Somers-Hall, (1.4), Deleuze’s Difference and Repetition, ‘1.4 Duns Scotus (35–6/44–5, 39–40/48–9)’, 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 1. Difference in Itself

1.4 Duns Scotus (35–6/44–5, 39–40/48–9)

Very brief summary:

The Aristotelian concept of classification and definition places being higher than God. The medieval theological tradition that builds from Aristotle’s system treats God’s being as different in kind from humanity’s being, which poses other theological problems. Duns Scotus solves all these problems by making being be a degree of perfection that modifies other things. God has an infinite degree of perfection and humans have a finite degree. Thus unlike in the Aristotelian system, being is understood univocally in both cases, as it is the same being in each case. Yet Scotus ultimately compromises this univocity by making the theological claim that the infinite difference in degree between God and humanity is enough to be a difference in kind. Deleuze, however, prefers a more univocal sense of intensive variation.

Brief summary:

The Aristotelian system of genus-species categorization and definition places ‘being’ as the highest category (or highest categories of senses of being). This presents a problem for medieval theologians who want God as the highest category. We note first that the Aristotelian / Aquinian solution is to say that ‘being’ is understood equivocally, in that there is the finite being of our world and the infinite being of God. But being applies to both, since they are analogical (as they have the same cause, God). Duns Scotus objects that we cannot know they are analogical unless we already knew of God’s perfection. Thus our own finite perfection cannot be the basis for us knowing of God’s perfection. Scotus identifies the problem as resulting from making finite and infinite be different in kind rather than different in degree. The infinite being / infinite perfection of God is just a much higher degree of being / perfection than our own. Thus when God’s infinite being is understood intensively, we understand being univocally. It also means that being is not a higher genus than God, since degrees of being / perfection are modes and not properties (and thus not predicates and thus not higher genera) of substances. However, Scotus’ theological position is that, nonetheless, the infinite difference in degree is a difference in kind between God and humanity, which compromises the univocity of his concept of being.

Summary

[We saw previously that Aristotle’s system of classification and definition, which is based on the genus-species distinction, runs into a problem at the highest level of the most general genus, ‘being’. As the most general, all things whatsoever have it has a predicate, since all other things fall under this most general category. However, we cannot define it, since doing so requires a higher genus and other species to distinguish it from. Aristotle offers a solution that compromises the consistency of his system. But perhaps the desire for univocity in a metaphysical system is what is important here. For,] Deleuze then claims that “‘there has only ever been one ontological proposition: Being is univocal’ (DR 35/44)” (SH 30). SH will examine Deleuze’s point of view by tracing his tradition of influence from Duns Scotus through Spinoza to Nietzsche. This will all us to better understand the univocal conception of being. (SH 30d)

We begin with the theological context of Scotus. Medieval theologians thought that God was infinite and as well there are other finite things that are fundamentally different from God. God’s nature is simple, meaning that it is not composed of parts, and God possesses every perfection, for example, God is infinitely good, infinitely wise, and so on (SH 31a). But when we look at objects that we have access to, objects in the finite world, we see that an object having several properties is a complex object” (SH 31) [unlike God, who has several properties but is a simple thing]. [SH then makes a point about equivocation. It seems the reasoning is this. God is of a fundamentally different nature than finite things. But we use the term ‘good’ for God and for finite things. This one term really refers to two concepts, the good of God and the Good of finite things. Since it is the same term in both cases, we are equivocating. By recognizing it as equivocation, we acknowledge that God is transcendent to our world.]

Now the very fact that a term like ‘good’ operates in these different ways when we use it to describe an object or person in the world or to describe God implies that when we use this term, we are equivocating. That is, that the same term names two different concepts, good-for-God, and good-in-the-finite-world. Such a position has certain advantages – in that it makes clear that God is a transcendent entity that cannot be adequately understood according to our categories of thought – but is ultimately untenable as it renders any relation to or understanding of God impossible.
(31)

[Recall that paronymous meanings refer to a focal meaning. SH refers again to this notion of focal meaning, but now in the context of analogy. (It is not clear to me if paronymous meanings are analogous.) Analogy here is matter of likeness. For Aquinas, if one cause causes two equivocal things, then they are analogous. Thus on the basis of finite good, we can understand by analogy God’s goodness, since God caused both.]

