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Henry Somers-Hall
Hegel, Deleuze, and the Critique of Representation.
Dialectics of Negation and Difference
Part 3: Beyond Representation
Very, Very Brief Summary:
Deleuze’s and Hegel’s interpretations of differential calculus tell us that for Deleuze the given world is made of indefinite yet reciprocally determinable parts and also that there is another transcendental plane, and for Hegel it is a matter of determinate parts and a single plane. Hegel goes beyond representational systems with his dialectic, but it is reducible within Deleuze’s philosophy and it is inadequate in application to evolution. Deleuze’s approach can subsume dialectic and also it better explains the genesis of variation in evolution.
Very Brief Summary:
Deleuze’s and Hegel’s alternative solutions to problems in classical representationalist systems can be compared first by seeing their interpretations of the calculus, next by seeing how successfully one theory can subsume the other, and finally by applying theories to anatomy’s role in evolutionary theory to see which one is more compatible with it. We find that Deleuze’s calculus differential reveals that for Deleuze there are two onological planes, virtual and actual, but for Hegel infinite thought keeps the dialectical process and its products on the same level. We also see that basic things in the given world for Deleuze are determinable in differential relations but indeterminate on their own, where for Hegel they are determinate on their own. Because Deleuze’s virtual and actual are not opposites, they cannot be subsumed into Hegel’s system through sublation; however Hegel’s dialectical movement can be seen as a false secondary movement to Deleuze’s genesis of difference. We also find that Deleuze’s theory of anatomy better explains variations that evolution requires, but Hegel’s teleological account does not.
Brief Summary:
Deleuze and Hegel offer theories that respond to the problems of representation. We can better make a comparison by first seeing their different interpretations of differential calculus. Hegel regards the differentials as vanishing values which are 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 all (conditioned) actual determinations. Kant has an antimony about whether or not the world has a finite beginning. For him, the unconditioned cannot be in the series of moments of the world; it is rather outside it as the thing-in-itself. For Hegel, the antinomy shows the sublation of finite and infinite, because one side argues that there must be a limit and the other side argues every limit is surpassed. For Hegel, the unconditioned, the dialectic, is in fact on the same ontological plane as the conditioned. For Deleuze, the unconditioned is on a different plane, the transcendental, but unlike for Kant, Deleuze thinks it is not indeterminable, because it is determinable as differential relations. If Hegel were to critique Deleuze, he would try to collapse Deleuze’s virtual/actual distinction on which Deleuze’s anti-Hegelian ontology is built. But since virtual and actual are two tendencies of the real and not opposites, such a critique would not hold. However, Deleuze could include Hegel’s dialectic into his own philosophy by seeing it as a false movement that is secondary to the real movement, the genesis of difference. Yet Hegel purely from a logical standpoint might say that Deleuze’s difference does not exist. So we find a common application, the structure of the organism and its role in evolution, to compare them. Deleuze’s response to representational philosophy, and not Hegel’s, is compatible with evolutionary theory. For, Deleuze’s virtual explains novel variation in the organism’s structure, but Hegel’s dialectic does not. Also, Deleuze’s three criticisms of Hegel exhibit themselves when we relate Hegel’s ideas to evolution: [1] dialectical movement would halt evolutionary movement, [2] Hegel’s logic circles around a center, the sublation of organ and organism, which blocks evolutionary progress, and [3] Hegel’s account misses the ambiguities and variations that are vital to evolution.
Summary
In the previous part we saw how Deleuze and Hegel propose alternative theories to overcome problems in the representational systems of Aristotle, Kant, and Russell. Both proposals revolve around a concept of unifying difference. Deleuze takes up Bergson’s continuously-integrated heterogeneous multiplicity, which considers terms as intrinsically and inseparably related. Hegel’s dialectic also conceives of terms being both different yet intrinsically and inseparably related, but in his case because of a process of productive negation that unites the terms in their genetic sequence.
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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