18 Dec 2008

Deleuze's Expressionism in Philosophy Ch.13 "Modal Existence," summarized

Gilles Deleuze

Spinoza et le problème de l'expression
Expressionism in Philosophy: Spinoza

Ch. 13
"L'existence du mode"
"Modal Existence"

Because the mode's essence is not the cause of the mode's existence, each existing mode is caused to be by another existing mode. Existing modes, then, need many other modes preceding them and coinciding with them, and thus a mode consists of many parts originating elsewhere that "begin to belong to it as soon as it comes to exist by virtue of an external cause, that are renewed in the play of causes while the mode exists, and that cease to belong to it when it passes away" (commencent à lui appartenir dès qu'il existe en vertu d'une cause extérieure, qui se renouvellent sous le jeu des causes, tant qu'il existe, et qui cessent de lui appartenir dès qu'il meurt) (183bc/201c) [Citations give French version first, followed by English.]

Thus modal existence consists in a mode's possessing a great number of parts that are external to the mode's essence and external to one another, because they are extensive parts (183cd/201cd).

For Spinoza, all modes consist of many extensive parts, including the soul, which is made-up of many ideas corresponding to its body's extrinsically distinct constituent parts (183-184/201-202). [See previous chapter for more on extrinsic extensive modal parts.]

a mode's essence is a determinate degree of intensity, an irreducible degree of power; a mode exists, if it actually possesses a very great number of extensive parts corresponding to its essence or degree of power.

une essence de mode est un degré déterminé d'intensité, un degré de puissance irréductible; le mode existe, lorsqu'il possède actuellement un très grand nombre de parties extensives qui correspondent à son essence ou degré de puissance.


[See previous chapter, Cours Vincennes: 10/03/1981, Cours Vincennes: 17/02/1981, and Cours Vincennes: 20/01/1981, for more on Deleuze's degrees of power. Also see Oresme's Latitude of Forms for degrees of intensity]

Spinoza's Letter on Infinity to Meyer helps us grasp what he means by "a very great number." Certain magnitudes are infinite on account of their being indefinite; their parts cannot be expressed by any finite number because they exceed any given or givable number [see the beginning of Deleuze's Cours Vincennes 10/03/1981 for more on indefinite magnitudes.] This is the second, modal, quantitative extensive infinity, which Spinoza illustrates with his famous diagram of the non-concentric circles whose sum of unequal distances cannot be given a finite number. (184b/202b). [see the previous chapter for further description of this extensive infinity; see Cours Vincennes: 20/01/1981 for Deleuze's explanation of Spinoza's diagram.]

This sort of infinity has three negative traits:

1) It is neither constant nor equal to itself, because we may conceive it as being both greater and less; for, in both the whole space between non-concentric circles as well as in half that space, there is in each case a quantity that exceeds any assignable number, and yet, in the whole space we know there still to be twice as many parts as the half-space. Thus we conceive extensive infinities in terms of their being greater or less, even if we cannot determine their exact numerical value. (184c.d/202c.d)

2) It is not unlimited, because it is contained within maximum and minimum boundaries delimiting a determinate space. (185a/202d)

3) It's quantity is not infinity due to the multitude of its parts, because if it were, then there would not be greater and lesser infinities. (185a/203a) [So what makes them infinite is the fact that an infinite substance underlies them, and is always "giving" more extensivity no matter how much it is divided. So it is infinite not on account of the number of divisions we may make, but on account of the fact that there is a principle of infinity which prevents any division from being final. As Deleuze writes: "It is not from the number of its parts that the quantity is infinite, but rather because it is infinite that it divides into a multitude of parts exceeding any number".]

Even though for certain purposes it is useful to identify number with modal quantity, really number can never adequately express modality. We know that substance along with its qualities is unitary, so it was convenient for us to consider modes as numerically distinct. But when we conceive modes numerically, we are merely imagining them in an abstract way. Nonetheless, modal being is quantitative, even if it is not numerical. (185b/203b)

The primary modal infinity is intensive infinity, which cannot be divided into extensive parts. We cannot separate from one another its intensive intrinsic parts, which are the modal essences. However, when we conceive them abstractly as though they were separate from one another, then number applies to them. [For example, when we regard general regions of common shades of white on the white wall as distinct from other ones, we are conceiving these regions not as they are in their complex continuity, but abstractly as though numerically different from one another. See previous chapter and Cours Vincennes: 10/03/1981 for Deleuze's elaboration of the white wall example.]

