Somers-Hall, (1.10), Deleuze’s Difference and Repetition, ‘1.10 Leibniz (43–4/54, 46–52/56–63)’, 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.]

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

1.10 Leibniz (43–4/54, 46–52/56–63)

Brief summary:

Leibniz presents an infinite representational system. The world is composed of monads with predicates. This means the world takes on the subject-predicate structure of judgments, and is thus representational. Each monad is in some relation to every other monad, and these relations are expressed in a monad’s predicates. Therefore each monad expresses the world in its entirety. There are infinitely many monads, so there are infinitely many predicates for each one, and thus what each monad represents in its predication is infinite. Since we have a world of coexisting differences, we would think in Leibniz’ system that we might have non-oppositional difference. However, we have just one world with its own defined limits, since it stands opposed to other possible worlds that have inconsistencies and thus were not created. So while within this world there is non-oppositional difference, between this world and the others that God did not create there is in fact an oppositional difference.

 

Summary

[A while ago we examined Aristotle’s system of classification and definition. We examined the issue and problems of the highest genus or genera. Given that this is the most encompassing level of classification, we called it the Large, and problems regarding it we called the problems of the Large. In the prior section we saw Hegel’s infinite representation and dialectical movement. All categories of thought come about through this movement. The movement is somehow infinite. It is infinite either because it has no beginning or end (however, it would really seem to have a beginning and end, namely, indeterminate being and the absolute), or because at each stage there is a sort of unlimitedness. For example, at the beginning being and nothing seem to ceaselessly revolve one into the other in a movement that is genetic of a third concept, becoming (it is not clear to me if there are determinate stages and thus not endless interaction at each stage, or if it is one ceaseless interaction after another, all adding together and remaining in motion). At any rate, we need somehow to conclude that this dialectical movement is infinite. It is still representation, because it generates the categories of understanding that we use to make judgments, which have the form of representation. And also, we have a structure similar to the representational structure of genus-species. In Hegel we have something more like a process-product or pattern-instance structure. This is as clear as I can conceive matters at this point, but surely there is a better explanation. It would seem that since Hegel is dealing with the movement that generates all categories, then we are dealing with the Large, that is, with something roughly equivalent to the most basic category. SH will then speak of “the notion of contradiction as the largest difference” (48). I am not entirely sure what is meant by “largest difference”, but perhaps it can be understood in this way. What makes the dialectic movement the largest is that it is inherent to each stage and each instance of production. Also, at each stage, contradiction is like a motive force in the movement. Since contradiction is a motive force at each stage and in each production, it is also ‘largest’ in that sense of being all-encompassing. At any rate, Hegel introduces the infinite into the Large by saying that somehow it is ceaseless. Each stage is finite, but the entire process is infinite. In that way, Hegel introduces the infinite into the finite. Leibniz will also introduce the infinite into the finite, but this time on the level of the Small, that is, of the individual rather then of the highest grouping.] Deleuze has a problem with understanding the world by means of judgments, which normally take the subject-predicate form [exactly what is wrong with representation seems just to be the unresolved problems it creates. I am not sure if there are any other motivations to oppose representation. For example, I am not sure if there is an anti-totalitarian political motivation to be against systems that organize all their parts around some fixed center of power and that use fixed meanings in symbolic language to convince people of the legitimacy of that centralized power.] Leibniz, [like Hegel and Aristotle, is a representational thinker, because he] “holds to the view that all truths take the form of subject-predicate judgements” (48). We already saw for example: “man is a rational animal”. [So the first step we are now taking in our thinking here is to claim that such predicative formulations can be true. The next step is to say that if they are true, then they correspond to some reality in the world, Thus,] this means that in reality, there are things which can take predicates, since they are things with properties. [We should distinguish the language of predication we are using here from the way we were using it for Aristotle (and Porphyry). In that prior case, we said that the genus serves as a predicate to its species: “man (species) is an animal (genus) that reasons (specific difference).” Now instead in this current section, we are not thinking of the genus being a predicate. Rather, we are thinking of specific things having properties, and those properties being ‘predicated’ to the thing. We might for example say something like, ‘This apple is red’. Here the ‘subject’ of the sentence is the individual apple, and its predicate is something like ‘has redness’ or ‘is a red thing’ or ‘is something which is red’ or just of course ‘is red’.]

At the beginning of this chapter, we saw how Deleuze’s central claim is that we need to find an alternative way of conceptualising the world to that provided by judgement. Now Leibniz holds to the view that all truths take the form of subject-predicate judgements: ‘In every categorical proposition (for from them I can show elsewhere that other kinds of propositions can be dealt with by changing a few things in the calculus) there are two terms, the subject and the predicate’ (Leibniz 1989b: 11). It is certainly the case that some truths take this form, such as the claim that ‘man is a rational animal’, or that ‘seven is a prime number’. If we hold that our judgements are able to accord with the world, then it is going to be the case that the basic elements of existence are also going to be substances of some form possessing properties (what Leibniz calls monads).
(SH 48)

[Now we will address a problem that arises were we to suppose all this that we said above. Some predicates place the subject into a reciprocal relation with another thing. For example, Paul is taller than Peter. Our basic claim is that there are individuals that have predicates. The problem here is apparently that reciprocal relations like this make it confusing which is the subject and which is the predicate, because our example sentence means the same as John is smaller than Paul. I do not understand exactly what the problem is yet. It seems we have two individuals, Paul and John, both of which have properties, being smaller or larger than the other. Why is it that if something is found in the predicate of something else, then it cannot itself be a subject with reciprocal properties? But we need to figure this out in order to proceed to the next idea. One reason I can think of is that for some reason being in another’s predicate is to eliminate one’s own individual existence. So we have monads. We assume Paul and Peter are monads. If we put Paul into the predicate of Peter, we either have two Paul’s, which is  impossible, or we removed Paul from the world of monads and inserted it into Peter. The other reason I can think of is that we are claiming that all things fit a subject-predicate judgment form without any ambiguity, but for relational predicates there is no clear subject. Again, it is still not evident to me why even under this assumption we cannot have two clearly discernible individuals, Peter and Paul, both having a predicate that places each in relation to the other. Maybe the problem is that there is one relation but it is expressed with two different and opposite predicates. There is just one relation of largerness/smallerness between Peter and Paul, so there should be just one predicate for some reason, but in fact we have two. Still it is unclear why one relation cannot have two expressions depending on the perspective taken. There must be some better reason to explain the problem here. We have to assume it is a problem for all relational predicates, which include cause and effect. For, if x is the effect of y, then y is the cause of x. Which then is the subject (assuming there can only be one for each relation). We are going with this idea that this is so problematic as to call into question the viability of the judgment of cause and effect, and thus somehow no objects can be understood as causes of any other objects. This is very interesting, but I cannot grasp the reasoning for it yet.]

