: I exist.

exister c’est avoir une infinité de partes extensives, de parties extrinsèques, avoir une infinité de parties extrinsèques infiniment petites, qui m’appartiennent sous un certains rapport. Tant que j’ai, en effet, des parties extensives qui m’appartiennent sous un certain rapport, des parties infiniment petites qui m’appartiennent, je peux dire: j’existe.

To die means that the parts which belong to us cease to belong to us.

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.

When we die, our relations are no longer put in effect. But recall how the differential relation remains as its terms vanish:

there is an eternal truth of the relation, in other words there is a consistency of the relation even when it is not put into effect by actual parts, there is an actuality of the relation, even when it ceases to be put into effect. That which disappears with death is the effectuation of the relation, it is not the relation itself.

il y a une vérité éternelle du rapport, en d’autres termes il y a une consistance du rapport même quand il n’est pas effectué par des parties actuelles, il y a une actualité du rapport, même quand il cesse d’être effectué. Ce qui disparaît avec la mort, c’est l’effectuation du rapport, ce n’est pas le rapport lui-même.

Also, the essence expresses a reality in the relation; in fact, "there is a reality of the essence independent of knowing if the actually given parts putting the relation into effect conform with the essence." (il y a une réalité de l’essence indépendamment de savoir si des parties actuellement données effectuent le rapport conforme à l’essence).

So both the relation and the essence bear a species of eternity that is eternal by virtue of its cause and not by virtue of itself,

therefore the singular essence and the characteristic relations in which this essence expresses itself are eternal, while what is transitory, and what defines my existence, is uniquely the time during which the infinitely small extensive parts belong to me, that is to say put the relation into effect.

donc l’essence singulière et les rapports caractéristiques dans lesquels cette essence s’exprime sont éternels, tandis que ce qui est transitoire, et ce qui définit mon existence c’est uniquement le temps durant lequel des parties extensives infiniment petites m’appartiennent, c’est à dire effectuent le rapport.

In a sense, our singular essence has an existence that should not be confused with the existence of the individual who has that essence.

It is very important because you see where Spinoza is heading, and his whole system is founded on it: it is a system in which everything that is is real. Never, never has such a negation of the category of possibility been carried so far. Essences are not possibilities. There is nothing possible, everything that is is real. In other words essences don't define possibililties of existence, essences are themselves existences.

C’est très important parce que vous voyez où tend Spinoza, et tout son système est fondé là-dessus: c’est un système dans lequel tout ce qui est réel. Jamais, jamais n’est portée aussi loin une telle négation de la catégorie de possibilité. Les essences ne sont pas des possibles. Il n’y a rien de possible, tout ce qui est réel. En d’autres termes les essences ne définissent pas des possibilités d’existence, les essences sont elles-mêmes des existences.

Spinoza then goes further then other 17th century thinkers. In Leibniz, essences are logical possibilities:

For example, there is an essence of Adam, there is an essence of Peter, there is an essence of Paul, and they are possibles. As long as Peter, Paul, etc. don't exist, we can only define the essence as a possible, as something which is possible.

Par exemple, il y a une essence d’Adam, il y a une essence de Pierre, il y a une essence de Paul, et c’est des possibles. Tant que Pierre, Paul, etc., n’existent pas, on ne peut définir l’essence que comme un possible, que comme quelque chose de possible.

To explain how possibility intersects with existence, Leibniz uses the notion of tendency, although in a way different from Spinoza.

With Leibniz singular essences are simply possibles, they are special possibles since they tend with all their force to exist. It is necessary to introduce into the logical category of possibility a tendency to existence.

Chez Leibniz les essences singulières sont des possibles simplement ce sont des possibles spéciaux parce qu’ils tendent de toutes leurs forces à l’existence. Il faut introduire dans la catégorie logique de possibilité une tendance à l’existence.

But Spinoza wants to do away with the possible.

What he wants is the radical destruction of the category of the possible. There is only the real. In other words, essence isn't a logical possibility, essence is a physical reality.

ce qu’il veut c’est la destruction radicale de la catégorie de possible. Il n’y a que du réel. En d’autres termes l’essence ce n’est pas une possibilité logique, l’essence c’est une réalité physique.

So when Paul dies, his essence maintains a physical reality. Thus there are two beings: the being of Paul's existence, and the being of his essence. Moreover, there are two existence's: Paul's existence and his essence's existence. His existence is transitory, his essence immortal.

