Conditions of Thought: Deleuze and Transcendental Ideas 0748676260, 9780748676262

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Conditions of Thought:  Deleuze and Transcendental Ideas

Plateaus – New Directions in Deleuze Studies ‘It’s not a matter of bringing all sorts of things together under a single concept but rather of relating each concept to variables that explain its mutations.’ Gilles Deleuze, Negotiations Series Editors Ian Buchanan, Cardiff University Claire Colebrook, Penn State University Editorial Advisory Board Keith Ansell Pearson Ronald Bogue Constantin V. Boundas Rosi Braidotti Eugene Holland Gregg Lambert Dorothea Olkowski Paul Patton Daniel Smith James Williams Titles available in the series Dorothea Olkowski, The Universal (In the Realm of the Sensible): Beyond Continental Philosophy Christian Kerslake, Immanence and the Vertigo of Philosophy: From Kant to Deleuze Jean-Clet Martin, Variations: The Philosophy of Gilles Deleuze, translated by Constantin V. Boundas and Susan Dyrkton Simone Bignall, Postcolonial Agency: Critique and Constructivism Miguel de Beistegui, Immanence: Deleuze and Philosophy Jean-Jacques Lecercle, Badiou and Deleuze Read Literature Ronald Bogue, Deleuzian Fabulation and the Scars of History Sean Bowden, The Priority of Events: Deleuze’s Logic of Sense Craig Lundy, History and Becoming: Deleuze’s Philosophy of Creativity Aidan Tynan, Deleuze’s Literary Clinic: Criticism and the Politics of Symptoms Thomas Nail, Returning to Revolution: Deleuze Guattari and Zapatismo François Zourabichvili, Deleuze: A Philosophy of the Event with The Vocabulary of Deleuze edited by Gregg Lambert and Daniel W. Smith, translated by Kieran Aarons Frida Beckman, Between Desire and Pleasure: A Deleuzian Theory of Sexuality Nadine Boljkovac, Untimely Affects: Gilles Deleuze and an Ethics of Cinema Daniela Voss, Conditions of Thought: Deleuze and Transcendental Ideas Forthcoming volumes: LeRon Shults, Iconoclastic Theology: Gilles Deleuze and the Secretion of Atheism Janae Sholtz, The Invention of a People: Art and the Political in Heidegger and Deleuze Visit the Plateaus website at www.euppublishing.com/series/plat

CONDITIONS OF THOUGHT: DELEUZE AND TRANSCENDENTAL IDEAS

2 Daniela Voss

© Daniela Voss, 2013 Edinburgh University Press Ltd 22 George Square, Edinburgh EH8 9LF www.euppublishing.com Typeset in Sabon by  Servis Filmsetting Ltd, Stockport, Cheshire, and printed and bound in Great Britain by CPI Group (UK) Ltd, Croydon CR0 4YY A CIP record for this book is available from the British Library ISBN 978 0 7486 7625 5 (hardback) ISBN 978 0 7486 7626 2 (webready PDF) ISBN 978 0 7486 7627 9 (epub) The right of Daniela Voss to be identified as author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.

Contents

Acknowledgements Abbreviations

vi vii

Introduction 1  The Dogmatic Image of Thought 2  The Demand for Transcendental Genetic Conditions 3  Ideas as Problems 4  Time and the Split Subject Conclusion

1 18 74 142 210 265

Bibliography Index

271 281

Acknowledgements

This book is the product of several years work which would have been impossible without the generous support and advice of all those who assisted me to bring this endeavour to completion. I especially owe my heartfelt thanks to Paul Patton who was always there for me to discuss problems and ideas and who encouraged me to overcome difficulties that I encountered over the course of this project. Thanks to him I also had the opportunity to pursue part of my research in the School of History and Philosophy at the UNSW in Sydney. The many kindnesses and friendship I experienced there throughout the duration of my stay leaves me with an immense debt of gratitude to many people too numerous to mention them all. I am also very grateful to Gunter Gebauer from the Free University of Berlin for his ongoing encouragement and enthusiasm for this project. Furthermore, I would like to thank my friends and fellow scholars Simon Duffy, Craig Lundy and Nick Midgley who have helped improve this work through their pertinent comments, critical questions and linguistic advice. My friend Elke deserves a special mention for providing the cover image for this book. My great thanks are due to Carol Macdonald and the team at Edinburgh University Press for their professional way of dealing with all inquiries and working with me throughout the publication process. My experience of publishing with EUP has been a very ­pleasant one. Finally, and above all, I would like to thank my family for their loving support and encouragement over all these years. Parts of Chapter 2 were published as ‘Maimon and Deleuze: The Viewpoint of Internal Genesis and the Concept of Differentials’ in Parrhesia, No. 11 (2011), pp. 62–74. Furthermore, some materials of Chapter 1 and 3 will appear in ‘Deleuze’s Rethinking of the Notion of Sense’ and ‘Deleuze’s Third Synthesis of Time’ in Deleuze Studies (2013). I would like to express my gratitude for the permission of the editors of these journals to reprint this material. vi

Abbreviations

The bibliography contains details of the editions and translations used for each text.