If we see the basic substances in existence as purely defined in terms of substances and properties, however, we encounter a problem when we deal with relations between substances, since these don’t seem to fit this structure. If we say, for instance, that ‘Paul is taller than John’, then it doesn’t seem clear what is the subject and what is the predicate (we might want to say that ‘Paul’ is the subject, and ‘is taller than John’ is the property, but what about if we rephrase the proposition as ‘John is shorter than Paul’?). Similarly, relations of cause and effect seem to involve two subjects and a relation between them. If all propositions can be reduced to judgements, therefore, we seem to be left with a world of non-causally interacting entities – ‘the monads have no windows through which something can enter or leave’ (Leibniz 1989a: §7).
(SH 48)

We now need to explain two problems. 1) [For the first problem, we are working with the notion that we cannot explain causality on the basis of relations. This still is not evident to me why, but it has something to do with the fact that our mode of subject-predicate judgment fails with reciprocal relations like cause-effect. X has the predicate ‘causes y.’ Y has the predicate, ‘is the effect of x. The claim is that we cannot answer, who is the subject? It cannot be X, since for the same relation, Y is also the subject when the relation is reformulated. For some reason, they both cannot be subjects even though they both are monads and even though there are no logical inconsistencies in these reciprocal formulations. At any rate, the first problem requires two ideas, a) we cannot explain causal interactions on the basis of relations between causing things and effected things, and b) the world is a system of causality that needs to be explained.] “First, how do we explain interactions without relations, given that we appear to live in a world of causally interacting substances” (48d). [SH will then tell us what the solution is, but I am unable to grasp it very well right now. The conclusion we will arrive at is that all things will contain relational properties to all other things, including causal relations. The way we get to this conclusion is by recognizing the above point that we have causality but we cannot understand causal interaction using the notion of relations. I do not grasp yet how this inference is made. If I wanted to come to this conclusion, I think I would first recognize that there are predicates expressing reciprocal relations, then next I would establish that for certain reasons all things in one way or another relate to all other things. One possible way are spatial relations of physical things. Each monad, if it lies in space, is to one side or another of some other monad, which is to one side or another of some other, and all are somehow spatially related. Another would be to see everything in the world as in a system of physical causality, where on the local level there are proximate causal interactions, but given that chains of effects spread that influence throughout the system, all things are either directly or indirectly related causally. I will quote.]

We now have to deal with two problems. First, how do we explain interactions without relations, given that we appear to live in a world of causally interacting substances; and second, how do we differentiate different monads? The solution to the first problem is to see each of these monads as somehow containing the relations between different substances as properties. This | means that ‘taller than John’ will be a property of Paul, and ‘shorter than Paul’ will be a property of John. If causal interactions are going to be understood purely as properties of each subject, then each monad will have to contain all of its causal interactions with the rest of the world. Leibniz therefore writes that [the following up to citation is Leibniz quotation]:

This interconnection or accommodation of all created things to each other, and each to all others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe. (Leibniz 1989a: §56)
(SH 48-49)

[So, by means of relational predicates, each smallest individual in the world express the entirety of the all other individuals in the world. [It seems we also assume that the world is infinite, thus] the infinite in a sense is contained in each monad. [Now, since each such relation is a relation of difference,] all the world’s difference in all its variety is contained in each smallest part.

Each monad is therefore made up of an infinite number of properties which together describe the totality of what would be its relations with the universe, and hence, in a sense, the universe itself. To this extent, the infinite, in the sense of even the smallest elements of the universe, is contained within each monad. The whole variety of difference is therefore brought into the notion of the essence of each particular monad. Deleuze writes that: ‘The inessential here refers not to that which lacks importance but, on the contrary, to the most profound, to the universal matter or continuum from which essences are finally made’ (DR 47/58).
(SH 49)

2) [The reasoning for the next problem is also a little hard for me to grasp. It seems like it goes like this. Suppose that each monad contains relational predicates that express its relation to every other part of the world, that is, to every other monad. Each one expresses the world in its entirety. Perhaps somehow then there is no way to distinguish each monad, since they all express exactly the same thing, the whole world. To continue our reasoning, recall the specific relational predicate Peter is taller than Paul. There is just one relation of size comparison between them, but two predicates, ‘is taller than’ and ‘is smaller than’. Both Peter and Paul can be the subject, so which is the subject? Well, it depends on which perspective you take. If we take Paul’s perspective, we make him the subject, and the appropriate predicates follow, and likewise for Peter. So return to the idea that each monad expresses every relation with every other monad. Each relation can put one or another monad as the predicate. Perhaps the idea is that if we take one monad and all its predicates, we can reexpress those predicates such that they become identical to the predicates of any of the other monads. Think of the simple world where there are just two monads, Peter and Paul.

(Peter > Paul) = (Paul < Peter).

So Peter can have this predicate: Peter is taller than Paul

And Paul can have this predicate: Paul is smaller than Peter.

Yet, the inverse is true for both.

So Peter can keep his predication: Peter is taller than Paul.

And Paul can invert his predication: Paul is smaller than Peter. Peter is taller than Paul.

Now, think of a world with infinitely many monads. The predicates for each can be made identical with the predicates for any, and thus, all others. All relational predicates of all monads can be made identical. So for monads, what distinguishes them is not what their predicates express, since they all express the sum of all differences constituting the world; rather, what distinguishes them is each one’s unique perspective, which might orient all the predications such that instead of taking the above third personal form, they instead substantiate their own selves in the formulations in a first personal way. So for example, Peter’s predication might be “I (Peter) am taller that Paul”. And Paul would say “I (Paul) am shorter than Peter”. But Paul’s predication would never be: Peter is taller than Paul (like in our substitution above), since we are taking his perspective and not Peter’s and so Paul will take the subject place of the sentence. Now, we need somehow to get to an idea of the distinct and confused expression of relations. This part I cannot follow well. But it seems that from one monad’s particular perspective, one can have clear knowledge of how it interacts with those other monads it is directly in relation to, but confused knowledge of its relation to all the other monads it is only indirectly related to, as mediated through the transitive chain of relations between continguously related monads. Thus perhaps we may say now that what distinguishes each one on the level of their predicates is that each will have some clear predicates and many other confusedly stateable predicates. But since each one takes a different relative position to the others and thus has different direct and different indirect relations, each monad will have as its ‘signature’ its own unique set of clearly stateable predicates. I am saying ‘clearly stateable’, because from the perspective of God, who created all the monads and their relations, I would think all is clear. The only way the predicates that a monad has, which were endowed by an omniscient being, would be unclear is if we think of the predicates being understood by means of a limited mind taking that particular limited perspective and stating the predicates as clearly as possible from that perspective. So for example, we can say that the earth’s gravity pulls on us and we on it to some much lesser extent. And we might also then say that at the furthest distance from us in the cosmos, we gravitationally influence those distant bodies but at some remarkably slight amount. We cannot however state what those bodies are, how we influence them, and so on.]

The second question was, how do we differentiate monads given that each expresses the whole of the universe? While each monad expresses the entire universe, each does so from a particular perspective, and so only that which is proximal to the monad is expressed distinctly. Events which are at some remove from the monad are only perceived confusedly [the following up to citation is Leibniz quotation]:

Monads are limited, not as to their objects, but with respect to the modifications of their knowledge of them. Monads all go confusedly to infinity, to the whole; but they are limited and differentiated by the degrees of their distinct perceptions. (Leibniz 1989a: §60)

[new paragraph] The difference between monads is therefore the difference between different perspectives on the world.
(SH 49)

[Note here that two monads relate without being opposed. It would seem then that we can have judgment without oppositional difference in Leibniz’ system. However, all the predicates must be consistent with one another for Leibniz. There is one consistent world to which all the monad’s perspectives are in harmony. We thus have a logic of identity, since we can only have one world and not many which are incompatible with that world. Somehow Deleuze sees there being as many worlds as there are perspectives, but the perspectives are all of one world. It is not clear to me how there are both many worlds and just one world at the same time, instead of there being one world with many perspectives.  Hopefully this idea becomes clearer as we proceed.]