The secondary modal infinity is extensive infinity, which is divisible into infinite collections of extrinsic parts composing existing things. Because they are always infinitely divisible, their sum always exceeds any given or givable number, so we cannot grasp the real being of extrinsic parts by means of number either. [Deleuze explains these infinities in the previous chapter; see also Cours Vincennes 10/03/1981 and Cours Vincennes: 20/01/1981.]

Spinoza's Letter on Infinity to Meyer articulates the variability and divisibility of the extensive modal infinity (185d/203d). Where these extensive infinities pertain to modal existences, intensive infinities belong to modal essences. So composite modes are made up of so great a number of parts that no number may determine the quantity. The existence of these modes depends on them actually having that infinity of parts. So modal essences have degrees of power. This is analogous to the limits of the circle: spaces with more distant limits have greater variations of difference, hence larger infinities. These greater ranges of differential variations corresponds to the higher degrees of power of the mode. (186a.c/204a.c) Modes with double the degree of power compared to another also have double the infinity of parts:

Existing modes have an infinity (a very great number) of parts; their essences or degrees of power always correspond to a limit (a maximum or minimum); all existing modes taken together, not only contemporaneous but also successive ones, constitute the greatest infinity, itself divisible into infinities greater or less than one another.

C'est le mode existant qui a une infinité de parties (un très grand nombre) ; c'est son essence ou degré de puissance qui forme toujours une limite (un maximum et un minimum) ; c'est l'ensemble des modes existants, non seulement simultanés mais successifs, qui constitue le plus grand infini, lui-même divisible en infinis plus ou moins grands.


But extensive parts are not atoms; for

1) atoms imply a void [I suppose either between them, which make them non-continuous, or within them, which makes them non-divisible], and

2) an infinity of atoms would not constitute something limited, because rather it would be unlimited and infinite.

Moreover, the extensive parts are not virtual components of infinite division, because if they were virtual, the modes they make up could not be greater or lesser infinities [in actuality]. (187a/204d)

The ultimate extensive parts are in fact the actual infinitely small parts of an infinity that is itself actual.

En vérité, les ultimes parties extensives sont les parties infiniment petites actuelles d'un infini lui-même actuel.


[for more on actual infinity, see Spinoza's 12th Letter and Gueroult's commentary, Deleuze's Cours Vincennes: 10/03/1981. and Deleuze's commentary on Spinoza's critique of Boyle's notion of divisibility].

Footnote eleven refers to the sixth letter to Oldenburg. [See entry on Boyle, Spinoza, and Deleuze for a more complete look at this debate.]

In the footnote Deleuze writes:

The reality of simple bodies lies beyond any possible perception. For perception belongs only to composite modes with an infinity of parts, and itself grasps only such composites. Simple parts are not perceived, but apprehended by reason.


Les corps simples ne sont réels qu'en deçà de toute perception possible. Car la perception n'appartient qu'à des modes composés d'une infinité de parties, et ne saisit elle que de tels composés. Les parties simples ne sont pas perçues, mais appréhendées par le raisonnement.


In the "On Fluidity" section of the sixth letter, Spinoza opens by saying that notions which explicate Nature insofar as she relates to our senses are not ideas of the highest generality, and they should not be mixed with pure ideas explicating Nature as she is in herself. Examples of notions explicating Nature in relation to our senses are visible, invisible, hot, cold, fluid, and solid; examples of pure notions explicating Nature are motion, rest, and their laws. (Spinoza 78b.c) So some aspects of Nature, such as its actual infinity, cannot be assigned sensible traits, but must be understood only by means of abstract concepts.

Spinoza later explains that no experiment can confirm the divisibility of bodies, because it is only by "reason and calculation that we divide bodies to infinity." (78-79)

Deleuze's point is that we cannot get stuck in what only seems to be contradiction in Spinoza's holding both that there is infinite divisibility as well as that there are absolutely simple bodies. Deleuze elsewhere gives the example of integral differentials to show how this combination of ideas is conceivable.

Thus attributes have both infinite intensive quantity, and as well infinite extensive quantity that is divided into an infinity of extensive parts, which act on one another exteriorly and are distinguished externally. (Deleuze 205a.b)

As a whole, and in all their relations, they form an infinitely changeable universe, corresponding to God's omnipotence. But in this or that determinate relation they form greater or lesser infinite wholes, corresponding to this or that degree of power, in other words, to this or that modal essence. (205bc)

Toutes ensemble et sous tous leurs rapports, elles forment un univers infiniment changeant, correspondant à la toute-puissance de Dieu. Mais sous tel ou tel rapport déterminé, elles forment des ensembles infinis plus ou moins grands, qui correspondent à tel ou tel degré de puissance, c'est-à-dire à telle ou telle essence de mode. (187c)

Motion and rest externally and extrinsically distinguish Extension's simple bodies. Certain infinite wholes are defined by the movement and rest of constituent parts, and these wholes correspond to their modal essences, which are certain degrees of power. (188b/205d) All extensive modes that are together related in one single whole make-up the "sum of all the variations of matter in movement" and thus "the face of the whole universe" in Extension. This whole of extensive parts corresponds to God's omnipotence (toute-puissance), because it comprises all the degrees of power, hence all the modal essences, in Extension. (188c/206a)

Rivaud's interpretation calls for an essence for each external part, but extensive parts and degrees of intensity (intensive parts) do not correspond term for term. So no matter how small the intensive degree, an infinity of extensive parts with extrinsic relations corresponds to it. And extensive parts always comes greater or lesser infinities. So no matter how small the essence, an infinity of extensive parts corresponds to it. Each part of the extensive infinity does not have an essence that belongs to it, nor do they have an independent existence, because they are extrinsically distinguished from and related to each other.

They have no existence of their own, but existence is composed of them: to exist is to actually have an infinity of extensive parts.

Elles n'ont pas d'existence propre, mais composent l'existence: exister, c'est avoir actuellement une infinité de parties extensives.


The infinities of simple bodies correspond to their essence "in a certain relation of movement and rest."

A given mode "comes to exist," comes into existence, when an infinity of extensive parts enter into a given relation: it continues to exist as long as this relation holds. Extensive parts are thus grouped together in various collections on various levels of relation (rapports gradués), corresponding to different degrees of power.

Tel mode « vient à exister » , il passe à l'existence, quand une infinité de parties extensives entrent sous tel rapport; il continue d'exister tant que ce rapport est effectué. C'est donc sous des rapports gradués que les parties extensives se groupent en ensembles variés, correspondant à différents degrés de puissance.


In one given relation, the extensive parts might correspond to some essence and existence, but then form another whole when entering into another relation, thus corresponding to another modal essence (190c/208b). [Deleuze's wording suggests a different interpretation as well, because he does not clarify if the relations are simultaneous or successive. If he means that they are simultaneous, then we can think of orders of relation: our heart has an essence, but because of its interactions of movement and rest with every other part of our body, the heart can simultaneously be thought of both a whole unto itself and a part of a larger organism. The other interpretation is dynamic as well as almost atomic: the simple bodies never change, only their relations change, so what was wood can become smoke when its component parts take on different extrinsic relations of movement and rest. Because in the next sentence he refers to this as the "coming into existence of modes," I have chosen the latter interpretation. And although I have decided on this meaning, we see that in an important letter for Deleuze, the 32 letter to Oldenburg, the Letter on Blood, Spinoza writes:

By coherence of parts I mean simply this, that the laws or nature of one part adapts itself to the laws or nature of another part in such wise that there is the least possible opposition between them. On the question of whole and parts, I consider things as parts of a whole to the extent that their natures adapt themselves to one another so that they are in the closest possible agreement. In so far as they are different from one another, to that extent each one forms in our mind a separate idea and is therefore considered as a whole, not a part. For example, when the motions of particles of lymph, chyle, etc. adapt themselves to one another in accordance with size and shape so as to be fully in agreement with one another and to form all together one single fluid, to that extent only are the chyle, lymph, etc. regarded as parts of the blood. But in so far as we conceive the particles of lymph as different from the particles of chyle in respect of shape and motion, to that extent we regard them each as a whole, not a part.

(Spinoza 192-193)]

Existing modes, then, are subject to "considerable and continual alteration" (variations considérables et continuelles) these relations might alter somewhat, but the mode maintains its integrity so long as the relations persist on the whole (190d/208c).

Deleuze then writes:

une essence de mode (degré de puissance) s'exprime éternellement dans un certain rapport gradué,

which Joughin translates as

It must then be recognized that a modal essence (a degree of power) expresses itself eternally in a certain relation, with its various different levels.


[given the following sentence, Deleuze seems here to be emphasizing the fact that the essence is eternal, because he next says that the mode only exists when an infinity of extensive parts enter into the relation that characterizes the essence. With my limited knowledge of French, I cannot know if there are other translations, but if Deleuze means that the modal essences express themselves in graduated relations, this could be important when considering the indivisible intensive infinity and the infinitely divisible extensive infinity: modal essences are in one sense distinct according to their grade of power, but in another sense there is an unbroken continuum of these values, so in another sense they are all one, that is, they are all modalities of one infinite substance. So "graduated" suggest continuum more so than "various."] The simple bodies might rearrange, and then correspond to some other essence.

So there are three components to Spinoza's theory of existence:

1) a singular essence: a degree of power or intensity

2) a particular existence: an infinity of extensive parts making up an existence

3) an individual form: the characteristic or expressive relation corresponding eternally to the mode's essence, but through which an infinity of parts are temporarily related to that essence.

(above quotations, 191b/209a)

The essence of existing modes has a degree of power (its singular essence). The existing mode itself is made up of an infinity of extensive parts (its particular essence). [The higher the degree of power, the greater the intrinsic differentiation, hence the greater the infinity of simple bodies. Because these simple bodies are in differential relations to each other, so we would expect them normally to not be so combined, so it would take greater force to keep them in their characteristic differential ratios together.] The degree of power expresses itself in relations of difference [with greater infinities of difference corresponding to greater degrees of power], and these differential relations characterize the essence [just as the ratio of lymph, chyle, etc. characterize the essence of blood]. Because these relations are differential but yet are "under the domination of one and the same nature," they are "'forced, as this nature demands, to adapt themselves to one another." (191b/209b)

[The original French reads:

D'où la formule de Spinoza: les parties, comme étant « sous la domination d’une seule et même nature » , obligées de s'ajuster les unes aux autres suivant que l'exige cette nature».

The English:

Whence Spinoza's formulation according to which the parts, being under the domination of one and the same nature, are "forced, as this nature demands, to adapt themselves to one another.


Here Deleuze cites letter 32 to Oldenburg, the Letter on Blood. See the quotation above where Spinoza explains that for there to be coherence among the parts, there must be the "least possible opposition between them" by means of their mutually adapting "themselves to one another so that they are in the closest possible agreement." What Deleuze stresses here is not just the agreement, but the fact that it is a matter of "least possible opposition;" so in other words, there is the most possible differential opposition before their whole breaks apart into different wholes, that is, the highest degree of power before that power is greater than the relational structure can handle, as determined by the nature of the characteristic ratios of movement and rest among the parts.]

But the modal essence itself is not what causes the extensive parts to enter into the relations corresponding to the ratios of movement and rest characterizing that essence. So the forces which cause the parts to come into differential relations do not originate in the essence itself. Rather, extensive parts extrinsically determine one another ad infinitum; so modal existences come about in accordance with mechanical laws that determine certain infinities of extensive parts to come into this or that relation, and the modal essence then expresses itself through that externally determined relation. A mode ceases to exist when its parts enter into some other relation that expresses another mode's essence. (191c.d/209-210)

The mechanical laws in Extension are the laws of motion communication. The infinities of simple bodies are "always grouped in constantly changing infinite wholes," (note the French: se groupent en ensembles infinis toujours variables.) There is a whole of all the infinite wholes that is not changing, and its fixity is defined by its total quantity of motion, which is its total proportion of movement and rest. This whole proportion itself contains an infinity of particular relations, that are "made and unmade according to the laws of composition and decomposition" (se font et se défont, suivant des lois de composition et de décomposition). (192a.b/210b.c)

