1 Apr 2015

Somers-Hall, (1.11), Deleuze’s Difference and Repetition, ‘1.11 Phenomenology (55–7/67–9)’, 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

1.11 Phenomenology (55–7/67–9)





Brief summary:

Many philosophical systems explain reality by means of such concepts as limitation, negation, and opposition. Deleuze showed these to be flawed concepts. However, there is a reason they arise. Our knowledge of the things in our world is limited to our perspectival knowledge of them. In perception we can only view an object from our perspective, and we never see it from all possible perspectives at once. Nonetheless, we regard it as a whole thing, even though our phenomenal data can only constitute it partially. Deleuze thinks that the way we do this is by placing the partially constituted object into oppositional relations with other objects, so to define its boundaries and to constitute it negatively. In reality, the object can be no more than our perspective on it. Merleau-Ponty’s perspectival phenomenology could perhaps be not based on identity, but in fact it is, since the body is taken as a center of perception and thus to have a fixed identity.

 



Summary


[Previously we noted that Deleuze for the most part is against difference understood in terms of opposition. We now learn that, nonetheless,] “Deleuze does have a place for the notion of difference as opposition, although he says that ‘negation is difference seen from its underside, seen from below’ (DR 55/67)” (SH 50). And it is “only ‘the shadow of the more profound genetic element’ (DR 55/67)” (SH 50). Negation is often understood spatially, since something’s not being something else can be thought of as it standing outside it. “This pencil is not this piece of paper to the extent that they occupy different positions within the same space” (SH 50). [The basic reasoning here seems to be this. Most basically there is not extensive difference but rather there is only intensive difference. How that can be so will hopefully be clarified. What would that mean in physics for example, which studies the motion of objects through extensive space? At any rate, take that claim to be true. Extensive space is an illusion, and  is not fundamentally real. The next step in the reasoning seems to be that you cannot have oppositional difference without extensive spatiality. Since extensive spatiality is an illusion, then oppositional difference would be illusory too. The question we might raise is, ‘Is there really no other way to conceive oppositional difference except on the basis of extensive spatiality?’ I cannot think of any. It does seem that opposition requires an external relation between separate entities, and that externality carries with it a spatial sort of relation. Is it possible to have self-opposition without the self becoming two selves, or without that opposition being internal, like two warring components of oneself (which would be external to each other even though internal to the self they compose)?]

We can see that the same is true of the concept of negation. If we think about something not being something else, then we normally think of them as being spatially separated from one another. This pencil is not this piece of paper to the extent that they occupy different positions within the same space. Deleuze argues that extensive space is an illusion, but one that emerges quite naturally from the way in which we relate to the world. Intensive difference is generative of our notion of objective space, and it is this space which forms the basis of oppositional difference. If we forget the fact that this conception of space is generated from something more primitive, then we end up in a situation where it is possible to introduce the notions of opposition and negation. The world thus has a tendency towards oppositional difference, but we make a mistake when we take this tendency to be a completed state of things.
(50)


So somehow we generate the illusion of [negation and opposition and thus] identity. Deleuze explains how this is so by revising one of Merleau-Ponty’s central phenomenological claims. Deleuze will give a ‘genetic account’ of how this illusion of identity comes about. To follow his reasoning, we need to look first at three statements Deleuze makes in DR. [The first is that there are an infinity of representations in infinite representation. This can take two forms, depending on whether it is an infinity of the Large as with Hegel or an infinity of the Small as with Leibniz. With Hegel, the whole of the dialectic’s movement is infinite in that it is ceaseless (although I am not sure how to explain the fact that it begins in pure being and ends in the absolute). For Leibniz, each smallest part of the world expresses the entirety of the rest of the world, which is infinite. The next two quotes I cannot explain on the basis of what we have learned so far.]