Different perspectives are not opposed to each other, and so Leibniz appears to have succeeded in coming up with a form of non-oppositional difference which explains all of the accidents of entities. If he had done so, then he would have developed a conception of non-oppositional difference founded on judgement, thus providing an alternative to Deleuze’s philosophy. In the end, however, this project fails, because the concept of difference is still founded on an identity. If we ask what these different perspectives | are perspectives of, then we are given the answer that they are perspectives of the universe. The notion of the universe itself has to pre-exist the different perspectives of it, since it is through this notion that God determines which of the monads can exist and which cannot. Only those which are compossible, that is, can simultaneously co-exist within the same world, can exist. We cannot have a world in which Adam both sinned and did not sin, as this would be a contradiction, nor a world in which different monads see the world in such radically different ways, as then the impression of causality would break down. ‘There are, as it were, just as many different universes [as there are monads], which are, nevertheless, only perspectives on a single one’ (Leibniz 1989a: §57). Leibniz’s notion of difference therefore still relies on the convergence of these different perspectives on a single identity, the universe itself [the following is quotation of Deleuze]:

Leibniz’s only error was to have linked difference to the negative of limitation, because he maintained the dominance of the old principle, because he linked the series to a principle of convergence, without seeing that divergence itself was an object of affirmation. (DR 51/62)
(SH 50)

 

 

 

 

 

Citations from:

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

Or if otherwise noted:

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

 

Leibniz, Gottfried Wilhelm (1989a), ‘The Principles of Philosophy, or, the Monadology’, in Roger Ariew and Daniel Garber (ed. and trans.), Philosophical Essays, Cambridge: Hackett Publishing, 213–24.

Leibniz, Gottfried Wilhelm (1989b), ‘Samples of the Numerical Characteristic’, in Roger Ariew and Daniel Garber (ed. and trans.), Philosophical Essays, Cambridge: Hackett Publishing, 10–19.

 

 

Somers-Hall, (1.9), Deleuze’s Difference and Repetition, ‘1.9 Hegel (44–6/54–6, 51–3/62–4)’, summary

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

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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.]

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

1.9 Hegel (44–6/54–6, 51–3/62–4)

Brief summary:

Hegel’s dialectic is an infinite movement. But it also generates the categories we use in representational thinking. Therefore, it is infinite representation, unlike the finite representation of Aristotle, which fixes things in a stable system of definitional limits. Nonetheless, 1) Hegel’s infinite representation still has a pattern-instance structure similar to Aristotle’s genus-species structure, 2) it makes no room for the uniqueness and singularity of each moment, since each in a sense is contained in or born out of prior states, and 3) the real world is too complicated and full of ambiguity to admit of Hegel’s system of cleanly distinct opposites.

 

Summary

[We previously made a general and brief distinction between finite and infinite representation.] Now we will begin by looking at two ways of putting the infinite representational approach into practice (44), namely, 1) Hegel’s synthetic approach, and 2) Leibniz’ manner of seeing “objects as fully defined by an infinite number of properties, thus making truths about them analytic” (44). [Perhaps the distinction here is something like the following. For Leibniz, objects from the beginning possess all their predicates, but there are infinitely many. So things still have a subject-predicate representational structure, but it is infinite. Hegel maybe would see things as part of a developmental movement by which they progressively obtain newer predications or traits or maybe substantialities, but infinitely so. Aristotle’s method of finitely fixing to things sets of properties without taking into account their development is what presents his problems, in Hegel’s view. The real totality is not all that is but rather the entirety of the movement which develops all that is in this motion of infinite becoming.]

In the case of Hegel, therefore, this means that the kind of thinking which has characterised representation so far is only a moment in a wider movement of thought. Thus, finite thinking, or ‘the understanding’ in Hegel’s terms, the mode of thought of Aristotle, is really just a single moment in a broader process called speculative reason. It is only by reifying specu- | lative thought that we end up with the problems we have encountered so far; that is, by denying that there is a greater moment to representation than finite representation, we find ourselves unable to explain the concept of totality.
(44-45)

Hegel’s infinite representation involves his notion of dialectic, which examines the development of concepts rather than seeing their senses as fixed.

Central to Hegel’s explanation of infinite representation is the notion of dialectic. Essentially, Hegel wants to argue that rather than the meanings of terms simply being given by definition, we find when we analyse the movement of thought thinking these terms that their meaning arises from the content itself.
(45)

[In his Science of Logic, Hegel shows this dialectical movement of concepts by tracing it to its origins in indeterminate being. See this entry on a text by Graham Priest for an explanation and quotation of the passages of the Hegel text. The idea is that even if we start with the most basic concept, indeterminate being, just by conceptualizing it, we obtain another concept, indeterminate nothing. Why? Well, try to think being in its purity, and with no reference to any beings, that is, with no determination whatsoever. What comes into your mind? Probably nothing comes into your mind. Voilà. The concept of nothing comes into your mind when you think the most basic concept, being. There is a dynamic built into this concept. Specifically we think indeterminate nothing, since we are not thinking some specific instance of nothingness or some particular negation of a being. But conceptually speaking, what is there to distinguish indeterminate being and indeterminate nothing in our minds? We conceive them as different notions. But each’s content is hard to unravel from the other’s, since both in a sense are empty of any determinate content. So, the first dynamic of thought is the production of opposition: being produces nothing, conceptually speaking. Next, there is a collapse of the two opposite concepts. So now see if this works for you. First conceive pure indeterminate being again, which should again bring to your mind the concept of pure indeterminate nothing. Now notice how they are individual and opposite concepts but are somehow difficult to pull apart on the basis of the conceptual content. The experience we are supposed to have now I am guessing is that we conceive the one rolling over into the other and that rolling back over into the first and so on. We think being, which makes us think nothing, which collapses back to being, which falls back to nothing, and so on. Their genetic pairing produces endless revolution. Voilà. We now have a third concept, arising from the mutual collapsing of the opposing first two, namely, we have the concept of pure becoming. Why? Because that is what happens in our mind when these concepts genetically produce and conflict with one another. The concepts are in a continual state of becoming their opposites. I have not studied the next step very well, but it might be something like this. At this point, we have the notion of becoming arising from the dynamic activity of the most basic ideas we can conceive. We have a dynamic unity of being and nothingness. But note that being at least in Aristotle is also understandable as ‘unity’. What do all beings share? They are all what they are. They are unified self-same things and they are not other to themselves (in this conception). Here now we have a unity (of being and nothing), so do we return to the indeterminate being of the first step? Perhaps we might consider indeterminate being also as indeterminate unity. But that is not what we have now at this stage of the dialectic movement. We specifically have the unity of being and nothing, and not the unity of anything whatsoever. So the concept of becoming leads to the notion of determinate unity, which is what? If something were determinate, we are dealing no longer with being in general but with some being in particular, and for that reason, perhaps the idea is that we are dealing with some existing thing. So the notion of determinate unity is also the notion of existence, perhaps. The concept of becoming (specifically of the becoming of being and nothing) gives rise to the concept of existence. I am not sure if becoming and existence are opposites and if they also dialectically sublate. But perhaps determinate existence is somehow incompatible with pure becoming, since pure becoming is more like a process of change, where determinate existence is something that may be lasting more than a timeless instant. At any rate, normally Hegel’s dialectic is thought to continue the same pattern, sometimes given the terms thesis, antithesis, and synthesis. The sublated third ‘category of thought’ (in our example ‘becoming’) will give rise to its opposite (which may be existence), and they will themselves produce yet another third category, and so on. The process supposedly ends with a final Absolute Idea (the Notion).]

