Pt3.Ch6.Sb1 Somers-Hall’s Hegel, Deleuze, and the Critique of Representation. ‘Introduction’ summary

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 3: Beyond Representation

Chapter 6: Hegel and Deleuze on Ontology and the Calculus

Subdivision 1: Introduction

Brief Summary:

Deleuze’s and Hegel’s anti-representationalist philosophies can be compared on the basis of their different interpretations of differential calculus and Kant’s antinomies.

Summary

In the previous section, we examined Deleuze’s and Hegel’s responses to the problems in Aristotle’s and Kant’s representational systems. Both Deleuze and Hegel make use of a concept of unifying difference. Deleuze’s is based on Bergson’s duration, a continuously-integrated heterogeneous multiplicity. Hegel’s is based on his dialectics, a process of productive oppositions united through their genetic relations.

Now we look more at the relation between Deleuze and Hegel, in particular, how each one might criticize the other. To do this we need a common basis for the comparison. “The present chapter will relate Hegel and Deleuze mediately through their different interpretations of the calculus and Kant's antinomies.” (161) For Hegel, calculus expresses what he calls the Notion. Calculus was based on infinite numbers until Weierstrass made it possible for calculus to be based on set theory, and this opened a new path for Russell’s philosophy.

for Deleuze as well as Hegel, what is important about the calculus is to be found in the "so-called barbaric or pre-scientific interpretations" (DR, 170). I n fact, for Deleuze, the calculus is even more central to his philosophy, since an interpretation of the calculus that moves away from the set-theoretic, and therefore spatial, understanding of mathematics opens the way for a philosophy of difference that truly understands difference apart from representation. As we shall also see, Hegel and Deleuze's interpretations of the antinomies mirror those of the calculus and show the applications of these principles outside of the mathematical realm. (162)

 

 

Somers-Hall, Henry (2012) Hegel, Deleuze, and the Critique of Representation. Dialectics of Negation and Difference. Albany: SUNY.