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Henry Somers-Hall
Hegel, Deleuze, and the Critique of Representation.
Dialectics of Negation and Difference
Very, Very, Very Brief Summary:
Deleuze’s subrepresentational self-differentiation is superior to Hegel’s infinite representational self-differentiation in solving the problems that self-identity causes in Kant’s and Aristotle’s (likewise Russell’s) representational systems.
Very, Very Brief Summary:
Self-identity in representational systems leads to problems in explaining the highest part, the lowest part, and the compositional principle of Kant’s, Aristotle’s (and Russell’s) representational systems. Hegel’s and Deleuze’s principles of self-difference can solve them. Hegel’s productive self-contradiction and sublation suffices logically but not in application to evolution. Deleuze’s non-oppositional subrepresentational difference however does suffice in this regard.
A strict view of logical identity leads to problems in Kant’s and Aristotle’s representational systems. The unities of and between concept and intuition that enable our subject-predicate judgments of the world for Kant are based on the unity of a transcendental self. But Sartre shows this is merely a convenient assumption, because for him the unity of consciousness of the object is based on the continuous unity of the object’s givenness. For Deleuze the grounds for our judgments are based on neither the unity of the subject, of the concept, nor of the object, but rather on the unity of incompossible undetermined predicates implying a subject with virtual variations. As it is made of the integration of incompossibilities, it lacks the coherence of self-unity necessary for representation. Another question regards the representational nature of the categories we use for judgment. Aristotle and Russell have hierarchies, but because they exclude self-reference and excluded middle, the very foundations (largest parts), compositions of individuals (smallest parts), and method of composition (division/class inclusion) of their representational systems are problematic and unrepresentable within the systems themselves. Hegel and Deleuze have different ways of solving this by incorporating self-difference into their systems. Hegel’s productive self-opposition creates a genetic line of sublated categories. Deleuze’s Bergsonian continuously integrated heterogeneous multiplicity allows a plurality of differentially related incompossible actualizations to coexist virtually. Hegel’s and Deleuze’s interpretations of differential calculus show us that for Hegel there are ultimately determinate parts that are not finite but make finite values when differentially related; where for Deleuze there are ultimate undetermined parts that are nonetheless determinable as extensive finite values when differentially related. For Hegel the unconditioned (dialectic) and the conditioned (categories it creates) are on the same ontological plane, but for Deleuze the unconditioned (genesis of virtual differentials) and the conditioned (actualization of extensities) are on two different planes, the virtual and the actual, so they cannot succumb to Hegel’s system by being sublated. However, Hegel’s dialectic can be seen within Deleuze’s system as a secondary movement to the genesis of difference. Hegel’s theory cannot explain the creation of variation needed in evolutionary theory, but Deleuze’s can.
Brief Summary:
Deleuze and Hegel offer solutions to the problems of representational systems, which are philosophical systems based on self-unity, identity, and the law of excluded middle. For Kant, our judgments of things have a subject-predicate structure that is parallel to the subject-predicate structure of concepts and intuitive objects (having the subject-property structure). What unifies each themselves and all with each other is the a priori unity of a transcendental self. Sartre thinks the unity of objects precedes that of the self. Deleuze’s transcendental empiricism posits neither the unity of the self nor of the object; things obtain something like a subject-predicate form from incompossibilities being various and indeterminate, but the thing taking these possible predicates is the subject of the judgments. A strict adherence to the principle of identity and the law of excluded middle causes problems in Aristotle’s and Russell’s logical systems of classification. For Aristotle, the highest genus is being or unity. But, as it has no genus above it, it cannot be defined according to the structure of this system of division (the problem of the large) and yet all beings under it are characterized by this unrepresentable classification. The species gives the essence, and under the species is the individual, which is distinguished from other