Central to Hegel’s explanation of infinite representation is the notion of dialectic. Essentially, Hegel wants to argue that rather than the meanings of terms simply being given by definition, we find when we analyse the movement of thought thinking these terms that their meaning arises from the content itself. Hegel’s Science of Logic therefore traces the development of concepts from the simplest concept, that of pure, undifferentiated being, through to what he calls the Absolute Idea, or the Notion. By tracing the development of ideas themselves, we are able to see the inherent connections between them. Philosophy is therefore this movement of concepts themselves.
(45)

[The next part is very difficult for me to grasp. It seems we are saying the following. Normally we understand the infinite as what is not finite. But that is to limit the concept by saying what it is not. This means that the concept for the infinite is itself a finite concept. I am not sure why this is a problem. Do all concepts as concepts need to have the same properties as that which they are concepts of? Is the concept for red itself somehow a red concept? But it does help clarify what a finite representation is. Perhaps Hegel is interested not just in a representation of the infinite, but in an infinite representation. In other words, he wants something to have representational powers without being finitely limited like how Aristotelian representations are limited by definitional distinctions. I now must guess to the next notion here. Recall from our commentary above how when we think ‘being’ we thereby think its opposite ‘nothing’, which collapses back to being, and they keep revolving endlessly. This gives us the notion of becoming, but also, it is based on this ceaseless exchanging of opposites. The same could be happening when we think the concept of infinite. It is not the finite. We think the finite. It is not the infinite. They are co-definitional, and they keep exchanging one to the next over and over without end. This movement is perhaps part of the dialectical interactions of all opposites, but SH is only here discussing the pairing infinite/finite. This circle of revolution it seems is itself infinite, in that it has no beginning or end. Likewise, we might also think that if the absolute is a limit that comes after an infinite and not a finite progress, then the whole dialectic itself is infinite. I am not sure about that, since any ending would constitute a limit. At any rate, the very basic idea here seems to be that the dialectic is representational, because it generates the categories of understanding, by which we form judgments, and I think SH is saying judgments based on such categories are the form of representation. And also, in some important sense, perhaps the dynamics of this are endless and therefore infinite. So it is infinite representation. (I am still not sure why the ceaselessness of the movement is not understanding something by means of limits. Hegel speaks of its beginninglessness and endlessness. Are not beginnings and endings limits? They are not conceptual limits like a definition makes, but they still define the limits of a process or movement. And so, if something is ceaseless, since it is beginningless and endless, then we are defining its infinity by means of a negation of confining limits, that is, by saying that it has no end and no beginning and is in that way limitless.) Furthermore, we need to get to the idea that “Such a process involves seeing the infinite as essentially a contradictory structure – the identity of identity and difference” (SH 46). I am not sure how we get here yet. The simplest possibility I can think of is that somehow, perhaps later in the chain of categories, we arrive at identity which gives rise to its opposite difference. They collapse into one another, which would be like their identification with one another, and thus it would be the identification of identity and difference. The other way I can think of for getting to this notion would be is if even in a pairing like being and nothing we have an identification of identity and difference. I am not sure how. Perhaps the idea would be, it is the identity of indeterminate being, its meaning and its being just what it is conceptually, that gives rise to what is different from it. In other words, to be what one is, to have an identity, is also to differ from oneself. At any rate, the next idea is that the finite is in a perpetual process of vanishing or negation. I think this is simply the fact that any dialectical pairing would be a finite representation, but these dialectically give rise to others. So the finite representations always vanish, and this happens perpetually.]

For Hegel, therefore, the problems of finite representation emerge when we ignore this movement, and assume that concepts are just given. In this way, Hegel criticises his predecessors as follows [the following up to citation is Hegel quotation]:

Such presuppositions that infinity is different from finitude, that content is other than form, that the inner is other than the outer, also that mediation is not immediacy (as if anyone did not know such things), are brought forward by way of information and narrated and asserted rather than proved. (Hegel 1999: 41)

Finite representation therefore emerges for Hegel from the fact that we take for granted the nature of the distinction between the finite and the infinite. We presume that: ‘There are two worlds, one infinite and one finite, and in their relationship the infinite is only the limit of the finite and is thus only a determinate infinite, an infinite which is itself finite’ (Hegel 1999: 139–40). If we just view the infinite as a ‘beyond’ of the finite, and remain with finite thinking, however, we end up with an infinite which is itself limited, and hence is finite: ‘Owing to the inseparability of the infinite and the finite – or because this infinite remaining aloof on its own side is itself limited – there arises a limit; the infinite has vanished, and its other, the finite, has entered’ (Hegel 1999: 141). The heart of the difficulty is that the infinite is supposed to be that which is beyond limitation, but the basic structure of determining the infinite is by opposition, in other words by saying what the infinite is not. But by doing so, we introduce a limit into the notion of the infinite. Possessing a limit, however, is what defines finite things. For this reason, Hegel defines this understanding of the infinite as a ‘spurious infinite’ (Hegel 1999: 142). | We attempt to determine the infinite as a beyond, but in determining it, we limit it and make it finite. We thus have an infinite progression and alternation between finite and infinite terms. If we are truly to understand the infinite, and hence the finite, we need to see both as moments of one process [the following up to citation is Hegel quotation]:

The image of the progress to infinity is the straight line, at the two limits of which alone the infinite is, and always only is where the line – which is determinate being – is not, and which goes out beyond to this negation of its determinate being, that is, to the indeterminate; the image of true infinity, bent back into itself, becomes the circle, the line which has reached itself, which is closed and wholly present, without beginning and end. (Hegel 1999: 149)

The true infinite emerges when we step back from attempting to formulate the infinite through the progression, and recognise that the process of the circular movement of the finite into the infinite and back again is itself the infinite. Such a process involves seeing the infinite as essentially a contradictory structure – the identity of identity and difference. The finite is in a perpetual process of vanishing or negation, and this movement itself is seen as the infinite. Everything therefore falls under conceptual determination. Hegel’s claim is thus that it is only by moving to a different way of understanding concepts, namely speculative reason, that we are able to truly understand either of the categories of finitude or infinitude.
(SH 45-46)

[The next part is a bit hard for me to grasp. We will look at Deleuze’s criticism of Hegel’s infinite representation. We need to see how Hegel pushes difference past opposition to contradiction. I am not sure how this is so, since I would have assumed that anything in opposition is also in contradiction. Perhaps the difference is that opposing things do not necessarily negate one another (or imply the falsity of the other), but contradictory things do. Let us take the example of being and nothing. We can say they are opposed. But we are not necessarily saying just yet that they are in contradiction. So again, perhaps the difference is that opposition here means somehow being incompatible or non-identical in some problematic way, but contradiction implies additionally the negation of one by the other. Hegel takes oppositions but says they sublate negationally on account of their mutual contradictoriness. But I am not sure if I interpret this correctly. The next idea is that Hegel’s dialectical movement seems univocal since there is just one process that is generative of many categories; however, it really is not. I do not understand why yet. And I cannot understand why yet from the quotation in Spinoza: Practical Philosophy. It has something to do with the organization of a Form and the formation of subjects. I am not sure, but maybe the problem is that the dialectic is univocal but it is used to explain distinct subjectivities and maybe substances, and is therefore really somehow equivocal. I will quote:]

What, therefore, is the relationship between the infinite and finite that Hegel develops? Deleuze’s claim is that infinite representation is no better than finite representation. In distinguishing the two, he writes that ‘it treats identity as a pure infinite principle instead of treating it as a genus, and extends the rights of the concept to the whole instead of fixing their limits’ (DR 50/61). The finite and the infinite are still understood oppositionally, as each is not the other, but at the same time, they are united together, in that they are part of one process. Now, if two terms are opposed to each other, but are both asserted simultaneously, then we have a contradiction. This is why Deleuze claims (and Hegel would agree) that speculative reason operates by pushing difference past opposition to contradiction. In that everything is one element (the infinite), it appears as if we have a univocal theory much like Spinoza’s. In actual fact, however, Hegel’s theory preserves the central features of representation: ‘Goethe, and even Hegel in certain respects, have been considered Spinozists, but they are not really Spinozists, because they | never ceased to link the plan[e of infinite representation] to the organization of a Form and to the formation of a Subject’ (SPP 128–9).
(SH 46-47)