Deleuze AO Anti-Oedipus: Capitalism and Schizophrenia (vol. 1) ATP A Thousand Plateaus: Capitalism and Schizophrenia (vol. 2) B Bergsonism CC Essays Critical and Clinical CIT Cinema 2: The Time-Image D Dialogues DI Desert Islands and Other Texts (1953–1974) DR Difference and Repetition ES Empiricism and Subjectivity: An Essay on Hume’s Theory of Human Nature F Foucault FLB The Fold: Leibniz and the Baroque KCP Kant’s Critical Philosophy: The Doctrine of the Faculties LK I Lecture Course on Kant held at Vincennes, 14 March  1978 LK II Lecture Course on Kant held at Vincennes, 21 March  1978 LS The Logic of Sense N Negotiations 1972–1990 NP Nietzsche and Philosophy PS Proust and Signs WP What Is Philosophy? Note on the citations: The order in which the page numbers are referenced is as follows: the first page number refers to the English translation, the second, italicised, number to the French original. vii

conditions of thought: deleuze and transcendental ideas

Kant CJ Critique of the Power of Judgment CPR Critique of Pure Reason Note on the citations: Page references to CPR are to the original German editions: A (from 1781) and B (from 1787).

viii

Introduction

This project on a Deleuzian transcendental philosophy is born out of a feeling of astonishment. On the one hand, the theme of the transcendental runs through many of Deleuze’s works, in particular those published between 1962 and 1968. On the other hand, the spirit of Deleuze’s philosophical thought seems so very different from that of Kantian transcendental philosophy: Deleuze does not bother to seek a justification or ground for the possibility of experience and its objects. He does not put together a table of categories, nor does he give any transcendental deduction of a priori conditions. Moreover, in Deleuze, there is certainly no transcendental subject, which would have the task of representing the world according to a priori conditions. So why should he label his own philosophy of the 1960s a transcendental empiricism (cf. DR 144/187 and 56/79–80)? In what way, if at all, is his philosophy transcendental? Our approach to this problem has been guided by the intuition that the key had to be found in Deleuze’s critique of the so-called dogmatic Image of thought, a critique that appears in almost every book from this early period and that makes up the central part of Difference and Repetition. The first thing to be noted is that Deleuze understands philosophy fundamentally as critique, and in Nietzsche and Philosophy he explicitly demands a rethinking and radicalisation of Kant’s critical project.1 The Kantian critique sought to describe and ultimately prevent the illusions of reason that are to be found on the ‘battlefield’ of metaphysics and to lead thought back to its proper use.2 By comparison, Deleuze also finds that Western philosophical thought has fallen prey to illusion, but for Deleuze it is the ‘illusions of representation’ (DR 270/346) that must be subjected to critique. Thought has been subordinated to some proper image of itself that ties it to a logic of representation. Kant’s critical philosophy sought to overcome the traditional metaphysical divide between the essences of things or Ideas and their mere appearance. For instance, he criticised Plato for the enthusiasm that led him to pass ‘beyond the concepts of experience to ideas, which seemed to him explicable only 1

