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Deleuze's Reading of Leibniz

My book Affirming Divergence: Deleuze’s Reading of Leibniz is available from Edinburgh University Press and Oxford University Press

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The book was based on my PhD research at the University of Warwick and is an account of Deleuze’s appropriation of concepts from Leibniz’s metaphysics, logic, and mathematics.

An endorsement from Henry Somers-Hall:

Leibniz’s influence on Deleuze has long been recognised, but rarely analysed, and Tissandier’s much-needed book provides an unparalleled analysis of the development of Deleuze’s relationship to him. Drawing together and reconstructing readings from across Deleuze’s career, Tissandier provides a nuanced, comprehensive account Deleuze’s increasingly radical reading of Leibniz, from the early, fragmentary readings of Expressionism in Philosophy: Spinoza and Difference and Repetition to the mature thought of The FoldAffirming Divergence is a deep, rigorous analysis that affirms the centrality of Leibniz for Deleuze’s thought, providing a major contribution to our understanding of Deleuze’s relationship to the history of philosophy, and to our understanding of his philosophy itself.

– Henry Somers-Hall, University of London

And an abstract:

Leibniz is a constant, but often overlooked, presence in Deleuze’s philosophy. This book explains three key moments in Deleuze’s philosophical development through the lens of his engagement with Leibniz. In doing so it hopes to offer a focused framework for understanding some of the most difficult aspects of Deleuze’s philosophy.

Part One examines Deleuze’s account of the “anti-Cartesian reaction” of Spinoza and Leibniz which culminates in their two competing theories of expression. It argues that in some key respects Deleuze favours Leibniz’s interpretation of this key concept over Spinoza’s.

Part Two looks at Deleuze’s critique of representation and his attempt to create a theory of difference that will underlie, rather than rely upon, conceptual opposition. It examines the crucial role played by the Leibnizian concepts of incompossibility and divergence in Deleuze’s theory of ‘vice-diction’, created in order to offer a sub-representational, or pre-individual, substitute for Hegelian contradiction.

Part Three looks in detail at one of Deleuze’s last major works, The Fold. It argues for Leibniz’s central place in this text, and shows how Deleuze uses concepts from across Leibniz’s philosophy and mathematics as a framework to articulate a systematic account of his own mature philosophy.

Deleuze’s Reading of Leibniz: Overview

Introduction

References to Leibniz’s philosophy appear constantly throughout Deleuze’s work. Despite often repeating the same themes, we find marked differences in tone, as if Deleuze is unable to arrive at a conclusive judgement. This book explores these various engagements and tries to account for these shifts in tone. Ultimately it will argue that focusing on Deleuze’s interpretation of Leibniz – both his appropriations and his criticisms – helps us to understand some key moments in Deleuze’s own philosophical development. A close reading, emphasising the particular context and terminology of Leibniz’s work, will open a narrow point of access into some of the most difficult areas of Deleuze’s philosophy. In the course of this reading, it will become clear that it is precisely Leibniz’s ambiguous status for Deleuze which makes an investigation into their relationship so fruitful: by not only explaining Leibniz’s positive influence, but also pinpointing the precise grounds for their eventual divergence, we hope to better articulate some of Deleuze’s own philosophical priorities.

The Evolution of Deleuze’s Reading of Leibniz

Deleuze’s reading of Leibniz can be divided into three distinct periods, which correspond to the three parts of this book. Part I begins with Deleuze’s minor thesis on Spinoza, Expressionism in Philosophy: Spinoza. Here we find a Leibniz who is a predominantly conservative thinker of sufficient reason, grounded by theological concerns. Deleuze is largely unable, or unwilling, to unleash the dynamism buried in Leibniz’s philosophy, reduced as he is to an opponent of Spinoza. Our discussion of this book will rely in part on the claim that we must draw a sharp distinction between the main text and the concluding chapter (‘The Theory of Expression in Leibniz and Spinoza: Expressionism in Philosophy’). The marked shift in tone and emphasis between the two suggests that they written at different times. Importantly for us, Leibniz is afforded a far more central role in the conclusion than his almost incidental presence in the main text would have led us to expect.

In Part II we turn to Difference and Repetition and Logic of Sense. Difference and Repetition presents us with a very different image of Leibniz, introduced, alongside Hegel, as a representative of ‘infinite’ representation. For the first time, Deleuze draws on a more dynamic side of Leibniz’s philosophy. Here, what interests Deleuze about Leibniz is his discovery, within or beneath each clear idea, of the ‘restlessness’ of the infinitely small. The obscure depths of the infinitely small, we’ll see, harbour a kind of intoxication, giddiness and evanescence (DR 45). It is this image of the obscure, confused depths of the infinitely small that Deleuze gradually comes to treat as central to all areas of Leibniz’s philosophy, and it’s an image which haunts and threatens to undermine Leibniz’s conservative façade.