1. Infinite representation includes precisely an infinity of representations – either by ensuring the convergence of all points of view on the same object or the same world, or by making all moments properties of the same Self. (DR 56/67)

2. The immediate, defined as ‘sub-representative’, is not therefore attained by multiplying representations and points of view. On the contrary, each composing representation must be distorted, diverted and torn from its centre. Each point of view must itself be the object, or the object must belong to the point of view. (DR 56/68)

3. Difference must become the element, the ultimate unity. (DR 56/68)
(SH 51)

SH then moves directly to a passage in Merleau-Ponty that Deleuze refers to. It comes from Phenomenology of Perception, and in it Merleau-Ponty gives “his account of the movement from our own perspective on the world to a positing of objective being” (SH 51). [In this quote, Merleau-Ponty first notes that our understanding of a phenomenal object is always limited by the fact that we can only see it from one perspective at a time. It is impossible to grasp it from all the infinitely many perspectives at once. This is not mentioned, but we might also think of how the object is internally composed and yet our vision often cannot penetrate most objects’ surfaces to see inside them. We might also note that there are many temporal perspectives as well. Nonetheless, instead of seeing the object itself as incomplete and unformed and missing the elements we cannot perceive, we instead ‘posit’ it as a whole object. Merleau-Ponty says this is a sort of ek-stase, which in other contexts he means a going outside of oneself. In this case it is perhaps us going outside the limitations of our own perspectival grasping of things and entering into a more third-person sort of position in relation to the objects of our experience]:

But, once more, my human gaze never posits more than one facet of the object, even though by means of horizons it is directed towards all of the others . . . If I conceive in the image of my own gaze those others which, converging from all directions, explore every corner of the house and define it, I have still only a harmonious and indefinite set of views of the object, but not the object in its plenitude . . . If it is to reach perfect density, in other words, if there is to be an absolute object, it will have to consist in an infinite number of different perspectives compressed into a single coexistence, and to be presented, as it were, to a host of eyes all engaged in one concerted act of seeing . . . The positing of the object therefore makes us go beyond the limits of our actual experience which is brought up against and halted by an alien being, with the result that finally experience believes that it extracts all its own teaching from the object. It is the ek-stase of experience which causes all perception to be perception of something. Obsessed with being, and forgetful of the perspectivism of my experience, I henceforth treat it as an object, and deduce it from a relationship between objects. (Merleau-Ponty 1962: 69–70)
(SH 51)

SH then explains what this passage means with regard to the limitations to perspectives. He also observes that when we posit the object, we seem to be treating all the perspectives on the object as inessential and logically posterior to the object itself. [It seems that originally the perspectives are essential to the object. I suppose we mean here essential to the phenomenal constitution of the object synthesized by means of our object-constituting consciousness.]

Merleau-Ponty’s point is that perception is always originally from and of a certain perspective. I can never see such a thing as a totalised object. As I move around the object, I begin to notice that although my | perspective on the object changes, when I return to my original position, something similar to the original perspective returns. On this basis of the fact that my own memory appears to preserve some perspectives, I posit what Merleau-Ponty calls ‘the memory of the world’ (Merleau- Ponty 1962: 70), which includes all possible perspectives on the object. Now, with an understanding of the object based on an infinite number of possible perspectives, my own view ceases to be relevant (I become ‘forgetful of the perspectivism of my experience’). I now suppose that rather than the object emerging from the accumulation of perspectives on it, the perspectives are in fact inessential, and logically posterior to the object itself.
(51-52)


[It seems that in order to move to the next point, we need to recognize that “the object is not considered to be constituted by perception”. We saw above that it is ‘posited’, but we never have sufficient perception to constituted it as a whole object. I suppose that is not controversial, but I assume that in phenomenology the object is still constituted in consciousness, using data from perception. I am not sure if the question is: using what other data is the object constituted? The remainder of this section I find very perplexing. I will go through it gradually.]