conditions of thought: deleuze and transcendental ideas by means of an intellectual communion with the origin of all things’.3 Kant argued against Plato that necessity and universal truth, which seem to pertain to the essence of things, actually have their ground in our own reason and its Ideas. A critical use of reason would abstain from any attempt at direct community with an intelligible world and focus instead on our world, which is given under the condition of transcendental concepts. But this means that for Kant our world is always a represented world, that is not an immediate presence but a world given within a conceptual scheme or structure that provides the limit to knowledge. Now, Deleuze certainly agrees with Kant on the need to overcome the metaphysical dualism between the essences of things and their appearance but he rejects Kant’s representationalist solution to the problem. Deleuze radicalises Kantian critique by bringing it to bear on the logic of representation itself. In his view, the idea of a representational logic is still too ‘foundationalist’, since it presupposes an a priori given ground that shapes our thinking. For Deleuze, a radical critique must lead to a liberation of thought from the fetters of representation; this means to render thought ungrounded. Although both Kant and Deleuze are committed to philosophy understood as critique and the uncovering and warding off of illusion, there thus remains a stark contrast between the two: while Kantian transcendental philosophy aims to provide an a priori ground, Deleuze precipitates transcendental philosophy into a ‘groundlessness’ (sans-fond) or ‘universal ungrounding’ (universel effondement) (DR 91/123). Deleuze dissolves the representational domain into a sub-representational play of intensities or pure differences. While Kant locates the ground of our represented world in universal reason or the transcendental subject, Deleuze admits no transcendental subject that would represent the world but seeks a point of view beyond representation, that is an a-subjective and unconscious transcendental field. While Kant’s transcendental principles are defined as a priori conditions that subordinate thought to a priori judgements, Deleuze, by contrast, seeks a transcendental principle that explains the genesis of the act of thought in thought. Given these fundamental differences between Kant and Deleuze, there need to be other and stronger reasons for Deleuze to adopt the concept of the transcendental. We will claim that one reason lies in the notion of necessity that is implied by the transcendental relation. In a Kantian sense, the transcendental relation is expressed in terms of a ‘conditional to the effect that some conditioned would 2

Introduction be impossible, if not for some condition’.4 The necessity involved is supposed to be more than a conceptual or logical necessity. Kant is referring to a transcendental necessity that establishes a necessary relation between concepts and objects. For if there were no necessary relation to an object then the concepts would remain empty, that is without any signification for us. The transcendental conditional can thus be expressed as follows. Concepts would have no sense for us at all, if they could not be constructed in a priori intuition, that is be incarnated in a formal intuition of space and time. Kant elaborates the construction in formal intuition as a non-conceptual and extralogical necessity for the apparition of sense. One could say that Kant’s transcendental logic is a logic of sense. Now, the Deleuzian concept of the transcendental also indicates a relation of necessity: something forces us to think.5 We would not be thinking if not for some transcendental condition. Furthermore, Deleuze considers the transcendental condition as the constitutive, genetic element of sense. That is, the sense and value of our thoughts follow necessarily from the way in which the transcendental conditions (Ideas or concepts) are incarnated in empirical terms and conditions. This is why Deleuze insists time and again that ‘we always have as much truth as we deserve in accordance with the sense of what we say’ (DR 154/200).6 The last and probably most important reason for Deleuze to adopt the notion of the transcendental lies in Kant’s definition of time as a form of interiority or inner sense. In fact, Deleuze claims that the essence of the transcendental is found here. Kant discovers the transcendental when he criticises Descartes for failing to recognise time as the form of the determinable, that is the inner form through which my undetermined existence can be determined. For Descartes, the form of the ‘I think’ immediately implies my undetermined existence, and too hastily he draws the conclusion that my existence can be determined as a thinking subject. Deleuze contends that ‘the entire Kantian critique amounts to objecting against Descartes that it is impossible for determination to bear directly upon the undetermined’ (DR 85/116). Descartes fails to recognise that my own being is given to the mind, or the form of the ‘I think’, only under the inner form of time. In other words, time is the form under which my being can be determined by the ‘I think’ as an appearance, that is a passive, receptive phenomenal subject in time. Descartes only sees an external difference between the determination and the undetermined, between thought and being, instead of viewing the difference between these 3

conditions of thought: deleuze and transcendental ideas two aspects of human nature ‘in the form of an internal Difference which establishes an a priori relation between thought and being’ (DR 86/116). This internal difference must be understood as what constitutes the transcendental distinction. Establishing a transcendental distinction means ‘interiorising it [difference] within being and thought’ (DR 86/117). For Deleuze, the Kantian subject is essentially a split subject, fractured by the pure and empty form of time. That is why, for him, the transcendental is not primarily rooted in the notion of a transcendental epistemic structure conditioning an empirical content (any such interpretation only re-inscribes hylomorphism, that is an external difference between form and matter), but in the notion of a fractured I. Before Kant, non-critical philosophies both of rationalist or empiricist legacy readily assumed as their point of departure the identity of the subject, or the unity of a consciousness.7 Now with Kant philosophy has to deal with a split subject and time as an inner form or form of auto-affection. ‘If the greatest initiative of transcendental philosophy was to introduce the form of time into thought as such, then this pure and empty form in turn signifies indissolubly the death of God, the fractured I and the passive self’ (DR 87/117). From this perspective, it becomes comprehensible why Nietzsche’s philosophy, in particular his thought of the eternal return, becomes such an important reference point for Deleuze. It also explains why Deleuze’s account of the split subject and his theory of the syntheses of time make up a vital part of his own ­transcendental philosophy. It is perhaps not surprising that Deleuze’s transcendental philosophy will ultimately undermine the Kantian version of transcendentalism. For Deleuze’s approach to the history of philosophy displays an extraordinary creativity of thought and boldness to read traditional philosophical texts in a new manner, sometimes even against their original sense (in a ‘contre-sens’ so to speak). Deleuze claims that critical engagement with the history of philosophy is of necessity creative: criticism has to lead to the construction of new concepts and thereby contribute to the creation of concepts understood as the essential task of philosophy (cf. WP 83/80). ‘Concepts’, Deleuze says, ‘are not waiting for us ready-made, like heavenly bodies’ (WP 5/11), they need to be created. Deleuze reveals his commitment to a creative conceptual constructivism throughout his writings on other philosophers (for example, his early books on Hume, Nietzsche, Kant, Bergson and Spinoza, as well as his book on Leibniz from 4