It is here that Aquinas brings in the notion of analogy. As we saw with Aristotle, analogy allows us to relate terms that have something in common (a focal meaning), but yet differ. Aquinas’ use of analogy relies on the likeness of cause and effect (our goodness is caused by God, so there must be some analogy between infinite and finite goodness, since effects resemble their causes). In this instance, therefore, God’s goodness is the focal meaning by which finite goodness gets its own meaning.
(31)

[We now get Scotus’ definition of univocity. But we do not get an example but rather only a counter example, so it as of now a little unclear to me. The counter example is health. It is not univocal. For, since it has a different sense in different applications, any some of those senses can be used in a particular case and others not. Nutrition is a cause of health, but it may not be a sign of health, as perhaps people who are otherwise unhealthy for other reasons can still eat nutritionally.]

It is against this view that Scotus develops his own position: a univocal theory of religious language. He defines univocity as follows: ‘I designate that concept univocal which possesses sufficient unity in itself, so that to affirm or deny it of one and the same thing would be a contradiction’ (Duns Scotus 1978b: 20). Effectively, univocity therefore means that a word is used in the same sense in all contexts, unlike ‘health’, for instance, whose meaning changes depending on what we are relating it to.
(SH 31)

[The implication here seems to be that, contra Aristotle, ‘being’ is univocal in this more absolute sense and not in Aristotle’s analogical sense.] There are two basic reasons Scotus thinks that ‘being’ has this sort of univocity. 1) [In the analogical account of knowledge of God, it might be implied that in order to know that God exists, we might need to see some kind of causal proof of his existence in the world. However,] “we can believe that God exists without knowing anything further about him, even whether he is finite or infinite” (31). And 2) [This one is built on a premise that I cannot explain. For some reason, in order to make the analogy that for example finite goodness is like infinite goodness, we need to have some knowledge of the relationship between God’s nature and his attributes. Perhaps the idea here is that we might see goodness in the finite world, but so long as we do not already have knowledge that God has goodness, we would never make the analogical association between finite and his infinite goodness. I will quote for your interpretation:] “Second, the alternative theory of analogy suffers from a key problem: in order for the analogy to work, we seem to require some knowledge of the relationship between God’s nature and his attributes. Such an analogical argument presupposes some form of understanding of God’s nature” (31d). [The reasoning in the following step is also unclear to me. It seems the thinking is this. To understand God in the Aristotelian / scholastic approach, we need to already know God is infinite and we finite. For otherwise, perhaps, there is no basis to say one is fundamentally different from the other and nonetheless analogical. I am not sure, but perhaps we also here must equate God with being. But if we take God/being to be univocal, we are not concerned with infinite and finite, since God/being is univocal only if it has the same sense in all its applications. I again quote for your interpretation:] “Scotus instead takes being to be univocal and ‘indifferen[t] to what is infinite and finite’ (Duns Scotus 1987a: 2)” (SH 32d). [Perhaps we are also assuming here that both the infinite of God and the finite of our world both have being. This also means that on the basis of the concept of being alone, we cannot differentiate God’s being from our own.] “Now | this raises a problem, since we want to see God as separate from man” (SH 31-32). [But by making the meaning of being dependent on whether or not it is finite or infinite, we seem to be placing it as a higher genus. Thereby, we make it higher in the hierarchy than God. Moreover, now that God is lower than being, we would say that ‘being’ is a predicate to God, in the sense of the sentence: God is a being / God has being / God is. So being is one of God’s attributes. Also, as we noted, God is not finite, so he also has infinitude as one of his attributes (but it is not clear to me if ‘infinite’ is a higher genus).]