The final stage is to recognise that now the object is not considered to be constituted by perception, we need another explanation of how it is constituted.
(52)

[SH will now explain that one way the object can be constituted is by deducing it by means relationships between objects. It is not clear to me if we are still talking about phenomenal object constitution or some other sort of constitution, like physical constitution. But it seems safe to assume that it is phenomenal constitution. So we begin by noting that we cannot see a table for example from all spatial  perspectives both outside and within it, during this moment and all others of its existence. Still somehow the table becomes fully constituted in our mind even with that missing information. Supposedly now we understand it by means of its relationship with other objects. I will try to find some ways to understand this. One way is that we see that the table is not the floor and it is not the air around it. So while we do not know all of the table, we can maybe see a lot of what it is not, and by that means we can develop a negative or a relational sense of the table’s constitution. The table is not a whole phenomena in the sense that it is a thoroughly and completely determined phenomena, but it is whole in the sense that it has boundaries that we can discern, or it has determinate relations to other things which help define its boundaries. The only other way I would offer for making sense of this has to do with Merleau-Ponty’s emphasis on the interconnectedness of all phenomena. I will not get into the details here, but if you want them you can read more in section 2 of my paper “Body and World in Merleau-Ponty and Deleuze”. The basic idea is similar to what we said in the prior section about Leibniz and the perspectival expression of the entire world in each monad. We look at the floor. It has certain shadings of color that tell us there is something obscuring the light falling on it. We indirectly perceive that there is a light and also a chair blocking that light, for example, even though we do not look up and see these other phenomenal objects yet. Each part of our phenomenal awareness is phenomenally connected with each other part, and they make a dense fabric. We in a way do perceive all corners of the cosmos, but just very, very implicitly. This is because the phenomenal traits of any part of our awareness are conditioned by phenomenal traits of nearby phenomena, which are conditioned by their nearby phenomena, and thus transitively the entirety of the phenomenal world is implied in each part. Perhaps SH means something else, but I cannot figure out what yet. He then says that these relationships are based on opposition and limits. So perhaps we might say that whatever other phenomena one phenomenon implies would lie outside its constitutional limits. (However, in the second possible interpretation I offer above, the absolutely thorough interpenetration of all phenomenal objects with all others would call into question the boundaries between any).

The final stage is to recognise that now the object is not considered to be constituted by perception, we need another explanation of how it is constituted. We thus alight on the idea that it can be deduced ‘from a relationship between objects’. This relationship is, of course, the relationship of opposition and limit. At this point, therefore, negation enters our world, as a precondition for limit.
(SH 52)

[The next point is interesting. So the reasoning again seems to be that perspectival perception is inadequate to constitute objects in their entirety, yet we still somehow do so, and we do so on the basis of negations, limits, and oppositions. For the next part of the reasoning, we need to assume that this negation, limit, and opposition were not already there, but were instead fabricated somehow by our consciousness. This seems perfectly possible, but it would help for some reasoning to understand why this might be. We seem to need to take it as an article of faith that negation, limit, and opposition are not inherent in the world. As far as I can tell, the reason we have to conclude this is that because these notions lead us to unresolved problems in explaining reality in its broadest and most specific senses (the problems of the Large and the Small), they must not be real. Therefore any instance of them must really be an illusion. But we seem to be begging the question here. How do we know that negation, limit, and opposition are phenomenal illusions or fabrications superimposed onto a world where there are none? Can it not be that they really are there, and that we are also phenomenally aware of them or that we phenomenally reconstitute them in our awareness? Our eyes move from left to right. We see a range of variations. We then draw lines in our world where before there was a continuous variation of visual information. But still, what we see on the left is different from what we see on the right. How could it possibly be that there is in reality not extensive space, with certain parts being external to other parts? I can understand how on the most local level of variation, for example our eyes just in the act of moving see a pure variation, that there can be no externality between parts but rather just pure intensive variation. However, our eyes make a wide sweep. How can it be that we see a different left from a different right side unless they are spatially distinct or somehow external to one another? Is it just because of the continuity of variation between one and the other makes them inseparable? At any rate, we are to regard the genetic conditions of negation and limit as being perspectivism. I am not sure, but I think what SH means here is simply that the limits of perspectivism create the conditions for us generating the illusion of negation and limit. Perspectivism does not however explain the actual genesis of negation and limit. This is perhaps irrelevant anyway. SH then asks how this fits in with Deleuze’s account, which implies I think that before we were indeed sticking with a Merleau-Pontian phenomenological sort of account.]