Introduction 1988). These monographs do not represent neat commentaries on other thinkers, but rather a sort of symbiotic style of writing: Deleuze enters into what Paul Patton has called a ‘dual and paradoxical relation’ with these philosophers, thereby undermining the traditional author-function.8 As Deleuze says, he always needed intercessors (intercesseurs) who would lend their words and through which one could say what one has to say (N 125/171). This technique of ‘ventriloquising’ another thinker allows Deleuze to express his own thoughts through the words of others, resulting sometimes in an indiscernibility between the different voices. Zourabichvili suggests calling this technique ‘free indirect discourse’ (discours indirect libre) probably referring to Deleuze’s definition of ‘free indirect discourse’ in A Thousand Plateaus.9 In the case of Deleuze’s co-authorship with Félix Guattari it is indeed almost impossible to discern the different voices; the two of them truly function as a ‘collective assemblage’ (agencement collectif) (ATP 80/101) and it is not necessary to ­emphasise that these works have a doubled, collective source. However, with regard to Deleuze’s writings on philosophers who already have a distinct identity in the history of philosophy, it is necessary to point out that his accounts of Plato, Nietzsche and Kant transform or metamorphose these thinkers into a Deleuzian Plato, a Deleuzian Nietzsche, a Deleuzian Kant. In the course of this book, we will at times call attention to this typical Deleuzian symbiotic style of doing philosophy, in order to prevent misunderstandings or accusations that Deleuze ‘misinterprets’ the philosopher under consideration. We also have to keep this in mind when we consider Deleuze’s notion of the transcendental. It is surely Kantian in origin, but Deleuze will transform the Kantian notion of the transcendental in order to remedy what he sees as a lack in that notion (i.e. the failure to address the problem of genesis) and thereby turn it into a weapon against Kant’s transcendental philosophy itself. In fact, Deleuze not only turns against Kant but against a whole tradition of Western thought obsessed with the idea of a ‘beginning’ in philosophy, that is the idea of a foundation or of grounding principles. His allies in this combat against ‘foundationalism’ are various post-Kantian philosophers such as Maimon, Nietzsche and Bergson. Deleuze will borrow from them ideas and concepts that will help him to invent a new type of transcendental philosophy that is genetic, sub-representational and differential. The aim of this book is above all to extract a Deleuzian concept of the transcendental from his philosophy of the early period, in 5

conditions of thought: deleuze and transcendental ideas particular Difference and Repetition (1968). We will also refer to Nietzsche and Philosophy (1962), Kant’s Critical Philosophy (1963), Proust and Signs (1964), Bergsonism (1966) and The Logic of Sense (1969), as well as to some articles and lecture courses mainly from the 1960s and 1970s. Only occasionally will we refer to Deleuze’s later œuvre and only in cases where the reference helps to bring out certain ideas that remain unclear or concealed in his early writings. As Deleuze becomes more involved with psychoanalysis and politics subsequent to the revolutionary events of May 1968 in France and the encounter with Guattari, his philosophy and style of doing philosophy change. His thought is captured by new problems that require a modified use of familiar concepts and the creation of entirely new concepts. Therefore it would have a confusing and distracting effect if we included some of the seminal concepts and thoughts of the later works. By no means do we want to claim that Difference and Repetition is Deleuze’s one and only masterpiece and the climax of his philosophical thought. This being said, the project of transcendental philosophy undertaken in Difference and Repetition deserves to be examined closely in its own right, not only for the contributions it makes to a criticism of Kantian transcendental philosophy but also for the elaboration of a highly original, differential and genetic model of the transcendental. When we started on this project in 2007 there was a conspicuous lacuna in the Deleuze scholarship with regard to the nexus Deleuze and Kant. The only monograph on the topic available at that time was Marc Rölli’s dissertation on Gilles Deleuze and the philosophy of transcendental empiricism, published in 2003. In this work Rölli undertakes a very detailed exploration of the respective traditions of empiricism and transcendental philosophy with a particular focus on Deleuze’s early book on Hume, Empiricism and Subjectivity (1953). He also devotes a great deal of attention to Husserl and Heidegger, pointing to the importance of Heidegger’s Kant and the Problem of Metaphysics for Deleuze’s three syntheses of time. Rölli’s study is very clearly written, he analyses Deleuze’s criticism of Kant with great accuracy and presents Deleuzian transcendental empiricism as a coherent philosophical system. He explains the genesis of experience by self-organising processes in the sub-representational realm of intensities and the production of concepts of experience out of passive syntheses such as habit. Rölli’s book certainly has great merit, but its relevance to our own project is somewhat limited. The two projects are quite different in focus and approach: rather than focusing on the 6