In Logic of Sense, meanwhile, Deleuze turns to Leibniz for both his concept of compossibility, which provides a ‘rich domain of alogical compatibilities and incompatibilities’ (LS 196), and for his concept of expressive individuals. These two books thus introduce a more sympathetic tone on the part of Deleuze. The infinitely small and the theory of compossibility form the basis of a ‘Leibnizian structure’ which Deleuze puts forward as an alternative to Hegelian contradiction. Nevertheless, Leibniz is still criticised for subsuming the excess of difference under a sufficient reason which ‘no longer allows anything to escape’ (DR 263). To this extent, Leibniz does not escape his conservative yoke. However sympathetic, there is always a point in these texts where Deleuze leaves Leibniz behind and instead finds inspiration elsewhere, citing the constraints imposed by Leibniz’s own ‘theological exigencies’.

Although Difference and Repetition and Logic of Sense present us with a much more sympathetic image of Leibniz than the one found in Expressionism in Philosophy: Spinoza, Deleuze’s readings of Leibniz in all three books still share one basic characteristic: they are essentially fragmented. Deleuze extracts disparate concepts from Leibniz’s philosophy and uses them like tools, often because they are representative of a particular moment in the history of philosophy, and more rarely because they coincide with his own philosophical objectives. But this always happens within the context of a larger discussion which has nothing in particular to do with Leibniz, and there is never any sense that Deleuze has an interest in Leibniz’s philosophy as a unified system.

This all changes with The Fold, published in 1988. Here Deleuze gives a much more general, unified account of Leibniz. He regards Leibniz’s philosophy, for the first time, as something more than just a collection of useful explanatory concepts to be deployed in some other context. Leibniz is promoted to the role of philosophical representative of the Baroque period itself, whose defining trait, Deleuze thinks, is a process of folding which continues indefinitely. But the themes which interested Deleuze in his earlier readings of Leibniz are not simply superseded by the much grander role he is now given. They return, without exception, in The Fold, but with this difference: where previously they were isolated from each other, they are now drawn together under this new concept of the ‘infinite fold’. In Part III we will look at the complicated relationship between the various aspects of Leibniz’s philosophy, the Baroque style and the concept of the fold.

Part I: Expressionism in Philosophy: Spinoza

Chapter One: Leibniz, Spinoza and the Anti-Cartesian Reaction

1.1 Definitions and God’s Possibility

1.2 Absolutely and Relatively Simple Notions: The First Criticism of Leibniz

1.3 Adequate Ideas

1.4 Symbolic Thinking and Relatively Simple Notions

1.5 Expression

1.6 Mechanism, Force and Essence

1.7 A New Criticism of Leibniz

Abstract

This chapter looks in detail at the three main engagements with Leibniz in the main text of Deleuze’s Expressionism in Philosophy: Spinoza. The first concerns the role of real definitions and proofs of possibility in arguments for the existence of God. The second concerns the theory of adequation in a logic of ideas. The third concerns mechanism, force and essence in a theory of bodies.

The chapter argues that these engagements all share the same form. First, Deleuze locates a similarity between Leibniz and Spinoza in their criticism of a particular Cartesian doctrine. Second, he grounds this criticism in a shared concern for the lack of a sufficient reason operating in Descartes’s philosophy. Third, he nominates expression as the concept best suited to address this lack and fulfil the requirements of sufficient reason. Finally, he shows that the way expression functions in Spinoza’s philosophy is each time superior to Leibniz’s own use of the concept.

Despite the priority given to Spinoza in this text, it nevertheless contains our first introduction to various key Leibnizian concepts which will become increasingly important in Deleuze’s later philosophy.

Chapter Two: Leibniz and Expression

2.1 Absolutely Simple Notions

2.2 Non-causal Correspondence

2.3 Leibniz’s Expressive World

2.4 Leibniz’s Theological and Political Motivations

2.5 The Double Movement of Expression and the World as Sense

Abstract

This chapter looks at Leibniz’s central role in the concluding chapter of Deleuze’s Expressionism in Philosophy: Spinoza. His elevated presence suggests a dramatic shift in Deleuze’s reading when compared with the rest of the text. It examines Deleuze’s lengthy discussion of Leibniz’s concept of expression and argues that within this discussion there is a shift from a ‘two-term’ concept of expression to a triadic concept which is closer to the one Deleuze finds in Spinoza.

It then re-examines Deleuze’s central criticism of Leibniz, this time understood as a criticism of his ‘equivocal’ concept of expression compared to Spinoza’s ‘univocal’ concept. It shows that ultimately all of Deleuze’s criticisms of Leibniz can be reduced to an aversion to certain of Leibniz’s theological commitments and motivations.

Finally, it looks in detail at the penultimate paragraph which, it argues, ends with a brief description of what will ultimately become Deleuze’s double process of actualisation and counter-actualisation. Crucially, Deleuze turns to Leibniz, rather than Spinoza, in order to explain these processes.