At this point, therefore, negation enters our world, as a precondition for limit. This account is therefore the account of the generation of an illusion, which, as Deleuze puts it, is nonetheless well founded. It shows how negation and limit enter the world through representation ignoring its genetic conditions (perspectivism). How does this then fi t in with Deleuze’s account?
(52)


[SH then will return to the three Deleuze quotations we began with. He says this account we give above fits in with what was said in those quotations. The first quote was: “1. Infinite representation includes precisely an infinity of representations – either by ensuring the convergence of all points of view on the same object or the same world, or by making all moments properties of the same Self. (DR 56/67)” (SH 51). SH says this account fits with “Deleuze’s characterisation of infinite representation as the convergence of all points of view (quotation 1)” (SH 52). I think I should try to make this clear, even though it seems quite clear already. The account we just gave said that we do not have all points of view. We compensate for this lack by fabricating oppositions. So perhaps this account ‘fits’ not in the sense that it matches up with its conclusion, but rather that it matches up with a claim that the account rejects. The only other explanation I can think of is that we are dealing with the thorough interpenetration of all phenomena that we discussed in our commentary above. That we noted is very much like the infinite representation of Leibniz. In that case, the need for negation and limit comes from the implicit/explicit distinction. Each phenomenal object is in fact thoroughly determined by means of its relations to all other phenomenal objects. However, much of our awareness of these infinitely many determinations is implicit and never comes to the surface of our consciousness. So perhaps it is on the basis of that implicit/explicit limitation somehow that we fabricate negation and limit.]

Such an account fits with Deleuze’s characterisation of infinite representation as the convergence of all points of view (quotation 1).
(SH 52)

[The next point is a bit difficult to grasp. The first part of it says that “Opposition comes into play through the gradual elimination of perspectives” (SH 52). I am not sure what is meant by ‘gradual elimination’. In the account as it was explained, there are perspectives that we have and those we do not have. We make up for our lacking knowledge by making use of fabricated limits and oppositional negations. I do not recall how any of those perspectives were eliminated. I can think of two ways this was so. First was that the other perspectives were possibilities or were otherwise hypothetical, and thus we eliminate them since they are not phenomenally available. The other way I can think this is so is that in fact we have all these other perspectives, but they are too implicit to make ready use of them in our object constitution, so we eliminate them. But in neither case do I understand how this elimination would be ‘gradual’. The next part of this point is that the account “fits with Deleuze’s desire that each point of view instead be the object, or the object must belong to the point of view (quotation 2)” (SH 52). This is not clear for me. Perhaps the reasoning is like this. We first take if for granted that for some reason the negation, limit, and opposition are illusory. That means the object is not fundamentally constituted by means of negation, limit, and opposition. That further means that we are left only with what we started with, our limited perspectival phenomenal data of it. On that basis, we noted, we cannot have the object as a unified and complete thing. At best, the object is little more than what is given in that limited perspective. Recall the quoted Deleuze passage was: “2. The immediate, defined as ‘sub-representative’, is not therefore attained by multiplying representations and points of view. On the contrary, each composing representation must be distorted, diverted and torn from its centre. Each point of view must itself be the object, or the object must belong to the point of view. (DR 56/68)” (SH 51). I am still not sure what is meant by the representation being distorted, diverted, and torn from its center. I was assuming that we are left with just our limited perspective. How is it torn away from us? Is it on account of the interpenetration of phenomena?]

