Deleuze and Mathematics (original) (raw)

Deleuze’s Philosophical Heritage

Cambridge Companion to Deleuze, 2012

In this paper, I want to look at Deleuze’s philosophical heritage in two different senses. In the first part of the paper, I explore his relationship to perhaps the most influential philosopher of the twentieth century, Martin Heidegger. Heidegger plays a central role in Deleuze’s early philosophy, and even when in his later collaborations with Guattari their explicit references to Heidegger are dismissive, Heidegger’s influence can clearly be detected, particularly in their critiques of other philosophers. In the second part of the paper, I look at Deleuze’s own contribution to philosophy, and to see how this contribution has been assessed by one of the most influential contemporary French philosophers, Alain Badiou. For Heidegger, Deleuze, and Badiou, perhaps the central problem for philosophy emerges from thinking about totality. For all three, the traditional metaphysical view of totality, derived from Aristotle’s concept of paronymy, occludes rather than solves the problem of how we characterise our most general concepts. As we shall see, Heidegger’s diagnosis of metaphysics, as constituted by what he calls onto-theology, is shared by all three philosophers, while their responses to this diagnosis differ. Deleuze and Badiou both reject Heidegger’s poetics of being in favour of the language of mathematics, but the question I want to explore in the final part of the paper is, which mathematics? The mathematics of the continuous, or the mathematics of the discrete?

Hegel and Deleuze on the metaphysical interpretation of the calculus

Continental Philosophy Review, 2010

The aim of this paper is to explore the uses made of the calculus by Gilles Deleuze and G.W.F. Hegel. I show how both Deleuze and Hegel see the calculus as providing a way of thinking outside of finite representation. For Hegel, this involves attempting to show that the foundations of the calculus cannot be thought by the finite understanding, and necessitate a move to the standpoint of infinite reason. I analyse Hegel’s justification for this introduction of dialectical reason by looking at his responses to Berkeley’s criticisms of the calculus. For Deleuze, instead, I show that the differential must be understood as escaping from both finite and infinite representation. By highlighting the sub-representational character of the differential in his system I show how the differential is a key moment in Deleuze’s formulation of a transcendental empiricism. I conclude by dealing with some of the common misunderstandings which occur when Deleuze is read as endorsing a modern mathematical interpretation of the calculus.

Difference as Rhythm and Thought as Subtractive Synthesis in Gilles Deleuze

LA DELEUZIANA – ONLINE JOURNAL OF PHILOSOPHY, 2019

This article discusses the place that the concept of rhythm occupies within Gilles Deleuze’s philosophy. I present a panorama of different ways to conceptualize thought throughout Deleuze’s writings from 1960’s to 1990’s, emphasizing the discussion about the threshold of thought. In the writings in partnership with Félix Guattari, Deleuze understand thought as an act of confronting chaos, what makes the problem of consistency a point of extreme relevance within his philosophical system. In this framework, the concept of thought is described as a tension between consistency and infinite speed (chaos). In order to elaborate this concept of thought, Deleuze resumes his conceptualization of the three syntheses of the time and formulates with Guattari the concept of refrain. I will show that the refrain is at the axis of an epistemological shift in the whole program of transcendental philosophy, by affirming a necessarily heterogeneous and aberrant Time, which features the concept of rhythm as the genetic element of difference. Within this conceptual framework, I follow the authors’ suggestion that the logic of schizoanalysis is analogous to the logic of subtractive sound synthesis. The main goal is to demonstrate that rhythm is at the core of Deleuzian concept of difference and sound is at the core of Deleuzian concept of thought.

Deleuze's Metaphysics of Structure in Difference and Repetition

2011

This essay describes and evaluates the conception of mereological structure that underpins Deleuze’s account of ontogenesis in Difference and Repetition. A theory of mereology is a theory of composition: it asks what it is to be a part making a whole, what it is to be a whole collecting its parts; in short, in what the relation of making or composing consists. The locus classicus for modern mereology is the third of Husserl’s Logical Investigations (‘On the Theory of Wholes and Parts’), which deduces the definitions, axioms and principles governing the relation of parthood and associated notions, such as wholeness, separation, simplicity and complexity. My question is this: what happens to these notions when they are no longer the terms of a ‘calculus of individuals’ and, instead, become the terms of a differential calculus of individuation?