Part II: Difference and Repetition and Logic of Sense

Chapter Three: Deleuze’s Critique of Representation

3.1 Hyppolite’s Logic and Existence

3.1.1 Pre-Critical Philosophy and Empirical Consciousness

3.1.2 Critical Philosophy

3.1.3 Absolute Philosophy

3.2 The Critique of Representation in Difference and Repetition

3.2.1 Plato and the Simulacrum

3.2.2 Aristotle and Finite Representation

3.2.3 Leibniz, Hegel and Infinite Representation

3.2.4 Vice-Diction

Abstract

This chapter introduces the motivations and method behind Deleuze’s philosophical project. It begins with a detailed reading of Deleuze’s review of Hyppolite’s Logic and Existence, in which Deleuze first articulates his claim that the goal of philosophy is to create a logic of sense, rather than a metaphysics of essence. This review introduces Deleuze’s central criticism that the history of philosophy has for too long given a foundational role to certain features of our naïve representation of the world, instead of explaining the genesis of these features. Among these is an understanding of difference as opposition that finds its ultimate expression in Hegelian contradiction. Deleuze briefly invokes Leibniz as a figure who is perhaps capable of providing an alternative concept of difference.

The chapter then turns to the opening chapters of Difference and Repetition, where Deleuze again outlines a critique of the history of philosophy’s treatment of difference and its subordination to the structure of representation. This time Deleuze traces a history through Plato, Aristotle, Leibniz and Hegel. In Leibniz he identifies for the first time a world of “restless” infinitely small differences which will become central to all his later readings.

Chapter Four: A Leibnizian World

4.1 The Continuum

4.2 Infinite Analysis, Singularities and Events

4.3 Incompossibility and Vice-Diction

4.4 Deleuze’s Critique of Leibniz

4.4.1 The Possible and the Virtual in Logic of Sense

4.4.2 The Possible and the Virtual in Difference and Repetition

4.4.3 The Clear and the Confused

Abstract

This chapter uses concepts from Leibniz’s philosophy to provide an account of the metaphysical system Deleuze constructs in Difference and Repetition and Logic of Sense. This account has four key components.

1) An ideal continuum populated by reciprocally determined differential relations, from which individuals are produced. Leibniz’s infinitesimal calculus is the technique most suited to describe this continuum.

2) The singularities or events which populate the continuum and which eventually form the “predicates” which are included within individuals. An inverted version of Leibniz’s theory of infinite analysis, which Deleuze dubs ‘vice-diction’, allows us to describe how these singularities are distributed and concentrated.

3) The relations of compossibility between singularities which allow the articulation of a structure prior to any logical relations of opposition or contradiction. In Leibniz, a divergence between singularities marks a bifurcation into two distinct possible worlds. In Deleuze, by contrast, divergent series resonate and communicate with one another.

4) An “ideal game” which presides over the actualisation of this pre-individual continuum through the genesis of individuals. In Leibniz this game is subject to the rules of a divine calculus in which God selects a “best of all possible worlds” whose harmony is guaranteed. Deleuze, however, will reject this theological constraint.

Part III: The Fold

Chapter Five: Material Folds and the Lower Level of the Baroque House

5.1 The Baroque

5.2 Folding and the Baroque House

5.3 Baroque Architecture and the Inorganic Fold

5.4 Baroque Biology and the Organic Fold

5.5 The Fold-between-the-two

Abstract

This chapter turns to one of Deleuze’s last major works, The Fold: Leibniz and the Baroque. It argues for Leibniz’s central role in the text, and explains the book’s complicated interplay between Leibniz’s philosophy and mathematics, and Baroque art and architecture. It rediscovers all the major elements of the Leibnizian structure outlined in the previous chapter, and finds them united by the new concept of the “infinite fold”.

It then looks in detail at the opening chapter of The Fold, where Deleuze uses Wölfflin’s theory of Baroque architecture and Leibniz’s theory of preformism and biological evolution to introduce the parallelism between the repeated folds of inorganic matter and the interior, enveloping folds of organisms. The interiority of the latter eventually forces us to posit monads, or souls, which exist elsewhere and serve as the principle of their unity.

Chapter Six: Spiritual Folds and the Upper Level of the Baroque House

 6.1 Klee, Cache and Points of Inflection

6.2 Inclusion

6.3 The Fold of the Baroque World

6.4 Mallarmé: The Visible and the Readable

6.5 The Neo-Baroque

Abstract

This chapter follows Deleuze’s metaphor of the Baroque House, which runs throughout The Fold, from the lower level of matter and organisms, to the upper level of reasonable souls. It shows how Deleuze uses concepts from Paul Klee to present a new theory of singularities or singular points as points of inflection or folds. Inflection gives us a topological model for understanding the inclusion of predicates within individual monads.

The chapter then turns to the most complicated theme of the book: the ideal curve or Fold which Deleuze locates between the two levels of the Baroque house itself. This Fold separates matter from souls, while simultaneously relating them to each other: in Leibnizian terms, they are really distinct but inseparable. What is actualised in individual monads is thus simultaneously realised in matter. Deleuze turns to Mallarmé to explain this complicated relationship between the visible and the intelligible.