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
Chapter 2: Difference and Identity
Very brief summary:
There are two important limitations in Aristotle’s and Russell’s representational hierarchies, stemming from them being based on identity and excluding self-contradiction: they cannot explain the motion of change, and they cannot account for ambiguous and paradoxical cases of classification (ring species and the set of all non-self-inclusive sets). Hegel’s solution is productive contradiction, where a concept’s self-contradiction produces something not already implied in it. Later we will see Deleuze’s solution, non-oppositional difference.
Brief Summary:
Aristotle and Russell have hierarchical systems based on a principle of identity, and they enforce the principle of excluded middle. But these systems run into problems, which call for the basic principles in them to be revised. One problem is explaining change, because in systems where individual’s identities are represented in their self-sameness, we cannot explain how one individual in the moment of transition has incompatible properties (like being both wood and fire in the transitional movement of ignition). Aristotle’s system of division into classes is based on specific differences that are the essence of the species. But individuals at the bottom of the hierarchy are not species, and they are not distinguished by essential differences. And being, or unity, at the top of the hierarchy, cannot be defined, because it is not a species with a difference from a higher genus. So the highest genus is more like a principle of self-unity or identity which allows for the unities and identities of all beings classified under it. Aristotle says that there are many senses of the same focal meaning being, which are the different ways that beings express being. But this still assumes a unitary meaning of being, so it does not place difference at the core of the system. Aquinas’ solution is to say that we cannot define the highest category (being, or God), but we can know the relation that beings have to it, by means of analogy from other relations between species and genera. This however reveals that there is an ambiguity in all relations between species and genera [which calls into question the differences that would make each individually itself. Perhaps it suggests that all we can talk about is inclusions, and not about the individuality of things.] Russell deals with set inclusions, and tries to build a system where something is said to belong to a set when that thing shares the property that all members of that set have. This creates a problem at the highest level, because we encounter a paradox with the set of all non-self-including sets. The solution is to say that each level of classification can only apply to the level immediately below it, and not to any other. This way there can be no self-including sets. But that also means we cannot make one universal statement holding for all levels. Instead, when we think we are making such a statement, we are really making a different statement for each level. Here again we have a problematic ambiguity between all levels of the hierarchy. What we note is that in these systems of classification, something either is in a class or it is not, there is no middle or ambiguous status. There cannot be self-contradiction, but this is what leads to problems with explaining ring species and transitions. Hegel’s solution is to embrace contradiction and make it productive. So being as purely indeterminate is indistinguishable from nothingness; they vanish into one another and produce becoming. So Hegel’s productive contradiction is one solution. Later we will see Deleuze’s solution being a non-oppositional sense of difference.
Summary
Previously in chapter 1, Somers-Hall (SH) discussed Deleuze’s transcendental empiricism. Kant’s transcendental apperception (the a priori unity of our self-awareness, the ‘I think’ that accompanies all our inner acts) provides the unity on the level of (a) empirical givenness, (b) concepts and understanding, and (c) the relation between these levels. This unity allows us to make subject-predicate formulated judgments of subject-predicate structured objects. Sartre, in his critique of Husserl’s transcendental ego (in defense of Husserl’s phenomenological project on the whole) argues that the self-consistency of phenomenal objects is the basis on which we derive a self-unified ego, and not the other way around. Deleuze also does not take up a unified transcendental ego to explain the grounds of our knowledge of objects. The logic of incompossibility allows there to be a subject with various predicates, depending on the various sorts of branching paths that subject might take in the next moment. So we can have the subject-predicate structure of objects on which to base subject-predicate judgments of them, and yet the predications are not determined. Hence the differential relations in the field of givenness (the bifurcations that create multiplicities of incompossible predications) are both empirically given and yet provide the non-empirical grounds for our knowledge of these objects. This is Deleuze’s transcendental empiricism.
In chapter 2, Somers-Hall examines how the prohibition of the principle of excluded middle in Aristotle’s and Russell’s representational, hierarchical systems limits their integrity and their capacity to explain change.
We will later articulate Deleuze’s concept of genetic difference. Aristotle’s system of hierarchical classificatory divisions is based on species difference, and so it would seem like a possible model for genetic differentiation. For Aristotle, there are the three main relational tiers: genus, species, and individual. What distinguishes a species is its special difference, which is its essence. Because it is essential, it precedes the division of the genus, and so it is productive of the different species rather than being something secondary to the division. However, the individuals in a species, like different people, are not distinguishable by what is essential to them, but rather by accidental traits [what makes one man distinct from another are traits they could have lacked, like hair color, and still have been themselves.] So Aristotle’s specific difference is not a model for the genetic production of individuals.
