8 Jan 2013

Pt3.Ch7.Sb5 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘The One and the Many.’ summary

Corry Shores
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[Note: All boldface and underlining is my own. It is intended for skimming purposes. Bracketed comments are also my own explanations or interpretations.]


Henry Somers-Hall


Hegel, Deleuze, and the Critique of Representation.

Dialectics of Negation and Difference


Part 3: Beyond Representation

Chapter 7: Force, Difference, and Opposition

Subdivision 5: The One and the Many

Brief Summary:

For Hegel, we encounter the problem of the one and the many when we do not use infinite thought to dialectically integrate them. For Deleuze we encounter the problem of the one and the many when we do not regard the many as a heterogeneous multiplicity of intrinsically related parts, like the colors making up white light or the phase portrait showing all the incompossible developments of a system. According to Deleuze, Hegel’s reliance on representation prevents him from seeing this other sort of difference which does not fit into Hegel’s system.


Previously we saw how for Deleuze, the actual and the virtual are not opposed terms but are rather two tendencies of the real. Thus they do not succumb to a Hegelian critique which would try to sublate them.

We turn now to Deleuze’s and Hegel’s different approaches to the problem of the one and the many.


Previously we examined how from a Hegelian perspective, Deleuze’s ontology could be undermined by dialectically sublating his virtual and actual. Recall our discussion of the dialectic of force. We saw that there is a side of force that unifies and a side of force that multiplies. [There is somehow the force that brings all the properties of something together and also the force that distributes that thing into various properties.]

The dialectic of force emerges from the dialectic of perception, in which consciousness struggles to reconcile two notions of the thing: on the one hand, the notion of the thing as simply a collection of properties, and on the other hand, the thing as a unity. (204)

There is a collection of properties united by sharing the same ‘here’. Because they share the same ‘here', they interpenetrate. But the properties inhere because they are held together by an indifferent ‘also.’ [continuing from the prior quotation:]

The first view emerges from our consideration of the 'also' and rests on viewing the object as a simple universal, a 'here,' which results from the previous dialectic of sense-certainty. The object is conceived of as a collection of properties, and this collection is united in that it shares the same 'here'. "All these many properties are in | a single simple ' Here,' in which , therefore, they interpenetrate; none has a different Here from the others, but each is everywhere, in the same Here in which the others are" (PS, 68). This view of the object as a mere collection of properties proves, however, to be inadequate. This is because what holds the various properties together is merely an indifferent 'also'. "This salt is a simple Here, and at the same time manifold; it is white and also tart, also cubical in shape, of a specific gravity, etc." (PS, 68). This 'also' is an "abstract universal medium" (PS, 68), within which the various properties inhere. [204-205]

So this ‘also’ is like Bergsonian extensive space. We have the fact that one object shares many properties, but we also have each of these properties being of different kinds and very distinguishable from another. The indifferent unity of the ‘also’ is not enough because that makes the object no longer determinate [perhaps because if the properties were not differentiated, the object’s properties would be indeterminable, making the object indeterminate.]

A condition of the many is therefore that we have not just an indifferent connection between the elements, that it is a pure many, but instead that we view it as a One, as a unity of elements that relate to each other directly by opposing one another. (205)

So we view the object as a One. But now we have other difficulties. [The one is not constituted merely by its properties, for then we have the problem of explaining their unity. However, if the One of the object is apart from its properties, then it is indeterminate and ungraspable.] “the One cannot be conceived of in terms of any of the properties, as this would be to return to the problem of the many. The alternative, however, is to conceive of the One apart from these properties, but this leaves it, like Aristotle's concept of being, without determinacy, as there is nothing by which we can grasp it.” (205) Consciousness wavers between these options but does not resolve the dichotomy, so then it posits the notion of force, which has two facets that are reconciled.

