by Corry Shores
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Henry Somers-Hall
Hegel, Deleuze, and the Critique of Representation.
Dialectics of Negation and Difference
Part 1: The Problem of Representation
Very brief summary:
We might think of representation as a manner of conceiving matters in terms of self-same unities whose identities and descriptions can be given explicitly and without self-contradiction. Representation has been used as a basic principle for many important theories throughout the history of philosophy. The representational unity of the transcendental apperception in Kant is the basis for our ability to make judgments of the world. But Deleuze’s logic of incompossibility accomplishes the same feat without representational unities. And Aristotle’s and Russell’s hierarchical classification systems are based on an overarching representational principle of identity and the law of excluded middle, but this principle is not representable within their systems. Also, they cannot explain change, cases of ambiguous classification, or paradoxes arising from their principles of class inclusion. Hegel’s solution is to make self-contradiction productive of new concepts, but Deleuze still finds this to have the problems of representation. Deleuze’s solution is non-oppositional difference.
Brief Summary:
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.
Summary
Part 1 examines developments in the history of philosophy that use identity and unity, more importantly representation, as their basic principle. Somers-Hall then examines how Hegel and Deleuze respond to the problems of these representational philosophies. One question is, on what basis are we able to make judgments about the empirically given world? For Kant, the unity of self-awareness (the transcendental apperception, the a priori self, the ‘I think’ that accompanies all inner acts) is what allows the parts and moments of empirical givenness to belong together and be synthesized with one another. This unity is also what allows us to synthesize the conceptual manifolds of our understanding. And finally it is what allows us to unite our concepts and intuitions. We are then able to make subject-predicate formulated judgments about subject-property structured objects. So the grounds for our knowledge of the empirical world is transcendental, the transcendental ego, and this is his transcendental idealism. Sartre indirectly criticizes the unity of Kant’s transcendental apperception when he critiques Husserl’s transcendental ego. Sartre argues that phenomenal givenness is already given to our awareness in its continuity, and the unity of the objects we perceive is what allows us to secondly unify our consciousness and ego, and not the other way around. For Deleuze, the subject-predicate structure is given without the objects being unified. This is on account of his logic of incompossibility. Here the same something, like Adam, before making the decision to eat the apple, has a plurality of incompossible predicates, like sinner and innocent, because his decision is not yet determined. So the grounds for our being able to make subject-predicate judgments is not representational and it does not rely on a unified subject or object. It is given in the bifurcational logic of the world of empirical givenness. This is Deleuze’s transcendental empiricism. [Deleuze’s theory is not representational, because there is no unified identity involved in it.]
The other representational systems in the history of philosophy are Aristotle’s and Russell’s hierarchical systems of classification. They are based on self-same identity and the law of excluded middle. Aristotle’s highest category, being, cannot be defined, because it has no difference from other other species and no higher genus with which to define it. It is more like a principle of unity shared by all beings falling under it rather than being a category of inclusion. Also, Aristotle’s theory of specific difference does not explain how the individuals on the lower end of the hierarchy can be distinguished, because they are differentiated by accidental and not by essential specific differences. Aquinas says that we can speak not of being (God) but of relations to him based on other relations between genera and species. But this blurs the important differences between relations to God and other sorts of relations between beings. Russell’s representational system is a theory of set classifications. Something is included in a set if it has the property all that set’s members share. [The highest set is the set of all sets. But how are we to conceptualize whether or not this set belongs to itself or not?] Self-inclusion is a problem however. Consider the set of all non-self-inclusive sets. It is impossible to say whether it is included in itself or not. The solution is to say that there is a hierarchy of levels of set inclusion, and one level can only refer to the level below it, and to not other. This means it cannot refer to itself. It also means that we cannot make a universal statement for all levels. And we cannot define a highest class, because this would require one higher to it that refers to it. Both Aristotle’s and Russell’s systems are based on a principle of identity. Contradictions in the system go against their unifying structural principle, that things are self-same and there is nothing whose identity is ambiguous or in self-contradiction. One problem is explaining ambiguous cases of classification like ring species. Another problem is explaining change, because they can account for each moment where something is self-same, but not the transitional phases between when they have contradictory properties. Hegel’s solution is to posit a productive contradiction. Being is purely indeterminate, as the case for the highest categories in Aristotle and Russell, but rather than creating a problem, this is the strength of Hegel’s system and its solution to the problem of representation. Being as indeterminate is indistinguishable from nothingness; the two vanish into one another, and out moves becoming. Thus he can explain change and conceptual ambiguities. Deleuze we will see has the solution of non-oppositional difference.
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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