But physical realities of essences are not the same as the physical reality of existences.

Spinoza has us imagine a white wall, and on it we draw two men, and we can say they exist. Before they were drawn, nothing exists on the wall.

The white wall is analogous to the attribute, to extension. In extension is found extension. Bodies exist in extension when they are effectively traced, that is, when it has a shape. An attribute's mode is such a shape, which is our only means for distinguishing bodies.

If you haven't traced the shape, you cannot distinguish something on the white wall. The white wall is uniformly white.

Si vous n’avez pas tracé de figure, vous ne pouvez pas distinguer quelque chose sur le mur blanc. Le mur blanc est uniformément blanc.

Essences are singular in the sense that we may distinguish the essence from the existence of Paul.

Now, if essences are singular, it is necessary to distinguish something on the white wall without the shapes necessarily having been traced.

Or, si les essences sont singulières, il faut bien distinguer quelque chose sur le mur blanc sans que les figures soient nécessairement tracées.

Furthermore, in Ethics Part II, Proposition 7, 8, etc., Spinoza makes the bizarre claim that

modes exist in the attribute in two ways; on the one hand they exist insofar as they are comprised and contained in the attribute; and, on the other, insofar as it is said that they have duration. Two existences: durational existence, immanent existence.

les modes existent dans l’attribut comme de deux façons; ils existent d’une part en tant qu’ils sont compris ou contenus dans l’attribut, et d’autre part en tant qu’on dit qu’ils durent. Deux existences: existence durante, existence immanente.

To explain how modes are distinguishable in their attribute, Spinoza only gives us an example.

does a shape have a certain mode of existence when it isn't traced? Does a shape exist in extension when it isn't traced in extension? The whole text seems to say: yes, and the whole text seems to say: complete this yourselves.

est-ce qu’une figure a un certain mode d’existence alors qu’elle n’est pas tracée? Et ce qu’une figure existe dans l’étendue alors qu’elle n’est pas tracée en extension? Tout le texte semble dire: oui, et tout le texte semble dire: complétez de vous même.

To complete the problem himself, he calls upon his heart:

But after all I'm trying to complete it with all my heart before completing it with knowledge. Let's call on our hearts. I take on one side my white wall, on the other side my drawings on the white wall. I have drawn on the wall. And my question is this: can I distinguish on the white wall things independently of the shapes drawn, can I make distinctions which are not distinctions between shapes?

Mais après tout j’essaie de compléter avec mon cœur avant de compléter avec du savoir. Faisons appel à notre cœur. Je tiens d’un côté mon mur blanc, d’un autre côté mes dessins sur le mur blanc. J’ai dessiné sur le mur. Et ma question est ceci: est-ce que je peux distinguer sur le mur blanc des choses indépendamment de figures dessinés, est-ce que je peux faire des distinctions qui ne soient pas des distinctions entre figures?

Indeed, there is another mode of distinction.

It is that the white has degrees! And I can vary the degrees of whiteness. One degree of whiteness is distinguished from another degree of whiteness in a totally different way than that by which a shape on the white wall is distinguished from another shape on the white wall.

the white has distinctions of gradus. There are degrees, and the degrees are not confused with the shapes. You say: such a degree of white, in the sense of such a degree of light. A degree of light, a degree of whiteness, is not a shape. And even though two degrees are distinguished, two degrees aren't distinguished like shapes in space. I would say that shapes are distinguished externally, taking account of their common parts. I would say of degrees that it is a completely different type of distinction, that there is an intrinsic distinction.

C’est que le blanc a des degrés. Et je peux faire varier les degrés du blanc. Un degré de blanc se distingue d’un autre degré de blanc d’une toute autre façon qu’une figure sur le mur blanc se distingue d’une autre figure sur le mur blanc.

leblanc a des distinction de gradus, il y a des degrés, et les degrés ne se confondent pas avec des figures. Vous direz: tel degré de blanc, au sens de tel degré de lumière. Un degré de lumière, un degré de blanc, ce n’est pas une figure. Et pourtant deux degrés se distinguent, deux degrés ne se distinguent pas comme des figures dans l’espace. Je dirais des figures qu’elles se distinguent extrinsèquement, compte tenu de leurs parties communes. Je dirais des degrés que c’est un tout autre type de distinction, qu’il y a une distinction intrinsèque.