individuals not by essential but by accidental traits. But in moments of change, something with one essence has contradictory accidents, and also we don’t know until after the change what was essential and what was accidental. So the individual cannot be represented properly in this system (the problem of the small). Also there are cases in the natural world, ring species, which cannot be classified using Aristotle’s system of division (the problem of division). Russell also has the problem of the large. He must ban self-reference from his system of set classifications so to avoid the paradox of the set of all non-self-including sets. Yet self-reference is needed to establish identity. Hegel’s dialectic and Deleuze’s philosophy of difference are competing solutions to these problems with representational systems. Deleuze’s system is based on Bergson’s continuously integrated heterogeneous multiplicity. We can understand it using Riemann topographical space. Deleuze’s virtual/actual relation is like topographical phase space portraits, where we can see all possible actual ways a system can behave. All the incompossible actualizations are differentially related yet are continuously integrated. Hegel’s internal dialectic makes use of productive contradiction: from out of a concept arises its contradiction, and from out of that opposition arises a new concept not implied in the first ones. So contraries are located within one another, and there is a genetic chain of production of the categories of understanding. Finite thought like that used in Kant’s and Aristotle’s systems would find such contradiction unthinkable, but Hegel’s infinite thought can think these contradictions. Hegel’s and Deleuze’s interpretations of the differential calculus help us elaborate their positions. For Hegel, the differential is a relation between vanishing values, they are caught in the act of the sublation of the finite and infinite: the values are vanishing and hence are not finite, but their differential ratio is a finite value; and each is constitutive of the other. For Deleuze, the differential values are not determinate, yet they are determinable in differential relation to one another. For, they are subrepresentational, meaning that they are on a level where parts are not externally exclusive like in extensity, so they are not self-identifiable. The important distinction is that for Hegel the terms are representable and determinate, but are only thinkable using infinite thought. In examining Kant’s antimony of the beginning or beginningless of the world, we see that for Kant, we have this antinomy because we mistakenly think the unconditioned is among the conditioned, when in fact it is noumenal; for Hegel the antinomy indicates the sublation of finite (the necessity for a limit) and infinite (the necessity for all limits to be surpassed), and for him the conditioned and unconditioned are on the same level; yet for Deleuze, the conditioned (actual) is on a different level than the unconditioned (virtual) but the virtual is not outside our knowledge, rather it is only knowable outside representational thinking. Hegel could subsume Deleuze’s virtual and actual by sublating them, but that would fail since they are two tendencies of the real and are not really opposites. Deleuze could subsume Hegel’s dialectic by saying it is a secondary movement to genesis of pure difference that happens on the level of actuality and representation. But Hegel could say that from the perspective of logic there is no such thing as Deleuze’s difference. So we test them by seeing how their theories of the composition of the organism suffice in evolutionary theory. Hegel is like Cuvier in thinking that the organism’s parts are matters of how they function in service of the whole (teleological); organ and organism, individual and species are like sublated opposing terms. But this means that deformations are deteriorations in structure and thus cause deficiencies in functionality. But evolutionary theory depends on a positive account of anatomical variations; natural selection needs to pick the best from a variety of mutations. Geoffroy’ s and Deleuze’s view sees variations as different actualizations of a transcendental model, so their view is more compatible with evolutionary theory. Because Hegel’s anatomy is representational, we can see one superiority in Deleuze’s subrepresentational response to representational philosophies as opposed to Hegel’s infinite representational approach.
Summary
Henry Somers-Hall will examine how Deleuze and Hegel respond to the shared problematic of representation in philosophy. He then pits them against one another, and applies them to the role of the structure of the organism in evolution, to evaluate them with respect to one another.