For the rest of the dialectic, consciousness oscillates between these two conceptions, in tum treating one aspect as essential to the thing while rejecting the other as unessential, and provided by consciousness itself. Finally, the failure to resolve this dichotomy leads consciousness to posit the notion of force, thus sacrificing the commonsense notion of the object as a unity of properties for one that instead sees it as a relation of forces, whereby the two aspects of me many, as expressed force, and me one, as the unity of law, are given separate ontological realms. When this concept is pushed to the limit, both aspects are again reconciled. (205)

Somers-Hall identifies two problems.

If we remain with the notion of the many, we lose me idea of essence, as there is nothing which unifies the various determinations. The individual therefore becomes merely a collection of accidental | properties. If, on the other hand, we rely on the notion of a genus, at the level of the One, this genus itself becomes indeterminate (as we saw for Aristotle), and we risk losing the notion of the accident in the face of the abstract universality of the species. (205-206)

Thus the one and the many is like the problem of the large and the small in Aristotle.

We return now to Deleuze’s differential geometry. The problem of the large and the small is also the problem of comprehension and extension. “Comprehension defines the totality of properties that an object has, while extension defines | the number of objects in a particular class (or what objects the concept ranges over).” (206-207) Normally comprehension and extension are inversely proportional, because the more determining properties something has, the fewer sorts of things will display it, and the fewer the properties (the more general the thing), the larger the extension. But this means that if the extension ranges over all objects, the comprehension is empty of content. “For both Hegel and Deleuze, the aim therefore is to reconcile these two tendencies of the concept.” (207)

For Deleuze, multiplicity does not need the unity of the One to form a system.

Deleuze takes as key to our notion of multiplicity that it is understood as a substantive: "Multiplicity must not designate a combination of the many and the one, but rather an organisation belonging to the many as such, which has no need whatsoever of unity in order to form a system" (DR, 182). [207]

So when we say many, as multiplicity, we are not saying many discrete things, but rather many itself. We are not using many as an adjective but as a noun.

What Deleuze is hinting at here is the fact that the one and the many both take their roots in an adjectival mode of expression. That is, we talk of the one and the many in terms of the many this-and-that and the one this. The one and the many therefore already point toward the idea of a set of discrete elements that essentially remain indifferent to one another. If the many is understood in these terms, the many, as adjectival, becomes something like the medium within which the elements reside or the relations that hold between indifferent elements. It is that which allows the many indifferent elements to be brought together, through what is an extrinsic description. (207)

Hegel does begin by assuming many as an adjective, many thises, but as we saw the indifference of the elements in insupportable, because their “their determination can only be understood mutually through their opposition to each other.” (207) Hegel then introduces the concept of negation “to both differentiate and relate the elements.” (207) For Deleuze, the multiplicity, the many, carries with it difference without discrete parts, like the example of white light being decomposable into many colors. To compose the light from the colors, each needs to be the unique color it is, but all are intensive degrees of variation within the white.

The Deleuzian conception of the multiplicity replaces the many not with a unity of the particular and the universal, but instead with the idea of a medium that is not indifferent but contains difference within itself, hence the Deleuzian example of the white light, within which all of the colors are united in such a way that they maintain their difference (207)

[If we were to distinguish the colors by placing them in subject-predicate [objectival] form, that would somehow render them unable to be considered as differentially combinable.]

In choosing this example, which as we saw comes from Bergson, we move away from an objectival conception of elements. The elements do not now exclude one another but interpenetrate. The example of light is supposed to show how the colors can coexist while still preserving their differences from one another. As such, it provides an idea of a concept of color which, as it is not grounded in the idea of an object, does not require the idea of opposition or negation. (207)

But even light needs a spatial medium in which to appear. So Deleuze uses differential geometry, which we saw allows us to picture all the incompossibly actualizable states of a system together at once.