This view is clearly heretical, since it appears to be the case that as being is somehow prior to finite and infinite beings, being appears to operate as a genus, with finite and infinite beings as its species. Thus being would seem to occupy a place higher in the Porphyrian hierarchy than God. We might also want to ask how Scotus is able to explain the simplicity of the nature of God, given that God’s nature seems to now be a compound of two different attributes: being and infinitude.
(SH 32)

Scotus has a solution for this problem of possible heresy. To understand it, we need first to return to Aquinas in his Summa Theologica. Here we get a definition of infinite as non limited. The passage adds the complicating issues of form and matter. Both in themselves are infinite, but in their union they limit one another. A form can take any instantiation, but as soon as it is, it is limited to being that particular determination. Matter can take any form, but as soon as it takes one, it is limited to that formation (SH 32c). [The reasoning in the next part is not entirely clear to me. It seems that because infinite and finite are relational concepts, with each co-defining the other, and because they are opposed, then the being must be the highest genus. Perhaps this is because neither one can be said to be higher than the other, but both can be said to have being.]

The concepts of finite and infinite are here relational concepts. The infinite is defined by not being limited, whereas the finite is defined through limitation (by matter). If the finite and infinite are understood in these terms, it is clear that we are going to end up with being as the highest genus, or at best an analogical conception of being, as these two terms are opposed to one another. Rather than finitude being defined by relation to a limit, Scotus instead therefore introduces the notion of an ‘intrinsic degree’ of being.
(32cd)

[Since Scotus does not want to place being above God, he also does not want to co-define infinite and finite. As we saw, this co-definition was based on finite being understood as having a limit and infinite as not having a limit. Thus] Scotus will not define finitude in relation to a limit. We will see how he instead uses the notion of ‘intrinsic degrees’ of being.

SH follows Richard Crosses’ (1999, p.40) account of Scotus’ ‘intrinsic degrees’ of being. [The following is complicated. We first must recognize that the for some reason, infinity for Aquinas is understood as extensive and divisible. This somehow applies also to God’s infinitude and his infinite perfection. But it is not clear to me how Aquinas thinks that God’s perfection is extensive and divisible. Perhaps by saying that the infinite is unlimited and the finite limited, we are saying that the infinite is an indefinite amount of finites, or in other words, that there is no limit to how many finites make it up. But again, how does this apply in the case of perfection? At any rate, we take it for granted that the Aquinas understanding of God’s infinite perfection is extensive and divisible, and we conceive instead that there are different degrees of perfection, none of which are divisible into constituent quantitative parts. They only admit of more-or-less, but not of divisible composition. Thus infinite perfection, and also all finite degrees of perfection, are intensive and indivisible magnitudes.]

Scotus firsts asks us to imagine an infinitely large magnitude. He then asks us to apply this model of extensive infinity to a qualitative perfection, such as goodness. The central claim is that much as we can determine spatial | magnitudes, we are also capable of ranking perfections in such a way that we can conceive of an infinite perfection. In the case of a perfection, however, it cannot be constituted of parts in the way that the extensive magnitude is. An infinite extensive magnitude is constituted from an infinite number of finite extensive parts, but a perfection would not be infinitely perfect if it were composed of finite (and hence imperfect) qualities. The notion of infinity that Scotus is developing is therefore of an intensive, indivisible form of infinity, rather than the extensive, divisible form that Aquinas favours.
(32-33)