In the first part, we begin by seeing how the history of philosophy contains tendencies toward building theories and systems on the basis of representation. This means that they make use of principles of self-unity, identity, and the law of excluded middle. There are problems with these approaches. Deleuze and Hegel offer solutions. There are two cases under investigation. The first is the transcendental grounds of our knowledge, specifically, what principle allows us to make judgments of the world? Kant offers a representational theory. It is representational, because it is based on a self-identical a priori unified self that is represented in all inner acts, in their accompanying ‘I think’. This unity unifies the empirical world into things with a subject-property structure, it unifies our concepts into subject-predicate structure, and it unifies our concepts and our intuitions into representable judgments with the subject-predicate structure. Sartre’s critical stance would say that it is really the unity of objects, and not subjects, that comes first and the unity of the self comes secondly. For Deleuze, a unity neither of consciousness, of self, nor of the objects, is what grounds our subject-predicate knowledge of things. Rather, each moment, events can go many different ways, so the same subject now has many various undetermined predicates, and they are incompossible. Because they are contradictory, the predication of a subject is not representable, even though the subject-predicate structure is there. This is Deleuze’s transcendental empiricism. Another case of representation in the history of philosophy is the use of the principle of identity and excluded middle in Aristotle’s and Russell’s theories of classification. For Aristotle, we define species on the basis of their differences. But the highest genus, being or unity, has nothing to differentiate from, no genus above it or species beside it, so it is indeterminate. However, it is the basic principle saying that all beings are self-unified and have identities (and thus also the system is thoroughly representational). The very representational basis of his system is not itself representational. Russell’s theory of class inclusion is also representational. Things are strictly categorized and defined by their groupings. There cannot be contradiction in the system, or instances when something’s identity contradicts its classification. So it cannot have the paradoxical class of all non-self-inclusive classes. Such a class is meaningless, it cannot be represented in the system. And yet, such a class is based on the same notion of inclusion as all the others. Hence class inclusion, as a universal concept that forms the basis of all instances of classification in his system, is not representable in this system. So somehow the nature of inclusion for each level is distinguishable, when in fact it is the same sort of inclusion each time. Also, identities and essences are representable, but moments of self-contradiction do not fit into such representable systems. This means that when something is changing, we cannot represent what is happening in the phase of transition when contradictory properties are coincident (like being both wood and fire in the action of ignition). Hegel’s solution is to make contradiction productive, using internal dialectic, where some concept brings about its own self-contradiction, and out of it comes a new concept not implied in the first. For Deleuze, this solution still has the problems of representation, as we will later see. Deleuze’s solution is a non-oppositional concept of difference.
In the second part, we formulate Deleuze’s and Hegel’s alternate proposals. Deleuze’s is based on Bergson’s duration, which is a continuously-integrated heterogeneous multiplicity, unlike the discrete multiplicity of externally related extensive parts characterizing homogeneous space. Bergson’s heterogeneous multiplicity better explains living systems.
Deleuze then uses Bergson’s continuously integrated heterogeneous multiplicity to characterize the Idea, the problem, and the concept. In all cases, they are terrains of virtual differential incompossibly-actualizeable paths of developmental explication. We can understand them with the model of topographical phase space portraits. They indicate all the tendencies for a system’s development using terrain features. This describes the system’s behavior on a whole, but in each instantiation only one possible line of development indicated in the map is actualized, because all the lines are incompossible yet coincident in this virtual form. They explicate into extensity. And any one actualization implicates the totality of the whole ‘problematic’.
Hegel’s dialectical movement brings contraries within one another, and also unites them on the basis of their genetic productions of one another. This allows him to go beyond Kant’s finite thought, and also to have totality to his system and an account of change, which is lacking in Aristotle’s system. Kant cannot go beyond finite thought, because it cannot think contraries together, like Hegel’s infinite thought can. And because Hegel’s concepts are united genetically, differences are inherently linked, and thus he can have totality to a system of differences without the need of some generic category to encompass them all, which was a source of a problem for Aristotle. Rather, their genetic process of unfolding is the glue uniting the differences. Thus Hegel can also explain the process of change, as he has accounted for the process that generates and unites the diverse contradictory changes when something alters.