SH then explains that Deleuze offers three criticisms to Hegel’s approach. 1) Because Hegel uses language and words, he is using finite representations and thus never escapes finite representation. [The next point about the universal I have difficulty grasping. I am not sure what the universal has to do with Hegel’s dialectic, at least as the term is meant here. Perhaps the dialectic is universal because all things come about through it. Then we need to somehow add into this the concept of the singular, which is neither particular nor universal. It seems Kierkegaard’s Abraham is singular. Recall SH’s discussion of this. God’s command goes against the categorical imperative, which is a universalization of moral behavior. Let us work with the categorical  imperative first. We should not steal, because if everyone did, there would be no sense of property, and thus no stealing would be possible anyway. The prohibition against stealing then is universal. Any one instance of stealing or choosing not to steal is a particular instantiation of that universal. So actual acts relevant to stealing are particulars to the universal. But Abraham’s intent to kill his son is not relevant to the universal, since God’s command overrides the universal (the categorical imperative would say ‘never murder’). It is also not a particular, since it is not one of many common instances relative to the universal prohibition against murder. It is a unique and singular situation, given that God very uncharacteristically makes this cruel and illicit demand. So for this reason perhaps it is singular rather than particular. Even with this in mind, I am not quite sure I grasp the point here yet. Perhaps SH is saying that for Deleuze, to see every moment as part of a universal movement is to not notice its absolute uniqueness and singularity. Maybe the view is that newness is radically new. It comes out of nowhere. It is not implied or somehow otherwise contained in the prior moment. Each moment is not an instantiation of some greater pattern. Each moment is singular and unique unto itself. I will quote:]

Deleuze makes three main criticisms of this approach. First, ‘[Hegel] creates movement, even the movement of the infinite, but because he creates it with words and representations, nothing follows’ (DR 52/63). Deleuze’s claim is that Hegel has misunderstood the cause of the movement of thought by continuing to represent it, rather than seeing it as escaping representation. The aspect of representation which Deleuze takes to be critical here is the universal. ‘“Everyone” recognises the universal because it is itself the universal, but the profound sensitive conscience which is nevertheless presumed to bear the cost, the singular, does not recognise it’ (DR 52/63). The singular, or singularity, which is neither particular nor universal, is excluded by beginning with a term which is essentially universal. We can return to the figure of Abraham. Abraham cannot be understood within the framework of the universal, which is the precise reason for Kierkegaard’s introduction of him in Fear and Trembling.
(SH 47)

Now for the second criticism. 2) [I do not understand this one very well yet. It seems to be that Hegel’s dialectic never breaks from the genus-species model and thus still has the problems of Aristotle’s representational system. The way it keeps this Aristotelian model seems to be that all the movement revolves around a basic concept of the infinite as beginningless/endless ceaseless movement. It is not a definitional sort of structure. But it does seem to regard all particulars as instances of a common pattern or dynamic. The movement from being to nothing is of the same sort of movement as that from becoming to existence, and so in each and every other instance of the dialectic.]

The second criticism is that this movement is always around a particular point. Deleuze is claiming that Hegel relies on a ‘monocentring of circles’ (DR 49/60) which Deleuze claims comes about through Hegel’s adherence to the species–genus model. In the case of the finite and the infinite, movement ‘revolves’ around the central moment of the true infinite. Hegel has not got rid of the idea of a central identity, therefore.
(SH 47)

Now the third criticism. 3) Hegel’s basic structure of opposition is too crude to apply to the real world where there is much more ambiguity, overlap, mixing, and so on.

The third point, which relates the previous two, is that the idea of opposition, which Hegel uses to unite the particular and universal, is too rough to provide an adequate description of the world. ‘Oppositions are roughly cut from a delicate milieu of overlapping perspectives, of communicating distances, divergences and disparities, of heterogeneous potentials and intensities’ (DR 50/61). That is, Deleuze asserts that simply relying on a reinvigorated understanding of the distinction between finite and infinite will not provide the kinds of fine-grained distinctions needed to describe the world adequately.
(SH 47)

SH ends by noting that we cannot reduce Hegel to Aristotle despite their similarities. Hegel in many ways has responses to the problems of Aristotle’s system, but we do not need to review them for our purposes in this guide (47).

 

 

 

 

 

Citations from:

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

Or if otherwise noted:

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

 

SPP:

[Deleuze] Spinoza: Practical Philosophy, trans. Robert Hurley, San Francisco: City Lights Books, 1988.

Hegel, Georg Wilhelm Friedrich (1999), Science of Logic, trans. A. V. Miller, Amherst, NY: Humanity Books.

 

 

Somers-Hall, (1.8), Deleuze’s Difference and Repetition, ‘1.8 Infinite Representation (42–4/52–4, 48–54/59–65)’, summary

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

[Central Entry Directory]
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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.]

[UPDATE: My lack of knowledge, cleverness, and time prevent me in some cases from being able to re-explain in my own way some ideas in Somers-Hall's text. We are fortunate that the author has taken the time to remedy these gaps in my summary. Please see his clarifications in the comments section.]

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

1.8 Infinite Representation (42–4/52–4, 48–54/59–65)

Brief summary:

Representational systems may be classified either as finite or infinite. In finite ones, finite forms are limited  by the matter they inform. But in infinite representation, all things are somehow expressions of one infinite concept. (This distinction will be clarified in forthcoming sections.)

 

Summary

[We had been dealing with the problems of Aristotle’s manner of understanding difference and being. He had a representational, identity-based conception of beings, with negation as a determinant of definitional limits, that in the end had to have an equivocal conception of being in order for it to be able to have sense within his system. We saw then how a univocal conception of being could remedy the problems of Aristotle’s system. But] Deleuze also says that there is a way other than a univocal understanding of being. So we have philosophies based on the notion of judgment [perhaps an example would be philosophies like Aristotle’s which regard things themselves as having a subject-predicate judgment structure. In Aristotle’s system, the genus is a predicate to a species, such that we might say, ‘a man (species) is an animal (genus) that reasons (specific difference).’] Deleuze distinguishes two ways to characterize such judgment-based systems. (44a). [The following is very complicated and yet brief. I will try to work through it, but I will be unable to articulate it very clearly. We first note Aquinas’ definition of limit. I am not sure if everything mentioned here was already said before. Previously we saw how Aquinas defines finite and infinite on the basis of limit, with the finite being limited and the infinite not limited. And we also saw how for him, matter on its own and form on its own are unlimited. Matter can unlimitedly take on any form, but as soon as it does, it is limited to that form. Form, however, is unlimited in that it can be instantiated in infinitely many cases, but as soon as it is instantiated in matter, it is limited to that instance (or that limited number of instances). I cannot connect that very well with SH’s point here that “Aquinas’ definition of limit […] showed that finite things failed to properly express their form because they were limited by matter” (44). I am not exactly sure why this would be. Perhaps the form itself has features that are not expressible in the matter they inform, maybe because the matter has physical limitations that restrict its ability to express those formal features. I am just guessing. Then SH says that this situation leads to a distinction between something’s essence and its appearance (perhaps because its essence somehow has features not found in its appearance, but I am not sure). And, perhaps the appearance can be more or less fitting to the essence (somehow), since “something expresses its essence to the degree that its actual finite form embodies its essence” (SH 44). This is finite representation, I am guessing because something finite somehow in a limited way expresses or represents its essence. Now we move to infinite representation, which I also have trouble grasping. First we are to recognize that in finite representation, there are finite forms which occur in matter. I did not in the prior text understand the difference between a finite form and an infinite form. Is the infinite form one that is not instantiated in a matter, and forms that are informing matter are finite given that matter somehow limits them? At any rate, in infinite representation, this is no longer the case. Instead, “everything that is exists as a moment of an infinite concept which encompasses everything” (SH 44). I am not sure how to grasp this. How would a concept be infinite? How would a concept encompass everything? If it is not like the highest genus, then how do we conceive it?