[What seems to be important here is the notion that now infinity is no longer a genus, that is something substantial, but rather it is a modality / modification of some substance. Perhaps we might have some reason to say that a human has more perfection than a rock, but infinitely less perfection than God. Perhaps also built into this thinking is that levels of perfection are amounts of being. This way, an infinite amount of being is not higher to God but is equated with God. There is also a somewhat confusing quote of Scotus about degrees of whiteness. We can have different degrees of intensity of white. The quoted material does not mention infinite whiteness. But SH says that infinite being is like infinite whiteness in this example. It is not entirely clear to me what that would be in this example. If we have different degrees of whiteness, then the higher degree, the closer we are to the infinite and also the closer to the absolute. Perhaps we are to think of it like this. Between Black (no degree of whiteness) and White (infinite degree of whiteness) we have an infinity of variations of white. So in order to go from black to white, we need to proceed through an infinity of variations, meaning that the highest one would itself be an infinite variation. But still the situation is not entirely clear to me. Say for example we look just at some middle section of grey variations between black and white. If we can keep finding smaller and smaller variations, would there not be an infinite number of variations within any one limited part or swath of the continuum? So even before arriving at pure white, we would still need to proceed through an infinity of variations of white, thus making the variation just prior to pure white still infinite, in the sense we began with. It must be infinite in some other sense. I can only also think that pure white is an infinite degree of white because there is no limit to how white it is. However, we already ruled out understanding infinity by means of the concept of limit. So one of SH’s points is that in this example, infinite whiteness is not defined by a lack of limitation. Yet I do not know how to conceive of why it is infinite. His second point is that we are not using some external concept to understand whiteness. Likewise for being, it would seem, perfect being, infinite being, and God, which may all be synonymous, do not require another concept for their perfection to be understood. This makes sense, but we might wonder if the infinite degrees of whiteness can be understood without reference to its lowest degree, which is either black or the first variation between black and white. And pure black is different in kind and not degree from pure white, I would think. The main idea we get from this is that finitude and infinity in this understanding are not properties of being, it seems because they are not predicated of being but are rather degrees of being. They thus instead are modes or modulations or modifications of being.]

God is not, therefore, superior to man in the quantitative extension of his being, but rather in the qualitative nature of his being’s intensity. This ultimately allows Scotus to solve the two difficulties of the highest genus and the simplicity of God. Instead of understanding infinity and finitude as species of being, they are rather modes or ways in which being subsists. Scotus gives the following example in terms of colour [the following up to citation is block quotation of Scotus]:

When some reality is understood along with its intrinsic mode, that concept is not so absolutely simple that it is impossible that this reality be conceived apart from this mode, although it is then an imperfect concept of a thing. For example, if there were whiteness in the tenth degree of intensity, however simple it may be in reality, it is nonetheless possible that it be conceived under the concept of so much whiteness, and then it would be conceived perfectly by means of a concept adequate to the thing itself. Or, it is able to be conceived precisely under the concept of whiteness, and then it is conceived according to a concept that is imperfect and lacking in perfection in the thing. But the imperfect concept is common to this and that white, and the perfect concept is more proper. (Scotus, Ord. I, d. 8, pars 1, q. 3 n. 138–9, taken from Hall 2007: 107)

Infinite being is like infinite whiteness in this example. Finite being in turn is like a finite degree of whiteness. In neither case are the notions relational. Infinite whiteness is not defined by a lack of limitation, but positively, in terms of its own intensity. Likewise, a finite degree of whiteness is not defined in relation to some other quality, but is intrinsic to the colour itself. Finitude and infinity are therefore modes, rather than properties of being.
(SH 33)

We recall Porphyry’s Aristotelian system of species and genera. Being would be the highest category. It is higher than humans, since humans exist, and it is also higher than God, since we can as well make the predication “God has being”. This is a problem of course for the medieval theologians, and Scotus has solved the problem. [We can have God as being different from other beings, as an infinite degree of being.] “Scotus’ notion of the distinction allows us to avoid this difficulty. Clearly there is a difference between whitenesses of different degrees of intensity” (34).

[It seems in the following paragraph that we return to the idea of perfection in the previous blocked Scotus quote. Here a concept is imperfect if it does not adequately correspond to what it is a concept of. In our experience, we only see different degrees of whiteness, whether that be finite or infinite. We never see whiteness without it taking on some degree of whiteness. The same it seems goes for being. We see only degrees of being (I am not sure how specifically. What existing things in our world of experience have less being than others?) Therefore, if we formulate a concept of being without involving the notion of its intensity, it is merely a formal conception.]

