Dialectics of difference and negation: the responses of Deleuze and Hegel to representation

Abstract
This thesis has the following aims. First, to show that Deleuze can be situated clearly within the post-Kantian tradition. This is achieved through an analysis of the relations between Kant's transcendental idealism and Deleuze's transcendental empiricism. Second, to explore the criticisms of representational theories of difference which can be found in the work of Deleuze and Hegel. Representational theories are best understood as theories which rely on a logic which is governed by relations between entities which pre-exist those relations. Deleuze argues that these logics presuppose the formal equivalent of a homogeneous space within which these relations can be construed. Hegel similarly understands representation as the utilisation of finite categories which rely on the fixity of the subject of predication. The third aim is to provide a rigorous explication of some of the key themes of Deleuzian ontology, particularly in relation to the problem of representation. This will involve looking at the logic of multiplicities, which attempts to provide a theory of difference that is non-oppositional. This logic will be clarified through a discussion of Deleuze's use of modern geometry, and his analysis of the foundations of the calculus. The fourth aim will be to contrast Deleuze's solution with that of Hegel, particularly with respect to their relationships to Kant and the calculus. This is achieved through the Deleuzian distinction between finite and infinite representation, the latter in Deleuze's view characterising the Hegelian attempt to bring the idea of transition into representation itself. Finally, having shown where Deleuze and Hegel differ in their respective projects, the thesis will explore whether either of these philosophies has the resources to provide a refutation of the other with reference to the dialectic of force and the understanding in the henomenology of Spirit, and the problem of the one and the many
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