I am a bit confused at this point. But SH says he will elaborate, so we should at this stage be patient. I quote SH in the following:]

At this point, he makes a distinction between two different ways in which we can characterise philosophies that are based on the notion of judgement. The first form, which we have been dealing with, is finite representation. This is based on the idea that judgements describe the essential structure of things. In other words, they set out the essential determinations which make up something. What makes it finite is the notion of limit. Aquinas’ definition of limit, for instance, showed that finite things failed to properly express their form because they were limited by matter. This led to a distinction between the essence of something and its appearance, in that something expresses its essence to the degree that its actual finite form embodies its essence (‘their degree of proximity or distance from a principle’ [DR 37/46]). Deleuze’s claim is that infinite representation replaces the notion of matter with a broader notion of representation. Rather than finite forms occurring in matter, everything that is exists as a moment of an infinite concept which encompasses everything. In effect, this is the claim that the world is therefore conceptual ‘all the way down’: ‘Instead of animating judgements about things, orgiastic representation makes things themselves so many expressions, or so many propositions: infinite analytic or synthetic propositions’ (DR 43/53). I want to spend a bit of time outlining how these approaches might function. In relation to the discussion of representation so far, the following comment by Deleuze sums up the difference between finite and infinite representation [the following quotes Deleuze]:

The signification of the very notion of limit changes completely; it no longer refers to the limits of finite representation, but on the contrary to the womb in which finite determination never ceases to be born and to disappear, to be enveloped and deployed within orgiastic representation. (DR 42–3/53)
(SH 44)

 

Citations from:

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

Or if otherwise noted:

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

 

 

 

Somers-Hall, (1.7), Deleuze’s Difference and Repetition, ‘1.7 The Eternal Return (40–2/50–2)’, summary

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

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Henry Somers-Hall’s Deleuze’s Difference and Repetition, Entry Directory]

 

[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.]

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

1.7 The Eternal Return (40–2/50–2)

Very brief summary:

By means of the Nietzschean idea of the eternal return, we may have a univocal understanding of being that would see difference as intensive. All being is variations in power between competing forces that express their will and potency at their fullest each moment. Such a purely affirmative view of the world would mean that we find every moment of our lives as perfect and as full as they can be, and thus we would want to relive these moments infinitely throughout eternity.

Brief summary:

In Nietzsche’s eternal return, we re-experience every moment of our lives exactly as we have, but infinitely more times throughout eternity. If we view the world as made of delimitable subjects that may make moral choices as to how much power to exert over others, then we would be inclined to think that certain circumstances in our lives could have been better somehow. We therefore would not want to affirm the eternal returnability of every aspect of our lives and self-experience. However, if we saw that fundamentally there are no such substantial divisions in our world but rather just forces competing and always expressing their will and power to their fullest in any instance, given their struggles with other forces, then we would see that every moment of our lives is as perfect as can possibly be. And for that reason, we would want to affirm the eternal returnability of our entire lives. By means of this concept of eternal return, then, we may have a univocal understanding of being, since all being is variations in differential power relations, while also maintaining an intensive view of differences in being.

 

Summary

[SH will draw from Nietzsche’s formulation of the eternal return in The Gay Science, §341.]

Nietzsche formulates the eternal return as follows [the following is Nietzsche quotation]:

What if some day or night a demon were to steal after you into your loneliest loneliness and say to you: ‘This life as you now live it and have lived it, you will have to live once more and innumerable times more’ . . . Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: ‘You are a god and never have I heard anything more divine.’ (Nietzsche 2001: §341)
(SH 42)

SH identifies two questions regarding the eternal return that are relevant at this place in Difference and Repetition (DR). 1) What is eternally returning? and 2) what is the eternal return a test for? SH begins with the first question. We previously saw Deleuze’s two ways to understand how the world is made-up: a) sedentary distribution “understands the world as a collection of things with properties” (SH 42). But Deleuze is not interested in this sort of understanding of the world as based on identities, so we will not regard what is returning as being a subject as a center of identity. Rather, b) “Instead, what returns is the nomadic distribution” (43). [What SH says at this point I do not entirely grasp, but that is probably because he is giving a preview of the elaboration to come. Somehow what returns is “the intensive, nomadic distribution”. This has something to do with the ground for modes being a “a pre-judicative field of becoming” (43). Whatever does return is something prior to identity. But how it is that the distribution returns is not entirely clear to me, especially since we cannot understand the distribution itself as an identifiable thing (as it is in the sentence) that returns.]

For Deleuze, taking up the eternal return, the ground (or, as we shall see, unground) for modes is going to be a pre-judicative field of becoming: it is the intensive, nomadic distribution which returns. ‘Only the extreme, the excessive, returns; that which passes into something else and becomes identical . . . Eternal return or returning expresses the common being of all these metamorphoses . . . of all the realised degrees of power’ (DR 41/51). The priority of difference does not, therefore preclude the existence of identities, but asserts that what returns is not these identities themselves, but something prior to identity, which Deleuze characterises as difference.
(SH 43a.b)

The ‘test’ of the eternal return is whether or not we can only see the world as a sedentary distribution or if we can instead also see it as a nomadic distribution. [I do not understand clearly what this has to do with the ‘what we can do’ idea, but perhaps the idea is if we can see that nothing about our lives is ever lacking, since each moment and its conditions are an expression of power in its fullness. And I suppose if we see each moment as perfectly full and lacking in no way, that we would want to affirm it and desire to re-experience it for eternity.]

The eternal return appears as a test – whether we can bear the heaviest burden of the demon’s truth. What is this a test for? The lamb and the bird of prey both see the world in terms of different distributions; the former according to the sedentary distribution, the latter according to the nomadic distribution. In this case, deciding between them is straightforward, but it may be difficult to see whether something is governed by a sedentary or nomadic distribution. The eternal return allows us to differentiate those two classes. Only that which is pure affirmation, or which is not separated from what it can do, can truly will the repetition of everything that makes it what it is. Those who cannot affirm this do not have their ground in the affirmative field of differences, but are instead, like the lamb, grounded in the sedentary distribution. The fact that they make a distinction between what can be done and what is done (they posit agency), means that they as agents are not the same as their actions. For the lamb, therefore, positing its own return is not identical with positing the return of everything which is. The eternal return therefore allows us to differentiate ‘the superior form of everything that “is” ’ (DR 41/51) from those beings that are really not (as the sedentary distribution is not a well-founded way of understanding the world). In doing so, it allows us to characterise that set of entities which genuinely are, and are not merely secondary effects, just as the lamb’s attitude is a secondary effect of the bird of prey’s.
(SH 43)

 

 

Citations from:

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

Or if otherwise noted:

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

 

Nietzsche, Friedrich (2001), The Gay Science, trans. Josefine Nauckhoff, Cambridge: Cambridge University Press.

 

 

Somers-Hall, (1.6), Deleuze’s Difference and Repetition, ‘1.6 Nietzsche (36–7/45–7, 40–2/50–2, 52–5/63–7)’, summary

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

[Central Entry Directory]
[Deleuze Entry Directory]
[Henry Somers-Hall, Entry Directory]
[Henry Somers-Hall’s Deleuze’s Difference and Repetition, Entry Directory]

 

[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.]

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

1.6 Nietzsche (36–7/45–7, 40–2/50–2, 52–5/63–7)

Very brief summary:

A Nietzschean univocal view of reality would say that there are not primarily independent beings choosing to exercise power morally or immorally. Rather, there are nothing more than competing forces in flux, all exercising their power purely affirmatively, since each force is exerted to the fullest it can be. This is a univocal understanding, since all being is understood as power. And, it is based on difference and affirmation.

