by 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 1: The problem of Representation
Chapter 2: Difference and Identity
Subdivision 9: Zeno
Very brief summary:
Hegel likes Zeno’s internal dialectical method that begins with a concept and then sees how it comes to contradict itself. For example, in Hegel’s aufhebung, being is completely indeterminate (as it is with Aristotle and Russell) and thus indistinguishable with nothingness. They vanish into one another and through this there is a movement to the concept of becoming. Unlike Aristotle and Russell, self contradiction here can not only be inherent to the highest genus, being, it can also be essential for making the system consistent and whole.
Brief Summary:
Hegel likes Zeno’s method of defending Parmenides’ argument that all is one. Zeno does not begin with axioms to come to that conclusion (external dialectic) but rather he begins with the concept of the many and shows it leads to a self-contradiction (internal dialectic). In Hegel’s aufhebung, being is indeterminate and so it is indistinguishable from nothingness, and they vanish into one another, and in that process move to the concept of becoming. So here we have contradiction with respect to the highest genus, being, not leading to a degradation of the integrity of his system, as it is the case for Aristotle and Russell, but rather being one of its strengths. Hegel, unlike Aristotle and Russell, can have a unified system, because he incorporates a productive form of contradiction, and as well, he, unlike them, can explain the process of productive change.
Summary
Previously we examined the similarities and differences between (a) Aristotle’s (and Russell’s) hierarchical systems of division and (b) Hegel’s dialectical system. The differences were that (1) Aristotle’s and Russell’s systems obey a strict law of the principle of excluded middle, which does not allow for ambiguous cases of identity like transitional phases between states where mutually exclusive states are coincident, and also for example ‘ring’ species where animal type A can breed with B, and B with C, but not C with A, leaving the species-classifications of these animal types ambiguous, and (2) The ‘movement’ between concepts for Aristotle (and Russell) is one of implication, meaning that the concept moved-to was implied in the first, but in Hegel’s dialectical system, there is a genetic movement when being and nothingness disappear into one another and move to the concept of becoming.
Somers-Hall now turns to Hegel’s reading of Zeno. Hegel’s interest here is the way Zeno arrives at his conclusion that there is no movement. In his analysis, Hegel distinguishes two types of dialectic, external and internal.
Hegel’s External and Internal Dialectics:
External Dialectic: Here the “ ‘movement is different from the comprehension of the movement.’ (LHP, 1, 264)” (64) It is the dialectic Parmenides uses to prove that “All is one”. Its limitation is that an interlocutor need not take up its assumed axioms. So even if the system built on the axioms is coherent, someone might still find these axioms to be false and exterior. “Thus the debate moves in the wrong direction. I try to prove my case by unfolding the implications of my position, while it is the grounds of the position itself that | are the issue." (64-65) The advantage of it is that it sheds light and reveals reasons. “The result of this is that the object of the debate is criticized, but only from one side, at best merely placing the held assumptions in question”. (65)
Internal Dialectic: This is "‘not a movement of our intelligence, but what proceeds from the nature of the thing itself, i.e. from the pure Notion of the content.’" (64) It “does not reason from alien premises but is itself the movement of the object under discussion.” This is Zeno’s dialectic. Unlike Parmenides, Zeno argues that “the Many cannot be”. It is true dialectic. It " ‘leaves nothing whatever to its object,’ leading it instead to ‘disintegrate itself in the entirety of its nature’ (LHP, 1 , 265). Thus Hegel follows Zeno in arguing that the motor of the philosophical process is contradiction." (65) But Zeno’s internal dialectic cannot move beyond its object’s destruction. So this dialectic results in the null or negative, and the affirmative does not yet appear in it. The negative in this dialectic is how a contradiction leads to the object’s negation; for Zeno, the many is negated. Recall Russell’s problem with his system of classification. He was worried that universality would lead to a contradiction [in his system, to say “the class of all non-self-inclusive classes” would refer only to the order of classes below it. If it were universal, it would refer also to itself, leading to a paradoxical contradiction. But if the system eliminates the distinction between true and false in this way, then all its propositions are simultaneously true and false.]
In talking of an 'affirmative' within contradiction, Hegel is going beyond the structures of classical logic. Russell's paranoia about the possibility that universality would lead to contradiction was grounded in the fact that the existence of a contradiction makes all propositions within a system simultaneously true and false. Thus, what Hegel is seeking is something between the mad proliferation of propositions within a system and the skepticism that "ends up with the bare abstraction of nothingness or emptiness and cannot get any further than there, but must wait to see whether something new comes along and what it is, in order to throw it too into the same empty abyss" (PS, 51). (65)
To do this, we need to regard the negation of the contradictory concept as a determinate negation,
meaning that in showing a particular object to be contradictory, we do not simply reject it, but trace out the path that its own rejection forces us to take. In this way, Hegel moves beyond a purely formal logic to one in which the content itself opens up a determinate movement beyond the impasse that contradiction leads to in earlier systems. (65)
[So if Hegel were just using formal logic, contradiction is not generative of new concepts. In formal logic, there are only conceptual movements of implication, when one concept emerges from another.]
Thus, in the case of the problematic concepts of being and nothingness, we are led not to a skepticism concerning these concepts, but rather to a further concept of becoming. Furthermore, the concept of becoming does not result from the destruction of these prior categories, but is instead the result of the resolution of this contradiction at a higher level. The contradiction is aufgehoben, that is, simultaneously surpassed and preserved. (65)
[In the case of Russell’s formal logic, a contradiction means that any conclusion could result. But in Hegel’s aufhebung, there is a determinate result.]
In this movement, the force of Russell's anxiety in the face of contradiction is removed. Instead of leading to an indeterminate proliferation of concepts, the unfolding of the contradiction is determinate and productive. (65)
[Before in Russell’s paradox of the non-self-inclusive class, what could be a highest genus here creates a contradiction whose resolution creates such deep problems as to call into question the integrity of the whole system. In Hegel’s system, being, the highest genus, is indeterminate and it intermixes with nothingness. This contradiction however leads to a new concept. This means that Hegel’s system solves important problems in the Aristotle/Russell systems. Their systems could not explain the movement of concepts, and it could not allow for contradictions involved in such cases as phases of transition. Here Hegel’s dialectic can still have a highest class of being (in its pure indeterminacy), and yet it does not have these problems.]
Through this moment of Aufhebung, the problems that occurred within the earlier representational systems are resolved. The contradictory nature of the highest genus, being, becomes instead positive | and productive. (65-66)
[So let’s recap. Zeno argues not that All Is One but rather that The Many Cannot Be. He uses an internal dialectic, (which means that he begins with the notion of the many, and shows that its implications are inconsistent, and hence it contradicts itself.) Hegel likewise sees negation and contradiction to be the motor of the philosophical process, but Hegel invents the aufhebung, which is a productive contradiction. Also, this process for Hegel comes out of the concept itself.]
The further lesson that Hegel draws from Zeno is that this dialectical process is not an imposition on the object (object in the sense of that which is analyzed-dialectic does not presume that the analysand must always be objectival), but rather the natural development of the object itself. For Hegel, this means that the method of dialectic itself is a product of the dialectic of the object itself, rather than being a presupposition of the analysis. Further, we saw that for Russell, unity and contradiction imply one another, hence the need to reject the former to safeguard against the latter. For Hegel, accepting the possibility of contradiction means opening the possibility of a unified, total system. (66)
Somers-Hall will return to Hegel’s philosophy to discuss it further in chapter 5.
Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.
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