Also, the highest genus, being, is not defined by (essential) specific difference, because there is no higher genus or other fellow species to differentiate from. To define something, we need both genus and species, so the highest genus, being or unity, has no basis to define it. However, the many beings classified under it exhibit their being in various different ways (qualitatively, like being straight, white, etc., quantitatively, being continuous, numerous, etc.). These are not higher categories of being, but are rather different acutalizations of the same focal meaning of being. So, the beings that fall under being (and the senses of being too?) do not have both the same name and the same definition, so they are not homonymous (univocal). Rather, they share a similar name but have different yes related definitions, and are thus are paronymous (derivative). So, the many senses of being are unified yet diversely applied. Yet, because all the senses revolve around a focal meaning, the core of the system, being, does not seem to be defined by difference.
So Aristotle’s system of divisions (based on specific difference) is organized around the highest category, being, which in a way is implicitly defined tautalogically (being is being, or unity is unity) because there are no differences that distinguish it. The system of difference, then, is based on a central self-identity. But all things fall under the category of being, which means all things are self-identical unities, and this creates a problem for explaining change. So Aristotle’s notion of essence can explain how something remains itself while changing, but it cannot explain how in phases of transition, it has contrary properties (like how an igniting piece of wood is both wood and fire in the same phase of alteration between determinate states). Another problem with Aristotle’s notion of specific difference is that it cannot be used for classifying ‘ring species’: animal type A can breed with B, and B with C, but not A with C. On the basis of specific difference, we cannot really say all three are in the same species, because A and C cannot breed. However, if we say A and C are in different species, then what species is B? Is it in both? And what if each were a different species, what about the fact that pairings can interbred yet are in separate species?
Porphyry shows that Aristotle’s paronymy is a type of homonymity, because in homonymity, there is the same name with different meanings, and paronymy is similar names with related meanings. Aquinas uses Aristotle’s concept of analogy to deal with the problem of characterizing the highest category, being, or God. We cannot determine anything about that category itself, but we can speak of man’s relation to God by analogizing it to isomorphic relations between other genera and species.
Russell deals with problems similar to Aristotle’s. In Russell’s set theory, something is included in a set if it has the property shared by that sets members. [The highest set I would think would be the set of all sets. But this highest set is based on a problematic structure that is revealed in another very high set.] We can define the set by its members or by the criteria for membership in that set. One such criteria might be ‘being a set that has itself as a member’. But this creates a paradox that tells us there is something wrong at the very basis of the system, that this notion of self-identical things contained in self-identical categories is not sound basis for the structure of the organization for all things. The paradox is that if the non-self-inclusive set itself is said to be one of its own members, then it contradicts its own definition of being non-self-inclusive. And if it is not said to be a member of itself, then according to the criteria, we should include it within itself, which goes against the original assumption that it is not included within itself. Russell’s solution is to say that there are different levels of classification, and one level can refer to the next one below it, but not to itself. So ‘a class that includes itself’ has no meaning in Russell’s system. Yet this also means that we cannot make one universal statement that holds for all things. Our statements always are limited to one level. This even means that a property like truth is not the same for all level, it would be ‘truth at level n’ for example. So when we do speak universally about something, we are implicitly making a different statement for all its substrata. Also, like with Aristotle’s hierarchy, we cannot define the highest class in Russell's system.
Both Aristotle’s and Russell’s systems prohibit the excluded middle, so it is always the case that something is P or not-P, but not both. This is why they are unable to explain transitional phases when something expresses contrary properties together and ring species where animal groups seem to both be and not be in the same species.
Hegel’s system, however, not only allows for contradiction, in fact, its coherence and ability to explain change is based on it. And the movement between concepts in Aristotle and Russell is one of implication, so nothing comes out of the movement that was not already there at the beginning. Being vanishes into nothingness, which produces becoming. However, like Aristotle’s and Russell’s systems, Hegel’s movement is not temporal.
Hegel likes how Zeno begins with the notion of multitude to find a contradiction in it, so to conclude that the many cannot be. This is like Hegel’s dialectic, in that contradiction is inherent to the movement, but Hegel goes an additional step with his aufhebung so to derive a new concept from the self-generated self-contradiction. So because being is completely indeterminate, it is indistinguishable from nothingness, so the two vanish into each other, and moving out from that opposition is the notion of becoming. The indeterminacy of being (or the highest category) was a problem for Aristotle and Russell’s systems, but for Hegel, it is one of its strengths, and it allows him to overcome the problems in their systems.
So Hegel’s solution to the problem of representation (in a system) is to apply the notion of productive contradiction. Deleuze’s solution we will see is to use the idea of a non-oppositional difference. Deleuze’s critique of Hegel is that his notion of productive contradiction does not extract him from the problems of a representational system. Hegel can criticize Deleuze’s use of essences, for example in his notion of the virtual.
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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