Deleuze proceeds to make terminological distinctions.

My white wall, the white of the white wall, I will call: quality. The determination of shapes on the white wall I will call: magnitude, or length --I will say why I use the apparently bizarre word magnitude [grandeur]. Magnitude, or length, or extensive quantity. Extensive quantity is in effect the quantity which is composed of parts. Recall the existing mode, existing me, is defined precisely by the infinity of parts which belong to me. What else is there besides quality, the white, and extensive quantity, magnitude or length, there are degrees. There are degrees which are what, which we call in general: intensive quantities, and which are in fact just as different from quality as from extensive quantity. These are degrees or intensities.

Mon mur blanc, le blanc du mur blanc, je l’appellerais: qualité. La détermination des figures sur le mur blanc je l’appellerais: grandeur, ou longueur — je dirais pourquoi j’emploie ce mot en apparence bizarre de longueur. Grandeur, ou longueur, ou quantité extensive. La quantité extensive c’est en effet la quantité qui est composée de parties. Vous vous rappelez le mode existant, moi existant, ça se définit précisément par l’infinité de parties qui m’appartiennent. Qu’est-ce qu’il y a d’autre que de la qualité, le blanc, et la quantité extensive, grandeur ou longueur, il y a les degrés. Il y a les degrés qui sont quoi, qu’on appelle en général: les quantités intensives, et qui en fait sont aussi différentes de la qualité que de la quantité intensive. Ce sont des degrés ou intensités.

Dun Scotus, like many Medievals, used the example of the white wall as well.

He said: quality, the white, has an infinity of intrinsic modes. He wrote in Latin: modus intrinsecus. And Duns Scotus here innovated, invented a theory of intrinsic modes. A quality has an infinity of intrinsic modes. Intrinsic modes, what are they, and he says: the white has an infinity of intrinsic modes, these are the intensities of white. Understand: white equals light in the example. An infinity of luminous intensities.

Il disait: la qualité, le blanc, a une infinité de modes intrinsèques. Il écrivait en latin: modus intrinsecus. Et Duns Scott, là, lui, innove, invente une théorie des modes intrinsèques. Une qualité a une infinité de modes intrinsèques. Modus intrinsecus, qu’est-ce que c’est ça, et il disait: le blanc a une infinité de modes intrinsèques, c’est les intensités du blanc. Comprenez: blanc égal lumière, dans l’exemple. Une infinité d’intensités lumineuses.

But when Scotus speaks of qualities, he also means forms, and so responds to Aristotle. Many theologians would not agree with Scotus that form has intrinsic modes, because they would hold instead that "a form would be invariable in itself, and that only existing things vary in which form puts itself into effect."

We must keep in mind three terms, form, extrinsic mode (that in which the form puts itself into effect), and latitude:

A form has also a kind [espèce] -- as they say in the Middle Ages -- a kind of latitude, a latitude of form, which has degrees, the intrinsic degrees of form. Good. These are intensities, therefore intensive quantities. What distinguishes them? How is one degree distinguished from another degree? Here, I insist on this because the theory of intensive quantities is like the conception of differential calculus of which I have spoken, it is determinant throughout the whole of the Middle Ages. What's more, it is related to problems of theology, there is a whole theory of intensities at the level of theology.

Une forme a aussi une espèce de — comme ils disent au Moyen Age —, une espèce de latitude, une latitude de la forme, elle a des degrés, les degrés intrinsèques de la forme. Bon. C’est les intensités donc, des quantités intensives, qu’est-ce qui les distingue? Comment un degré se distingue-t-il d’un autre degré? Là, j’insiste là-dessus parce que la théorie des quantités intensives c’est comme la conception du calcul différentiel dont je parle, elle est déterminante dans tout le moyen âge. Bien plus elle est liée à des problèmes de théologie, il y a tout une théorie des intensités au niveau de la théologie.

The theology of intensity involved an individuation of the Trinity by means of intrinsic modes.

[Tape ends]

Deleuze, Gilles. "Cours Vincennes: 10/03/1981". webdeleuze.com

English and French versions available here. With profound gratitude I thank Richard Pinhas for providing these texts.

Image of compound pendulum as meter stick:

Huygens and image of different mass points on compound pendulum:

Physical pendulum defined as compound pendulum:

Description of construction of compound pendulum:

Physical pendulum as being made up of infinite mathematical pendulums at each point: