Somers-Hall, (4.8), Deleuze’s Difference and Repetition, ‘4.8 Essence, Possibility and Virtuality (186–8/235–7, 208–14/260–6)’, summary

by Corry Shores
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[The following is summary. All boldface, underlining, and bracketed commentary are my own. Proofreading is incomplete, so please forgive my typos and other distracting mistakes. Somers-Hall is abbreviated SH and Difference and Repetition as DR.]

Summary of

Henry Somers-Hall

Deleuze’s Difference and Repetition:
An Edinburgh Philosophical Guide

Part 1
A Guide to the Text

Chapter 4. Ideas and the Synthesis of Difference

 

4.8 Essence, Possibility and Virtuality (186–8/235–7, 208–14/260–6)

 

 

Brief summary: 
For Deleuze, Ideas are actualized, but they are not essences in the conventional sense of the term. Deleuze, following Bergson, notes two ways we may understand essences. The first is the Aristotelian way of removing everything non-essential. So if we wanted to know the essence of color, we would remove each of their accidental traits. But this gives us only an abstract and empty notion of color. The other way to understand the Idea as an essence is to consider how it implicates complicatedly (that is, how it ‘perplicates’) all actualizations it can take. To make an analogy, the essence of color under this view would be like white light, since we can break white light down into every actualizable color of the spectrum and also recompose that white light by recombining all actual light colors. This notion of the Idea is tied to the distinction between the virtual, actual, and the possible. The Idea is virtual, and the instantiations in spatio-temporal reality that the Idea somehow generates are actual. The virtual is not the possible, since the possible is a deprivation of the existant and also since the possible is not “real,” while instead the virtual is real and is also not deprived. The virtual, then, has three important features. 1) The virtual is real without being actual, since “it provides the structure responsible for the genesis of the qualities we find in actual entities”. 2) The virtual is complete without being entire, because it implies all actualizable determinations and thus is lacking nothing (it is complete), but at the same time, it is infinitely rich in such implications, and thus it can never be exhausted by its actualizations (it is not entire). 3) The Idea is differentiated without being differenciated, since it is composed of differential relations (it is differentiated) whose related parts are by themselves undetermined, meaning they lack an identity to which predicates may be ascribed (it is not, then, differenciated).

 

Summary

We have been looking at how for Deleuze, Ideas find many actual instantiations. But this does not mean for him that Ideas are essences. We could only call an Idea an essence if we mean it in a different way than we normally do, namely as instead “the accident, the event, the sense” (SH 250 qtg. DR 191/241) [But I am not sure what that means yet].  SH says that this claim [that Ideas are not essences at least in the conventional sense] “is inseparable from his claim that Ideas ‘perplicate’ or interpenetrate one another (DR | 187/236)” (SH 150-151). To explain more what he means by Ideas, Deleuze makes reference to examples in Bergson’s “The Life and Work of Ravaisson,” namely that the Idea of color is like white light and the Idea of sound is like white noise. Bergson is concerned with the question of what different colors have in common. [Since what they would all have in common is something very general about color] this inquiry  is about the question of “how we are to think, philosophically, the notion of colour. In effect, we are therefore asking the question ‘what is X?’ for colour, the question Deleuze takes to be ‘the question of essences’ (DR 188/236)” (SH 151). Bergson says there are primarily two ways to answer such a question as this. 1) With an Aristotelian manner of determining essences by removing from each instance whatever is non-essential to it:

The first is the traditional answer to the question of essences provided by Aristotle. In order to determine the essence of something, we abstract from it those properties that are inessential (or accidental), to arrive at purely those properties that every individual in the class has. Thus, ‘we obtain this general idea of colour only by removing from the red that which makes it red, from the blue what makes it blue, from the green what makes it green’ (Bergson 1992: 225). If we try to answer the question ‘what is colour?’ by this means, we end up with a concept that is abstract and empty, as we have proceeded ‘by gradual extinction of the light which brought out the differences between the colours’ (Bergson 1992: 225).
(SH 151)

2) By means of “perplication” [This one is harder to grasp, so let me quote it first.]

The alternative is what Deleuze takes up with his concept of perplication. Bergson suggests that rather than proceeding by abstraction, we proceed by [the following up to citation is Bergson quotation]

taking the thousand and one different shades of blue, violet, green, yellow and red, and passing them through a converging lens, bringing them to a single point. Then appears in all its radiance the pure white light which, perceived here below in the shades which disperse it, enclosed above, in its undivided unity, the indefinite variety of multicoloured rays. (Bergson 1992: 225)

Such an account can only be an analogy, as light is still seen in this case too much along the lines of actual phenomena, but it clarifies the interpenetrative notion of the Idea. Just as the conjunction of the two terms of the differential relation allow us to specify all of the points on a curve, the differentials of the Idea together specify all of the possible states of affairs that a given system can exhibit. Rather than achieving this by excluding what is non-essential, it does so by positively specifying the genetic conditions for each of these states. In this sense, for Deleuze, the Idea does not so much contain the essence of a state of affairs, as the grounds for the totality of possible accidents a system can | exhibit. Depending on how the elements are related to one another, different states of affairs will be generated.
(SH 151-152)

[What we need to take from the example perhaps is that if we start with white light, we see that it implies the full range of color possibilities, since it can be broken down into them, and also the white light can be recomposed were all those colors of light combined. So white is the “essence” of color, in Deleuze’s sense of the Idea, since it contains ‘perplicated’ (perhaps meaning something like ‘implicated complicatedly’) within it implicitly “the totality of possible accidents” the system of color can exhibit. I wonder then if this is like what SH says about state diagrams in his Hegel-Deleuze book. This is another of the great sections in this other book.]

[The next point seems to be that Ideas as these totalities of possible accidents are not of the same nature as the accidents themselves and thus are not of the same nature as the states of affairs, which are actualizations of the accidents. Yet, recall in the example of light that the colors together imply white light and vice versa, even though they are qualitatively different sorts of things, since one has color and the other has none. Thus the genetic conditions for states of affairs, that is, the Ideas, are immanent to the states of affairs while being different in kind. I quote to be sure:]

Clearly, if an Idea is to be understood as forming a multiplicity of interpenetrating elements, then it cannot have the same nature as states of affairs. Elements in states of affairs are determined in an opposite manner to the interpenetrative structure of perplication, namely by determining their limits (what they are not). Furthermore, we can see that just as problems were immanent to their solutions, the genetic conditions for states of affairs (Ideas) are simultaneous with states of affairs themselves. Thus, for Epicurus, atoms co-existed with the sensible objects that they constituted, and for Althusser, the mode of production co-existed with the actual relations that it determined. We thus have two series that differ in kind: actual events that occur within the world, and the ideal events of ‘sections, ablations, adjunctions’ that engender them (DR 188/237).
(SH 152)

SH will now jump [it seems by about 20-30 pages in DR] to the related topic of the Idea and possibility. For Deleuze, the Idea is virtual, and he makes three claims regarding the virtual: 1) it is real without being actual, 2) it is complete without being entire, and 3) it is differentiated without being differenciated. SH will go through these claims, all the while being sure to contrast them with the structure of possibility, since for Deleuze the virtual should never be confused with the possible (152).

1) The virtual is real without being actual. We first consider Kant’s point that there is not difference between a possible and a real object. A hundred real silver coins has the exact same value as a hundred possible ones. The only difference between them is their existential status, since the one actually exists physically and the other does not. “Now, the virtual is instead ‘Real without being actual, ideal without being abstract’ (DR 208/260)” (153). [SH then gives two reasons why this is so. The second one I grasp much better. It is that since the Idea provides the structure responsible for the genesis of actual entities’ qualities, it therefore must be real, even if it is not actual. The first idea I am not sure about. Let me just quote it since it seems to be presented as the less important idea and since I will not interpret it properly myself. Perhaps the thinking here is that actuality and possibility are different in kind, and that is already a strong enough distinction that we do not need to bring into the matter their difference in terms of reality, and then this has something to do with the issue of the virtual being real without being actual. I will quote since as you can see I got it wrong:]

Now, the virtual is instead ‘Real without being actual, ideal without being abstract’ (DR 208/260). Throughout this chapter, we have seen that Ideas are different in kind from actual states of affairs, just as differentials differ from actual numbers. In this sense, we do not need to distinguish possibility from actuality in terms of reality, as they can be distinguished by this difference in kind itself. More than this, however, the virtual is real to the extent that it provides the structure responsible for the genesis of the qualities we find in actual entities. ‘The reality of the virtual is structure’ (DR 209/260). It provides a complete account of the structure of the actual state of affairs that results from it, and is no less a real part of the object than the actual object itself.
(153)

2) It is complete without being entire. [I do not follow this one very well either. Let me quote it first.]

‘The reality of the virtual is structure’ (DR 209/260). It provides a complete account of the structure of the actual state of affairs that results from it, and is no less a real part of the object than the actual object itself. In this regard, Deleuze notes that it is ‘complete without being entire’ (DR 214/266). Deleuze’s point is that the virtual does not rely on any reference to the actual, although in fact it is always found to be associated with the object which it engenders. In this sense, it escapes from the limitation of possibility we discussed in the previous chapter. There, we saw that the concept of possibility could not give us the sense of an object, because it merely reduplicated it at a higher transcendental level of analysis. As such, a possible object is not complete, since it is dependent on the notion of a real object to which we add the concept of non-being. The completeness of the virtual is thus what allows us to understand it as giving the sense of a proposition, even though it is not whole, since ‘every object is double’ (DR 209/261).
(SH 153)

[I do not recall off the top of my head this point about possibility from chapter 3. Perhaps it is in reference to possible states of affairs suggested by the sense of a statement, from section 3.8. There was also discussion of a problem understood in terms of the possibility of its solution in section 3.9, but that does not seem related enough as far as I can tell. I am sorry that I cannot pin this one down. At any rate, we might still be able to extract the important idea here. Perhaps the notion is the following. A possible object is not complete, since we obtain it first by taking the notion of a real object and then subtracting the notion of its actual existence. But that is not how we obtain the notion of the virtual. Rather, it is perhaps like a map of all the differential relations which can find various instantiations in actuality. So it is complete in that no differential relation that could be actualized is left out, just as every variety of color is implicated in the white light. However, perhaps also it can never be exhausted by any actualizations or by any series of them, as perhaps it is infinitely rich, and for that reason it perhaps is complete without being entire, since it can never be fully exhausted. I am guessing.]

3) The Idea is differentiated without being differenciated. SH says this means, “That is, it operates according to an entirely different procedure of determination to that of the possible” (153). [The following is very complicated, and so I am afraid my summary will lack overall coherence. I will just follow the ideas as they are presented, and I will quote it all in the end so it can be understood better.] We first need to recall from chapter 1 how we differentiated things on the basis of ascribing to it its own properties, and thus we needed a concept of identity [in order to make predications to it]. So when “we describe an object by ascribing predicates to a subject,” “we differenciate it” (153). “The other procedure of determination generates structural properties by bringing into relation with each other elements which are in themselves undetermined (they are differentiated, in the sense of the differentials we looked at in 4.2)” (153) [I am not sure what might be an example of this, but perhaps the light example somehow works here]. SH explains that Deleuze uses Leibniz’ distinctions between clear and confused, and distinct and obscure in order to characterize these two sorts of organization. Recall how Leibniz traces the world back to possibility, that is, to possible worlds that God chooses from. So at first it seems that Leibniz will not provide for us a good philosophy for the notion of the virtual. However, his ideas regarding perception will give us “an important insight into the relationship between virtuality and actuality” (154). [The next idea is very complicated. We begin first with an example Leibniz gives of microperceptions, which are the small perceptions of, for example, all the tiny sounds each little wave makes, which together give us the composite total perception of the roar of the sea. What makes this seem complicated at least at first is we have these two levels of micro and macro perceptions, but we also note two languages, which each having two counterpart concepts. So we have the language of the roaring noise of the sea. It is a language of the clear-confused. The clarity comes from the roar being one unified thing that we might distinguish from other things. The confusion comes from the fact that we mix up all the constituent parts in order to make one coherent whole. Then we have the language of the individual waves themselves. This is the language of the distinct-obscure and also of the virtual (but I am not sure if the language of the whole roar is of the actual). It would be distinct if we hear each differential relation, that is, each wave by itself, but that would make the whole obscure, since we then would not be able to take in the roar as a whole mixture of them all. So the basic idea seems to be that there is always a tradeoff. Either we hear it coherently and clearly as a whole, in which case we lose the distinctness of the parts, or we hear the parts distinctly, and thereby lose the sense of the whole that the parts together are making up. Now we need to relate this to the notion that Idea is differentiated without being differenciated. The way this is so is not directly stated, so let us work with the definitions given above. SH explained that we differenciate when “we describe an object by ascribing predicates to a subject”. And something is differentiated when “determination generates structural properties by bringing into relation with each other elements which are in themselves undetermined,” and this is differentiation like in the calculus. In that case, it seems the Idea is differentiated in the sense of it being made of differential relations, but it is not differenciated, since each differentially related undetermined part is not perceived or conceived distinctly from one another, as none have an identity to which predicates can be ascribed.]

Finally, the virtual is differentiated without being differenciated. That is, it operates according to an entirely different procedure of determination to that of the possible. As Deleuze puts it, ‘one [the possible] refers to the form of identity in the concept, whereas the other designates a pure multiplicity in the Idea which radically excludes the identical as a prior condition’ (DR 211–12/263). We saw that Chapter 1 of Difference and Repetition deals at length with the claim that in order to determine something through the properties it possesses, we need some kind of concept of identity. This is because we describe an object by ascribing predicates to a subject (we differenciate it). The other procedure of determination generates structural properties by bringing into relation with each other elements which are in themselves undetermined (they are differentiated, in the sense of the differentials we looked at in 4.2). Deleuze characterises these two modes of organisation in terms of Leibniz’s distinctions between the clear and confused, and the distinct and obscure. We saw in Chapter 1 that Leibniz’s understanding of the world ultimately traces | it back to the notion of possibility, as God chooses the best of all possible worlds. Nevertheless, in his claim that perception of spatio-temporal objects is a confused perception of conceptual relations, we have an important insight into the relationship between virtuality and actuality. In the New Essays on Human Understanding, Leibniz puts forward the claim that perception of objects is based upon microperceptions below the threshold of the senses. In support of this theory, he gives the following analogy [the following up to citation is Leibniz quotation]:

To give a clearer example of these minute perceptions which we are unable to pick out from the crowd, I like to use the example of the roaring noise of the sea which impresses itself on us when we are standing on the shore. To hear this noise as we do, we must hear the parts which make up this whole, that is the noise of each wave, although each of these little noises makes itself known only when combined confusedly with all the others, and would not be noticed if the wave which made it were by itself. (Leibniz 1997: 54)

Deleuze interprets this passage as presenting ‘two languages which are encoded in the language of philosophy and directed at the divergent exercise of the faculties’ (DR 214/266). On the one hand, we have the language of the roaring noise of the sea. This is the language of the clearconfused. It is clear, in so far as I am able recognise the roar of the sea as a whole and take it up as an object, but it is confused as I only do so in so far as I do not take account of the elements (the waves) which together determine it as an object. On the other hand, we have the language of the waves themselves, which is the language of the virtual, and of the distinct-obscure. If, on the contrary, we focus on the noise of the waves themselves, the waves are perceived distinctly, as we grasp the differential relations that make up the noise as a whole, but also obscurely, since our focus on these particular relations precludes our comprehension of the ‘white noise’ of the sea as a whole. In contrast to Descartes’ notion of clear and distinct ideas, Deleuze’s claim is that ‘the clear is confused by itself, in so far as it is clear’ (DR 254/316). It is this radical divergence between the two languages of philosophy that allows us to give the sense of a proposition, or the conditions of experience, without simply falling into a banal reiteration of the structure of actuality.
(153-154)

 

 

 

Citations from:

Somers-Hall, Henry. Deleuze’s Difference and Repetition. An Edinburgh Philosophical Guide. Edinburgh: Edinburgh University, 2013.

Or if otherwise noted:

DR:
Deleuze, Gilles. Difference and Repetition, trans. Paul Patton, New York: Columbia University Press, 1994/London: Continuum, 2004.

Bergson, Henri (1992), The Creative Mind, trans. Mabelle L. Andison, New York: Carol Publishing.

Leibniz, Gottfried Wilhelm (1997), New Essays on Understanding, trans. and ed. Peter Remnant and Jonathan Bennett, Cambridge: Cambridge University Press.

 

 

 

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

by Corry Shores
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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.

(184a/202a)

[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.

(186c/204c)

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.

(187b/205a)

[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.

(381c)

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.

(187d)

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.

(189-190/207c)

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.

(190bc/208b)

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.

(191a/208d)

[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.

(191b/209b)

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 ».

(196b/214cd)

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.

(196c/214-215)

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.