Now in this final part, we examine how Deleuze and Hegel propose theories that try to overcome the problems of representational theories like the ones we saw in the first part, and we pit the theories against one another and apply them to evolution so to better evaluation them. First we examined how Deleuze’s and Hegel’s responses to classical representationalist philosophical can be compared on the basis of their different interpretations of differential calculus and Kant’s antinomies. We found that for Deleuze we have an unconditioned ground of sensible and intelligible things that is subrepresentational, and for Hegel it is representable, using infinite thought. The calculus differential determines the varying relation between variables that vary with respect to one another. Leibniz saw it as the relation between infinitesimal magnitudes but there are formal problems with this. Newton saw it in terms of vanishing values. Hegel regards the vanishing values as being determinate values that combine finite and infinite, and being and nothingness. This contradiction is only thinkable with infinite thought. For Deleuze the terms of the differential relation are undetermined and subrepresentational, but they are determinable in relation to one another and are the unconditioned condition of conditioned actual determinations. Kant thinks we arrive at antinomous theories regarding whether there is a temporal beginning to the world because our understanding is unable to grasp the unconditioned, the thing in itself, with its categories. Hegel thinks the antinomies go together. Together they express the genuine infinite, because they affirm both that there is a limit and also that it is surpassed. For Hegel the unconditioned, the dialectical contradiction, is representable with infinite thought. Deleuze thinks that the unconditioned is thinkable but not using representational thought but rather using the logic of incompossibility.
We then saw how Deleuze’s philosophy of difference is more resilient to attack than Hegel’s, when both are pitted against one another. If Hegel wanted to critique Deleuze’s philosophy of difference, he would show how Deleuze’s virtual and actual as contraries dialectically sublate, which collapses the basic distinction of Deleuze’s ontology. However, because Deleuze’s virtual and actual are two tendencies of the real and not contraries, such a Hegelian critique would not hold. From a Deleuzean perspective, Hegel’s dialectic could be viewed as a false movement, with Deleuze’s genesis of difference being the real movement. Yet Hegel purely from a logical standpoint might say that Deleuze’s difference does not exist.
So we then applied Deleuze’s and Hegel’s responses to representation to evolutionary theory to see which one is more compatible and also to see if Deleuze’s three criticisms of Hegel still hold: [1] Hegel’s is a false movement, [2] Hegel’s logic revolves around a single center, and [3] Hegel’s dialectic does not provide enough precision for characterizing the world. For Hegel, nature is the one totality and it externalizes into multiplicity, but these form unified systems where parts and their whole are reciprocally determining. Hegel’s dialectic is not temporal, so it does not describe an evolutionary progress through time. The structure of the organism is the reciprocally determining relation between organism and organs, which are opposing dialectical pairs like the one and the many. Individuals and species bear this organ/organism relation too for Hegel. Hegel’s structure of the organism is more closely tied to Cuvier’s anatomy, which is functional and teleological, meaning that organisms’ anatomical structures can be understood in terms of their functional purposes. Geoffroy’s homological theory of the unity of composition does not identify anatomical parts on the basis of their functions. Rather, he looks to see if the relations between the parts are isomorphic to a transcendental model which is so abstract that it can actualize in a wide variety of forms, such that a fin can be identified with an arm. This is compatible with Deleuze’s transcendental empiricism and theory of the virtual, which sees there being a transcendental level that is actualized in various ways. Cuvier’s and Hegel’s theories, as teleological, regard deformations or mutations in negative terms, as degradations of the organism’s structure and thus functioning as well. But evolutionary theory needs a positive view of aberrations. Geoffrey’s and Deleuze’s theories see variation positively, because variations are considered novel actualizations of the virtual model. Thus Deleuze’s response to the problems of representational theories is better than Hegel’s at least with regard to its application in evolutionary theory. We also see that Deleuze’s three criticism’s hold, because [1] Hegel’s movement is a matter of (infinite) representation, but because it cannot explain novel evolutionary variations, there is no real evolutionary movement involved. [2] Hegel’s structure of the organism has a teleological unity, and so there is a ‘monocentering of circles’ [around the organic unity of the organism.] [3] Hegel’s account is not precise enough. Because it understands the differentiation in the natural world in terms of determinate oppositions, Hegel’s dialectic too strongly divides the world rather than seeing the blurrings of boundary that allow for evolutionary variation.
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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