This is why Deleuze moves to the conception of a differential geometry, as here the space itself is one in which the very fabric of its dimensions is no longer uniform but contains deformations and perturbations. As such, differential geometry contains the possibility of capturing a field of differences without having to rely on objects that inhabit a | medium. Here, the multiplicity becomes substantive in its own right. Such a geometry can be used to show all possible states of a system simultaneously, as any particular state represents one trajectory through its space. Thus, the space itself allows us to represent both the specificity of a particular state (207-208)

[For Hegel, difference does not relate indifferent elements as if they occupied different places in a spatial medium and took external relations to one another, rather, differences are inherent within something, the opposition is internalized. But for Deleuze, any use of the notion of determination as opposition or negation is a spatialization, because it prevents things from being coincident variations or intensities.]

Instead of moving to the Hegelian concrete universal by rejecting the spatial notion of difference as relating indifferent elements, as we found Hegel doing, Deleuze rejects what he takes to be the essentially spatial idea of determination as involving opposition and negation. It is this difference in approach that leaves Hegel unable to think Deleuzian difference. (208)

[Hegel’s dialectic has both the dialectical movement and the terms generated by this movement. But for Deleuze, for some reason, the process of generation and the product are not two concepts or things that can be thought apart. Perhaps this has something to do with the virtual and the actual not being opposites but rather two tendencies in the process of genesis.]

As we saw, however, Deleuze is still able to understand the process of Hegelian dialectic, since for Deleuze, this involves making the mistake of thinking the result of a process of generation apart from the process itself. For Deleuze therefore, Hegelian logic is in fact an epilogic, since the play of being and nothing relies on the exclusion of the generative field of depth. This does not, of course, prove Deleuze's point that Hegelian dialectic provides an inadequate tool for understanding the world, but it does provide some circumstantial arguments for suggesting that Deleuze may have a more powerful alternative. (208)

Deleuze assesses the logical consequences of Hegel’s dialectic, which we turn to now.

We will examine three of Deleuze’s critical statements about dialectic, and they follow from his move to transcendental empiricism. [1] Because Hegel makes use of universals, he is using representational thought, and this representation is used to explain the movement of thought. But for Deleuze, this misses the subrepresentational origins of the movement of thought. [The universal at the beginning of the dialectic never arrives at singularity.]

The aspect of representation that 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). In this case, therefore, it is the singular, or singularity, that is neither particular nor universal, is excluded by beginning with a term whose universality instigates a set of related concepts that exclude the singular from consideration. (208)

[2] Hegel uses the species-genus model, which causes his dialectic to revolve around a particular point.

The second criticism is that this movement is always around a particular point. This criticism is derived from Althusser's study of dialectic (DR, 186, 207) and argues that Hegel relies on a "monocentring of circles" (DR, 49), which Deleuze claims comes about through Hegel's adherence to the species-genus model. In doing so, all movement must be understood as being referred to a central point, just as the many must be referred to the one in the dialectic | of perception. (208-209)

[3] Hegel’s concept of opposition is too rough a concept to apply to our world of fine-grained variations.

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) . That is, Deleuze asserts that simply relying on a reinvigorated understanding of the concrete universal will not provide the kinds of fine-grained distinctions needed to adequately describe the world. (209)

For Deleuze there is a true “movement provided by the difference between the transcendental and empirical fields” that underlies the false movement of dialectic (209). Thus

In showing that Deleuze is able to support a conception of difference that is unthinkable by Hegel, we have gone a long way toward showing that Deleuze offers a coherent alternative to Hegel's thought. In providing a differential ontology, Deleuze has avoided Derrida's famous challenge that to oppose Hegel is ultimately simply to reinstate the dialectic that reabsorbs the opposing position into the dialectic as a whole. (209)

But to place their confrontation in the field of logic might be unfair to Deleuze, who is a transcendental empiricist [and thus thinks that there is only the logic of the given?, or that there is an incompossible logic which cannot be formally represented in order to compare with Hegel?] In the next chapter we discuss a confrontation not based on pure logic.

Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.

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