Brief summary:

If we understand ‘being’ as power rather than as substantiality, then we can grasp it as univocal and affirmative. Deleuze builds from Nietzsche’s notion of subjectivity being a fabrication created by the weak in order to externalize blame for their weakness. In reality there are just competing forces expressing themselves at their fullest and finding relative value in their competitions. This is a nomadic understanding of what makes up the world. It sees the world as made of pure difference, that is, exclusively of differential relations between competing forces. And it is affirmative, since these powers are understood as being as great as they can be and never arbitrarily self-limiting. They are expressions of a pure affirmative will.  A sedentary understanding would instead section off regions in this field of differential power relations and say we have substances with different moral values, depending on how they seemingly choose to dominate others. This sees one thing as being defined by the limits that separate it from other things, thus it is based on negation rather than affirmation. Also, it can only come after the more basic differential field of change and becoming.

 

Summary

[We previously examined Spinoza’s univocal understanding of being. There is one substance (being/God), but it has an infinity of intensive modal variations/determinations and an infinity of essences. SH will now look at a critical problem Deleuze finds in this, which is that it still in a sense is like Aristotle’s genus-species predicative structure and thus may have its problems of representation. For Aristotle, the genus is a predicate to the species. For example, “Man is (a type of) animal).” Also, the genus is like a substance and the species are like determinations of it. So, an animal can be more determinately a man, a dog, etc. Spinoza’s system still places modes as determinations of being, and in that sense takes this form of (predicative) judgment and thus of representational thinking. I will venture a guess at how this might look. For example maybe we could say something like: ‘this modal variation in the attribute of extension, specifically, myself, is a modal variation of being’. In that way, being still functions like a genus to which we are a predicated determination.]

Despite the fact that Spinoza represents an advance over the work of Scotus, Deleuze claims that for Spinoza, ‘substance must be said itself of the modes and only of the modes. Such a condition can be satisfied only at the price of a more general categorical reversal according to which being is said of becoming, identity of that which is different, the one of the multiple, etc.’ (DR 40/50). Deleuze’s point is that the relation of modes to being is still structured like the terms of a judgement. The modes are said of being, in the same way that we might say of a man that he is rational, and so we still understand being as if it were a subject, even if we know that in reality it is singular rather than one, and thus different in kind from the object of a judgement.
(SH 38)

[While Spinoza (and similarly Scotus) provided an intensive understanding of difference, he still in a sense places being (God/substance) as the highest term in the hierarchy. So we turn now to Nietzsche.] “In order to overcome this limitation, we need somehow to replace our account of | being as the highest term in our hierarchy with difference, whilst retaining the insights given by the intensive understanding of difference; it is Nietzsche, Deleuze claims, who provides the means to do this” (SH 38-39). Although SH will return to Nietzsche later, he will in the following locate two parts of Nietzsche's writings that Deleuze bases his argument on: 1) section 13 of Essay I of Genealogy of Morals, “where Deleuze sees Nietzsche as opposing the subject–property view of reality,” and 2) aphorism 341 of the Gay Science “where Nietzsche presents the eternal return.” For Deleuze, Nietzsche’s eternal return is a univocal principle (SH 39).

In section 13 of Essay I of Genealogy of Morals, Nietzsche contrasts “two basic attitudes towards the world, that of the lamb and the bird of prey” (SH 39). The lamb is weak, and it views its predator birds as evil, since they gain dominance and advantage over the lambs. Whatever is opposite to the birds, that is, whatever is more like the lambs, would then be good in the eyes of the lambs. Their values then are not based on some intrinsic value to the birds’ traits and behaviors, but rather based on whatever is superior in power and more threatening to them. Consider instead good and evil from the perspective of the birds. The predator birds do not in this relation see any threats or superior powers. So there is no evil here. And in fact, the lambs are delicious to them. So lambs are not evil but rather good. [I am not sure if this next point is inferable from the prior ones we just made, but the next idea we move to in the Nietzsche quotation is that there are no subjects or actors. This is a mistake we make by using language (and its conceptual structures, like subject-predicate) to understand how events transpire.  For example, we see lightning and its flash. We conceptualize it (in certain Western languages) in a formulation like, “The lightning flashed.” This grammatical structure leads us to conceptualize the lighting as distinct from its flash, as if there is an actor that may choose one action or another. In reality there are just competitions of power operating according to quantities of force (drive, will, action). Perhaps in the case of lighting, we do not have a subject, lighting. Rather we have a competition of positive and negative charges, and as a result of that struggle of force quantities, there is the event of lightning-flash. But I am not sure if I am picturing this properly, since in this illustration, we seem to have two distinct actors, namely, the competing forces or ‘charges’. At any rate, the relevance here is that in reality there is an amoral situation. The powerful force prevails over the less powerful. But both are reciprocally determined in their mutual conflict, so more basically there is just force-differentiation. Language misleads us to misunderstand the situation. We think that there is a dominating party acting immorally upon a dominated party. We hold a supposed subject responsible for the immoral act. But really as we said there is no blame to be given and no subject who could receive blame anyway. Another idea here is that the more powerful side of the conflicts does not really have a choice to be less powerful. This may be because again there is no such actor who might have that option, or perhaps it is because the weak cannot help but be weak and similarly the strong cannot help but to be strong.]

Nietzsche presents a contrast between two basic attitudes towards the world, that of the lamb and the bird of prey [the following up to citation is quotation of Nietzsche Genealogy of Morals]:

There is nothing strange about the fact that lambs bear a grudge towards large birds of prey: but that is no reason to blame the large birds of prey for carrying off the little lambs. And if the lambs say to each other, ‘These birds of prey are evil; and whoever is least like a bird of prey and most like its opposite, a lamb, – is good, isn’t he?’, then there is no reason to raise objections to this setting-up of an ideal beyond the fact that the birds of prey will view it somewhat derisively, and will perhaps say: ‘We don’t bear any grudge at all towards these good lambs, in fact we love them, nothing is tastier than a tender lamb’ . . . A quantum of force is just such a quantum of drive, will, action, in fact it is nothing but this driving, willing and acting, and only the seduction of language (and the fundamental errors of reason petrified within it), which construes and misconstrues all actions as conditional upon an agency, a ‘subject’, can make it appear otherwise . . . no wonder, then, if the entrenched, secretly smouldering emotions of revenge and hatred put this belief to their own use and, in fact, do not defend any belief more passionately than that the strong are free to be weak, and the birds of prey are free to be lambs: – in this way, they gain the right to make the birds of prey responsible for being birds of prey. (Nietzsche 2006a: §13)

Nietzsche is here presenting an argument which combines moral and ontological aspects. The natural state of affairs is that of the bird of prey, who exercises his strength, and sees itself as good. The lamb, however, sees the bird of prey as evil, and therefore sees itself as good. The symmetry between these two positions is misleading, however, and each rests on fundamentally different ways of seeing the world. For the bird of prey, its action is simply an expression of its strength, or, in more Nietzschean terms, we might say that the bird of prey itself is an | expression of strength: ‘It is just as absurd to ask strength not to express itself as strength . . . as it is to ask weakness to express itself as strength’ (Nietzsche 2006a: §13).
(SH 39-40)

[The next paragraph continues ideas made in our prior bracketed commentary regarding grammar and subjectivity.]