When two composite bodies of different compositional relations meet, their relations may combine upon contact in such a way that all the parts adapt to one another so to compose a third relation. For example, chyle and lymph combining to make blood. However, when relations meet, they might either be indifferent to one another, or one might decompose the relations of the other, thereby destroying it. For example, toxins decompose the blood. Likewise with nutrition, but in a strange way: when we nourish ourselves, we destroy our body's previous relation, but so reconstitute ourselves into a new relation that conforms with our essence. In this way, we "force" (force) our nourished body parts to enter into new relations. (192-193/210-211) [We might explain how we can change our relation and in that way come to conform to the relation characterizing our essence in this way: our essences are part of an intensive continuum in which the degrees of power and their corresponding extensivities are only abstractly distinguishable. So the relation between our extensive parts changes in accordance with the variation in that continuum, and this only seems contradictory if we mistakenly imagine that essences are discrete and that existences are essentially discrete. This of course is mistaking number for magnitude. The existence has degrees of power manifesting as variations in extrinsic relations, with more differential relation corresponding to greater degrees of power. So just as it is illusory to consider one relational whole as distinct from another, so to is it illusory to consider one essence's degree of power as distinct from the others. So it is a matter of our abstract thinking. When does someone die? When the heart stops? When the brain ceases all activity? When the body turns cold? When the body decomposes completely to earth? There is a continuum of passage of the decomposition of the parts from one essential relation to the next. It is up to our abstract thinking to determine when our body is us and when it is decomposed earth. So when we recompose ourselves by nourishing our bodies, our relation changes slightly, but so too does the essence corresponding to those relations change slightly. Those who feel one with the cosmos may likewise consider a much wider range of essential characteristics to belong to them. So in other words, it is up to our own imaginations to arbitrarily cordon off a region of variation of extensivity and essentiality that we call our own, when in actuality there is no such discrete independence: all is substance.]

The laws of composition and decomposition determine when relations become actualized or dis-actualized in existence. So relations are different from essences, because they merely characterize that essence. But the order of relations does not correspond exactly with the order of essences, because all essences are in agreement, but many relations are opposed to each other. Although Deleuze does not have a clear answer to why this is, he still stresses the difference between the orders of essence and relation. (193a.d/211b-212a)

Coming into existence is never a transition from possible to real, because the essence exists necessarily on account of its necessary and infinite cause (194a.c/212b.d).

Because essences were a part of an infinite continuum not with actual parts but with degrees of power, none of which discrete from the other, all essences then are "complicated" (compliquées) in their attribute. When extensive parts relate in such a way as to express a certain modal essence, the mode acquires size and duration, which its attribute does not have. Hence existing modes are extrinsically distinct from one another and from their attribute (194c-195/212-213c) [even though they are all intrinsically one, all degrees of power of substance.]

So the distinction between essence and existence is not a real distinction: the modal essence's existence exists in the attribute, the mode's existence exists outside the attribute. This might seem to contradict Spinoza's immanence; but it does not, because modes continue to be contained in substance even when they come into existence and exist outside one of substance's attributes. So existing modes are not merely contained in substance, they are contained in it and are something more, because while existing in substance or attribute, existing modes take on extrinsic modal distinctions. So when a mode comes into existence, it is posited outside its attribute, but not outside substance, so modal existences are not substantially different from their essences. Deleuze offers an analogy with Kant: both external things and internal things are presented internally to us, but external things are internally presented as external things whereas internal things are internally presented as internal things. So for Spinoza, extensive and intensive quantities belong equally to their attribute, only the extensive quantity takes on a strictly modal form of exteriority. So while it presents the modes as external to their attribute, they are nonetheless contained in it. Thus Spinoza's immanentism is compatible with his theory of extrinsic modal distinction. (195a-196a/213c-214c)

When a mode's essence exists without a corresponding modal existence, it is complicated with other essences and the attribute itself. But when modes become posited extrinsically, they cease to exist in this complicated form.

Their new existence is an explication: they explicate the attribute, each "in a certain and determinate way."

Leur nouvelle existence est une explication: ils expliquent l'attribut, chacun l'explique « d’une manière certaine et déterminée ».


So each existing mode is constituted by a relation that characterizes part of the attribute's essentiality, and thereby the existing modes express their attribute. Their particular manner of explication is one in which parts of the attribute are expressed as relations that are extrinsically distinct from one another and from the attribute itself.

An attribute no longer expresses itself only in the modal essences that it complicates or contains according to their degrees of power; it also expresses itself in existing modes that explicate it in a certain and determinate manner, that is, according to the relations corresponding to their essences. Modal expression as a whole is constituted by this double movement of complication and explication.

L'attribut ne s'exprime plus dans les essences de mode qu'il complique ou contient, conformément à leurs degrés de puissance; il s'exprime en outre dans des modes existants, qui l'expliquent d'une manière certain et déterminée, c'est-à-dire conformément aux rapports qui correspondent à leurs essences. L'expression modale entière est constituée par ce double mouvement de la complication et de l'explication.


The movement of complication is the attribute's bringing the essences together into continuous agreement, and the movement of explication is the modal existences expressing degrees of that continuum extrinsically and extensively, rather than intrinsically and intensively.

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

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