[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.
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