The lamb’s reaction is a moral reaction, and one that is made possible by an illusion fostered by grammar: it posits a subject who is responsible for exercising its strength. Nietzsche gives the further example of lightning. When we say that ‘lightning strikes’, we are forced by the structure of language to posit a distinction between a subject (‘lightning’) and an act (‘striking’). Now we might recognise in this case that in fact there is nothing other to the lightning than its striking itself – there is no hidden subject behind the act – but language opens up a way of thinking of the world in terms of agents and actions. Once the lamb understands the bird of prey as an agent acting, he can posit the (illusory) possibility of the agent withholding this action. Thus, the bird of prey, once it is seen as a subject, becomes culpable for what it does.
(SH 40)

SH will now use this distinction [I think, between a subject-structured understanding of events and a force-conflict understanding] to explain Deleuze’s other distinction between sedentary and nomadic distributions. A distribution is a way “of thinking about what something is essentially, or more generally, what kinds of things the world is composed of” (SH 40). [Perhaps it is considered a ‘distribution’ because it is concerned with how compositional parts are arranged.] Our attention in the following will be working for a while on sedentary distributions, regarding which Deleuze writes, “‘A distribution of this type proceeds by fixed and proportional determinations which may be assimilated to “properties” or limited territories within representation’ (DR 36/45)” (SH 40). We are here reminded of Aristotle’s system of division which differentiates things on the basis of clear defining limits that define what is special and proper to each thing. In the above bird/lamb illustration, the lamb would be working with sedentary distributions, since it regards itself and the birds as different actors with distinct traits that have very different moral values (40).

We also note that in this Aristotelian sedentary conception, limits serve to define what makes one thing what it is and what makes something else not that thing but rather something different entirely. This notion of delimiting then makes us conceptualize notions spatially, as if one could occupy one part of conceptual space and have a limit, outside of which it does not belong but in where other concepts do [think for example of Venn diagrams]. It also involves a concept of negation [since we understand each concept in terms of how it is not the others, and vice versa]. [This conception also would have us judge the degree to which an actual instance fits with its proper concept. Perhaps for example we might characterize something as more typical or exemplary of its class.] “Finally, it provides ‘a hierarchy which measures beings according to their limits, and according to their proximity or distance from a principle’ (DR 36/46); in other words, according to how closely a being conforms with its essence or is a degenerate instance of it” (SH 41). This means that the sedentary distribution regards the world on the basis of opposition and negation.

A sedentary distribution therefore is a way of ordering the world that is hierarchical, and proceeds by the delimitation of the world according to oppositional determinations. The notion of difference is grounded in negation and operates according to a spatial metaphor.
(41)

The Aristotelian system regarded difference as being a matter of ‘this and not that’. Yet we saw how for Scotus and Spinoza we may regard difference not as difference in kind but rather as intensive qualitative variation, that is, having more or less a degree. We are not in these cases working with “a spatial conception of organisation” (41). Thus “Deleuze introduces the univocal conception of being in order to explain those features of the world which escaped something like an Aristotelian conception of the world” (41). [I do not completely grasp the next quotation about Oedipus. Perhaps it is similar to the idea we examined before that for Scotus, there is just an intensive difference between God’s infinite being and our own finite being, but still we make a difference-in-kind distinction between the two. Or we might also think that the difference between ice and water is quantitatively (and intensively) a small change, but qualitatively it is a complete difference in kind.]

Deleuze introduces the univocal conception of being in order to explain those features of the world which escaped something like an Aristotelian conception of the world. The nomadic distribution is intimately connected to this univocal conception: ‘Oedipus’ chorus cries: “which demon has leapt further than the highest leap?” The leap here bears witness to the unsettling difficulties that nomadic distributions introduce into the sedentary structures of representation’ (DR 37/46).
(SH 41)

[The next part is a bit confusing for me. My impression is that it is a reference to Deleuze’s Spinozistic notions of ‘what a body can do’, limit, and perfection. In this talk here Deleuze discusses the difference between spatialized limit and the limit of power or action. There is more discussion of ‘what can a body do’ here, and also in this and this talk. And see again especially Deleuze’s commentary on Spinoza’s correspondence with Blyenbergh regarding the perfection of essence and modal expression. It seems in the quoted Deleuze passage that instead of limit being understood spatially, we are to understand it more as a limit of action or power, a limit of what one body can do. One main idea in the Blyenbergh correspondence is that everything is doing everything that it can do in any given moment. If it seems to be weak, that is because it finds itself in a certain relation of forces, including the competing forces within it and also including the competing forces between itself and other external competing forces, in which it is expressing the fullest power it is able to have in that moment. Deleuze gives the example of meditating in the dark, and someone turns on the light suddenly. The person loses power, since the light dazzles them and makes them lose meditative concentration. The person is still functioning at their optimum even when blinded, but just under these circumstances the optimum is relatively lower than before. If however the person were looking for their glasses in the dark, and someone gradually turns up the light so they can better see them, then their power is increased relatively given that situation. These fluctuations in power are not however fluctuations in perfection. All is equally perfect in a sense, since everything is operating at its maximum (and also, from the perspective of substance itself, nothing is being subtracted from it even though its modal parts are varying in power in relation to one another). It is perhaps for this reason that Deleuze says in the quote to follow that “the smallest becomes equivalent to the largest”, in that all are equally affirmative of the power they have in any given situation. The point SH seems to be making here is that we do not think of the world as being made up of things that choose whether or not to exercise their power but rather we have competing forces in a world of fluctuating changes. SH’s further points become slightly more difficult for me to grasp. The next point is that for Deleuze, negation results from affirmation. To get to this point, perhaps we first recognize that the substance-property based ontology which fixes subjects who perform actions and express properties is based on negation, since it depends on definitional limits. But if we follow Deleuze’s Nietzschean-Spinozism, we would say that more primarily there are competitions of forces, whose limits are not spatially substantial but are rather intensive degrees of moreness or lessness. This is purely affirmative, since everything expresses its power in complete fullness, given the affective circumstances of their situation. Then secondly, on account of feelings of powerlessness, we externalize blame to subjectivities we fabricate in this indeterminate field of forces. (I still cannot make my account consistent regarding how it is that  we can have entities which place blame on other entities they fabricate but supposedly there never were any entities to begin with). So first the world in its basis is affirmative (in that there is will to express power in fullness each moment) and composed of pure difference (in the form of differential relations between competing forces). Only secondly and on a less fundamental level do negations arise in the form of fabricated or conceptualized limits between supposed agents wrongly understood to be making moral choices of whether or not to artificially limit their own power.]

If a sedentary distribution is fundamentally tied to an understanding of the world in terms of subjects and properties, how are we to understand this notion of a nomadic distribution? The key point is Deleuze’s claim that everything goes to the limit of what it can do. He elaborates on this as follows [the following up to citation is quotation of Deleuze]:

Here limit [peras] no longer refers to what maintains a thing under a law, nor what delimits or separates it from other things. On the contrary, it refers to that on the basis of which it is deployed and deploys all of its power; hubris ceases to | be simply condemnable and the smallest becomes equivalent to the largest once it is not separated from what it can do. (DR 37/46)

When we separate the bird of prey from its action, or lightning from its striking, we institute the two moments of an ontology of judgement: the subject and the property. This moment of separation of something from what it can do is what gives us the Aristotelian idea of a world of fixed things. If something is not separated from what it can do, then instead of an ontology of being, we have an ontology of forces, or becoming. There are not static points from which movement originates, but rather just movement itself. We can tie together a number of results at this stage. Just as Scotus shows that analogy can only operate within a prior univocal framework, Nietzsche shows that the point of view of the lamb is derivative of that of the bird of prey. Deleuze similarly argues that ‘negation results from affirmation: this means that negation arises in the wake of affirmation or beside it, but only as the shadow of the more profound genetic element – of that power or “will” which engenders the affirmation and the difference in affirmation’ (DR 55/67). Difference is therefore primary in this scheme. This leads us to the last aspect of Deleuze’s discussion of univocity: how are we to conceive of a univocal conception of becoming?
(SH 41-42)

 

 

 

Citations from:

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

Or if otherwise noted:

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

Nietzsche, Friedrich (2006a), On the Genealogy of Morality, trans. Carol Diethe, Cambridge: Cambridge University Press.