When we look at the concept of the intensity itself, however, it should be apparent that this notion of intensity cannot be grasped as really distinct from the whiteness itself. If we take away the concept of whiteness, we simply have the concept of ‘degree’, which is meaningless on its own – ‘degree of what?’ Nevertheless, the degree clearly does distinguish different ‘whitenesses’. We can note however, that it is possible to formulate a concept of whiteness that does not make reference to its degree of intensity. Such a concept would, however, be ‘an imperfect concept of a thing’ as whiteness always shows itself with a given intensity. It should be clear that we can apply this conception to the notion of being. Scotus’ claim would then be that being always presents itself with a given degree of intensity which is inseparable from it. While we can therefore formulate a concept of being without reference to its intensity, such a conception is only formal, as actual being is always finite or infinite.
(34)

[We might think of water heated or cooled to different degrees. There is only relative quantitative difference between each degree. But there is a difference in kind if we look at the states of matter the water changes through while its temperature varies. But the intensities themselves do not admit of such categories of difference in kind. So we would think that God and man stand at different degrees of intensity of being, and as such, are not yet understood as being different in kind. It is this understanding of intensity that Deleuze seems to be after. However, Scotus still maintains the theological position that God is fundamentally different than man, and this would be because the infinite perfection is so much greater than our own degree of perfection that an absolute gap divides us. As a result, his understanding of univocity is compromised, since God’s being in the end is a different kind of being than our own, and not just another degree of the same being.]

Intensity as it stands is purely a difference in the degree of something’s being, and is also pre-categorial. As such, it does not constitute the kind of distinction that would allow a proper separation between God and man. Such a position in fact is the one that Deleuze wants to develop in his own philosophy. For Scotus on the contrary, the difference in degree between God and his creation becomes a difference in kind once we recognise that infinite intensity is simply incommensurate with any form of finite intensity. The gap between finite and infinite is therefore still a chasm which allows the separation of God and his creation to be maintained. While being can conceptually be said univocally, in practice, we always encounter being with a given intensity, and so in reality being is always encountered in different forms [the following up to citation quotes Scotus]:

As said of the ten categories, neither metaphysically nor naturally does the term ‘being’ signify one concept; and being is not a genus of these, neither naturally nor metaphysically. However, logically speaking, being is univocal. (Duns Scotus, In De an., q. 22, n. 33 taken from Hall 2007: 20) |

By making this difference a difference in kind, Scotus separates man from God, but at the cost of making the thesis of univocity a purely formal thesis. This is why Deleuze claims that Scotus ‘only thought univocal being’ (DR 39/49).
(SH 34-35)

 

 

Citations from:

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

Or if otherwise noted:

Cross, Richard (1999), Duns Scotus, Oxford: Oxford University Press.

Duns Scotus, John (1978a), ‘Concerning Metaphysics’, in Allan Wolter (trans. and ed.), Philosophical Writings, Cambridge: Hackett Publishing, 1–12.

Duns Scotus, John (1978b), ‘Man’s Natural Knowledge of God’, in Allan Wolter (trans. and ed.), Philosophical Writings, Cambridge: Hackett Publishing, 13–33.

Hall, Alex (2007), Thomas Aquinas and John Duns Scotus: Natural Theology in the High Middle Ages, London: Continuum.

In the Brush. [9] Study of a Figure in Landscape, 1952. Deleuze on Bacon, Painting Series

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
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[I am profoundly grateful to the sources of these images:

phillipscollection.org

thecityreview.com

Credits given at the end.]

[The following is quotation. My commentary is bracketed in red.]

In the Brush

(Thanks phillipscollection.org)

Francis Bacon

Study of a Figure in Landscape, 1952

The Phillips Collection, Washington, D.C.

Painting 13 of Deleuze's

Francis Bacon: Logique de la sensation. Tome II - Peintures

Painting [9] of the English translation

and Painting [13] of the Seuil 2002 French

What fills the rest of the painting will be neither a landscape as the correlate of the Figure, nor a ground from which the form will emerge, nor a formless chiaroscuro, a thickness of color on which shadows would play, a texture on which variation would play. Yet we are moving ahead too quickly. For there are indeed, in Bacon's early works, landscape-Figures like the Van Gogh of 1957 [23]; there are extremely shaded textures, as in Figure in a Landscape (1945) [2] and Figure Study I (1945-6) [4]; there are thicknesses and densities like those of Head II (1949) [5] (Deleuze, 2003: 3b.c) [...] But destiny can sometimes pass through detours that seem to contradict it. For Bacon's landscapes are a preparation for what will later appear as a set of short "involuntary free marks" lining the canvas, asignifying traits that are devoid of any illustrative or narrative function: hence the importance of the grass, and the irremediably grassy character of these landscapes (Landscape, 1952 [8]; Study of a Figure in a landscape, 1952 [9]; Study of a Baboon, 1953 [14]; Two Figures in the Grass, 1954 [17]). (Deleuze 2003: 3c.d)

Ce qui remplit le reste du tableau, ce ne sera pas un paysage comme corrélat de la figure, ni un fond dont surgirait la forme, ni un informel, clair-obscur, épaisseur de la couleur où se joueraient les ombres, texture où se jouerait la variation. Nous allons trop vite pourtant. Il y a bien, ou début de l'oeuvre, des Figures-paysages comme le Van Gogh de 1957 ; il y a des textures extrêmement nuancées, comme « Figure dans un Paysage » ou « Figure étude I », de 1945 ; il y a des épaisseurs et densités comme la « Tête II » de 1949; [...] Mais il n'est pas exclu que ce qui est destin passe par des détours qui semblent le contredire. Car les paysages de Bacon sont la préparation de ce qui apparaîtra plus tard comme un ensemble des courtes « marques libres involontaires » rayant la toile, traits asignifiants dénués de fonction illustrative ou narrative : d'où l'importance de l'herbe, le caractère irrémédiablement herbu de ces paysages (« Paysage » 1952, « Étude de figure dans un paysage » 1952, « Étude de babouin » 1953, ou « Deux figures dans l'herbe » 1954). (Deleuze 2002: 13-14)

[Deleuze would like to generalize a stylistic feature of Bacon's works. We see in many of them that there is a single-colored field that is like a screen that Bacon pins his figures to. On the one hand, this creates a stark contrast between the figure and the field. On the other hand, they are both side-by-side, in a way, as if sharing a two-dimensional space. The depth is not extensive. But it is intensive. There are many internal tendencies for the tones and colors to alter (modulate) from one region to the next. So perhaps by making the background perfectly flat, Bacon opens our awareness not to extensive depth but to intensive depth, that is, the dimension of alteration-tendencies, which means the dimension of wrestling forces. Concretely, we might experience this in the ways our eyes are pushed-and-pulled in various directions at once, depending on the changes or modulations in the paint. (For more on this idea of intensive depths on a flat monochromatic surface, see Deleuze's discussion of Spinoza's white wall: Cours Vincennes 10-03-1981; Expressionism in Philosophy Chapter 12 and Chapter 13).

And yet in this painting, there is a thick field of browned grass. It suggests extensive depth and diminishes contrast to the depicted figure.

(Thanks phillipscollection.org)

Deleuze writes that this painting is still in line with the greater development of Bacon's works. Later Bacon will disfigure his works with chance-operation techniques, as part of his strategy to remove the representative and narrative components of the painting. One such technique, 'local scrubbing', involves using a brush to scratch and scrape the paint. According to Deleuze, we see that brush technique employed in this work. In a sense, this painting highlights one aspect of the style that pervades all his works. And thus we might benefit by looking for the grassy-field-like areas in his other works, which are found in limited zones that Deleuze calls diagrams.]

(Thanks thecityreview.com)

Deleuze, Gilles. Francis Bacon: The Logic of Sensation. Transl. Daniel W. Smith. London/New York: Continuum, 2003.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Paris: Seuil, 2002.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Editions de la différence [Littératures], 1981.

Images obtained gratefully from:

http://www.phillipscollection.org/willo/w/size3/0046w.jpg

http://www.thecityreview.com/bacon.html

Scraped Landscape [2] Deleuze on Bacon, Painting Series. Figure in a Landscape, 1945

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]

[Index of painting entries in the Deleuze on Bacon series].

[Entry collecting the images of the paintings.]

[I am profoundly grateful to the sources of these images:

www.alexalienart.com

wikipedia.org

also available at:

www.tate.org.uk]

[The following is quotation. My commentary is in brackets.]