Opposition comes into play through the gradual elimination of perspectives. It also fits with Deleuze’s desire that each point of view instead be the object, or the object must belong to the point of view (quotation 2). Such a view is a return to a form of perspectivism such as that found in Merleau-Ponty.
(SH 52)

[Merleau-Ponty was saying that we are limited to our perspectives (although this is only with explicit phenomena). Deleuze says that there is a “superior empiricism” that helps us understand “the reason behind the qualities and the being of the sensible”. I am not sure why from a perspectival phenomenology we would be unable to understand how the qualities of the sensible are given. (Also, I do not know what is meant by the ‘being of the sensible’). The issue as I understood it was that the perspectival phenomenology was unable to account for the phenomenal object in all its phenomenal properties. Also, Merleau-Ponty’s claim was that we do in fact go beyond our limited perspective to posit the object in its wholeness. Perhaps the difference here with Deleuze is that the positing is done without recourse to limitation, negation, and opposition. But I am not sure. Please judge for yourself.]

What about Deleuze’s final claim that ‘difference must become the element, the ultimate unity’? In the next paragraph, Deleuze claims that ‘the intense world of differences, in which we find the reason behind the qualities and the being of the sensible, is precisely the object of a superior empiricism’ (DR 57/68–9). This suggests that Deleuze’s analysis is going to go beyond the kind of perspectivism Merleau-Ponty proposes.
(SH 52)

[Also, it is still not clear to me how for Deleuze difference will be the element and ultimate unity. Is it that reality is somehow fundamentally a continuous intensive variation; since it is continuous, it is a unity, and because it is intensive variation,  it is differential? I think we will learn this later.]


[The next paragraph is also very difficult for me grasp. For Merleau-Ponty, as perhaps for Husserl too, the body is the the orienting center of all our perceptions. The first point SH seems to be making is that because it is a center, it is singular and has an identity. And because it is conceived as having an identity, it is improperly conceived, since we have rejected the possibility that things can fundamentally have an identity (again, perhaps on account of the problems of the Large and Small which tell us this identity is an unsuitable basis for our accounts). SH’s next point is that Deleuze will “explore what makes possible the kind of account Merleau-Ponty gives” (52d). I suppose this means Deleuze will explain on what basis we are able to incorrectly build a theory of phenomenal givenness that has a perspectival center of orientation, namely, a body which has an identity. Somehow that deeper basis is intensive difference. To get to the final point, it seems we need to regard certain assumptions phenomenologists make, such as that we have a body as a center of perception, as being byproducts of more basic genetic elements. Thus these assumptions are really “epiphenomena.” But I am not sure if by this Deleuze means that the more basic elements are themselves phenomenal, and the higher flawed ones are also phenomena but secondary and thus epiphenomenal. That does not seem right, so perhaps the ‘phenomenal’ here does not mean ‘phenomena’ in the sense of ‘givenness to our awareness’, but rather more like how it is used in science to refer to observable events.]

For Merleau-Ponty, what makes possible the field of perspectives is the body, but the notion of a body operates as an identity. Instead, Deleuze is going to try to explore what makes possible the kind of account Merleau-Ponty gives. Such an account will be what Deleuze calls elsewhere a ‘transcendental empiricism’, since it will deal with the | conditions of real experience. Intensive difference will therefore take the place of identity as being generative of our experience of the world. This means that while Deleuze can accept the phenomenological criticism of the objective understanding of the world, he can also reject phenomenology’s own account as not truly explaining the genesis of its own account. Phenomenology rejects the notion that the self-identical object gives coherence to perception, but fails to recognise that perspective itself still needs an explanation, this time in terms of difference. Phenomenology provides a description of phenomena, but what is needed is a genealogy of phenomena. Thus, Deleuze claims that ‘the whole of Phenomenology is an epiphenomenology’ (DR 52/63).
(SH 53)

 


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.


 

Merleau-Ponty, Maurice (1962), Phenomenology of Perception, trans. Colin Smith, London: Routledge & Kegan Paul.

 





 

31 Mar 2015

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.

 





 

30 Mar 2015

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

1.9 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.

 





 

29 Mar 2015

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
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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.