Scraped Landscape

Deleuze on Bacon, Painting Series

Francis Bacon

Figure in a Landscape, 1945

The Tate Gallery, London

Painting 7 of Deleuze's

Francis Bacon: Logique de la sensation. Tome II - Peintures

Painting [2] of the English translation

and Painting [58] of the Seuil 2002 French

(Thanks www.alexalienart.com)

What fills the rest of the painting will be neither a landscape as the correlate of the Figure, nor a ground from which the form will emerge, nor a formless chiaroscuro, a thickness of color on which shadows would play, a texture on which variation would play. Yet we are moving ahead too quickly. For there are indeed, in Bacon's early works, landscape-Figures like the Van Gogh of 1957 [23]; there are extremely shaded textures, as in Figure in a Landscape (1945) [2]. (Deleuze, 2003: 3bc)

Ce qui remplit le reste du tableau, ce ne sera pas un paysage comme corrélat de la figure, ni un fond dont surgirait la forme, ni un informel, clair-obscur, épaisseur de la couleur où se joueraient les ombres, texture où se jouerait la variation. Nous allons trop vite pourtant. Il y a bien, ou début de l'oeuvre, des Figures-paysages comme le Van Gogh de 1957 ; il y a des textures extrêmement nuancées, comme « Figure dans un Paysage » (Deleuze, 2002: 13d)

[Deleuze will later speak of the "shallow" or "superficial" depth in Bacon's paintings (p.83). The figure is not projected from the background, not does it blur into it. Rather, they are side-by-side. If the figure were to stand-out from the background, then there would be a visual depth to the painting. There would be space extending between the figure and the surrounding field. However, there is also another type of depth that is even deeper than extensive depth. There is an intensive depth, which does not extend in space. Deleuze also uses the medieval example of the white wall to explain. There are variations in the whiteness of the wall. As our eyes move from place-to-place along the white wall, we sense tendencies for the tone to change. (For more on Spinoza's white wall, see Deleuze, Cours Vincennes 10-03-1981, Expressionism in Philosophy Chapter 12 and Chapter 13). Those tendencies are found already in an indivisible point on the wall, just as calculus determines differential values at limits, which also can be thought of as tendencies for a curve to change. These tendencies do not yet actualize as extensive, qualitative differences. They are tendencies tending inward, that is to say, they are intensities. Bacon's paintings are flat, whether as figures scrambled into an adjacent indeterminate landscape, or as figures flat beside a mono-colored field. Either way, he may make use of the flatness' potential to express intensity, which produces sensations in us. Deleuze also writes that the scrambling we see in the landscape is a preparation for a technique he later employs: diagramming.

(Thanks wikipedia.org)

When Bacon diagrams, he begins with a formation, then scrambles part of it using chance-guided motions, like throwing the paint. This creates a painting that both causes us to try to make sense of it while that being an impossibility. We are continually confronted with differences upon differences, which causes us intense sensation. (For a more detailed explanation of diagramming, see this entry).]

Deleuze, Gilles. Francis Bacon: The Logic of Sensation. Transl. Daniel W. Smith. London/New York: Continuum, 2003.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Paris: Seuil, 2002.

Deleuze, Gilles. Francis Bacon: Logique de la sensation. Tome II - Peintures. Paris: Editions de la différence [Littératures], 1981.

Images obtained gratefully from:

http://www.alexalienart.com/Bacon%20News%20Archive.htm

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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, and Deleuze's commentary on Spinoza's critique of Boyle's notion of divisibility].

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 "Spinoza's Letter on the Infinite." 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 §§553-554]

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 § 570]

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.

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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:

http://web.centre.edu/crummett/phy210labexercises/Lab%209%20Compound%20Pendulum.pdf

Huygens and image of different mass points on compound pendulum:

http://ppp.unipv.it/PagesIt/StoriaScienza/PDF/Swinging%20Open%20off.pdf

Physical pendulum defined as compound pendulum:

http://www.stubpass.com/concerts/pop-rock/pendulum-wiki/

Description of construction of compound pendulum:

http://farside.ph.utexas.edu/teaching/301/lectures/node141.html

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

http://kr.cs.ait.ac.th/~radok/physics/b11.htm

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