Introduction sense in which Deleuze’s philosophy is transcendental, Rölli focuses on the second part of the term ‘transcendental empiricism’, which is why he gives so much space to Deleuze’s reading of Hume. Now it is certainly true that Hume plays a role in Deleuze’s criticism of representation. In Empiricism and Subjectivity Deleuze puts great emphasis on the external character of relations: Hume’s principles of association are not subordinated to any representational totality, logic or scheme. However, Hume provides no insight into the genesis of real experience and as such, the reference to Hume is not relevant to Deleuze’s project of rethinking the transcendental as a genetic principle. In fact, it is to rationalists such as Leibniz and Maimon that Deleuze turns in order to extract the concept of internal differential relations which function as the genetic element of the production of the real. In Difference and Repetition, Deleuze underlines the importance of internal relations, that is relations of difference where the connecting factor is difference qua difference,10 and even calls it a ‘mistake’ of empiricism ‘to leave external what is separated’ (DR 170/221).11 Rölli does not elaborate the notion of differential relations, instead giving preference to the concept of intensity. Not surprisingly, he mentions Salomon Maimon only in passing12 and even criticises Daniel Smith for having overestimated the importance of Maimon for Deleuze in his (unpublished) doctoral thesis on Deleuze’s philosophy of difference.13 Our study seeks to show, to the contrary, that Maimon’s influence and the theory of internal differential relations are of central importance to Deleuze’s rethinking of the transcendental. For this reason we will focus on the contribution of Maimon, Nietzsche and Bergson to Deleuze’s thought, rather than on that of Hume or phenomenology. Only in recent years have there been further publications on Deleuze and Kant, and on Deleuze’s transcendental empiricism. Levi Bryant’s book Difference and Givenness: Deleuze’s Transcendental Empiricism and the Ontology of Immanence appeared in 2008. It is a very fruitful examination of Deleuze’s relation to Kant and provides many interesting insights. For Bryant, the crucial point of divergence between Deleuze and Kant bears on the character of intuition: While Kant takes intuition to be something given, Deleuze claims that intuition is essentially productive. It itself creates the objects of intuition by means of differential mechanisms. Bryant concludes that ‘insofar as differentials function as the productive rules for the qualitative givens of being, Deleuze’s position is best 7

conditions of thought: deleuze and transcendental ideas thought of as a hyper-rationalism rather than an empiricism’.14 Bryant clearly recognises the importance of internal differential relations for Deleuze’s philosophy (although he refers to Maimon only occasionally).15 However, we would argue that Bryant’s choice of terms is not always helpful; for instance, it is rather misleading when he states that ‘Deleuze is led to rationalize intuitions themselves’16 or that ‘experience is for Deleuze intelligible in principle’17 and that Deleuze’s philosophy ‘locates intelligibility at the level of the aesthetic or sensible itself’.18 We believe that these traditional philosophical concepts relating to rationalism and empiricism cannot easily be applied to Deleuze’s thought. Both rationalism and empiricism take as their point of departure the presupposition of a pre-existing consciousness endowed with ready-made faculties and then go on to examine its possible relation to an objective world. For Deleuze, on the contrary, the subject and the object are not determined entities given in advance but the effect of differential processes that take place in the virtual and extend themselves into processes of actualisation. Hence choosing the viewpoint of a subjective consciousness and analysing experience in terms of intellectualised intuitions is a rather ill-advised strategy, for it neglects Deleuze’s endeavour to seek a viewpoint of intrinsic genesis beyond a philosophy of mind and a theory of representation. In his attempt to formulate Deleuze’s philosophy as an ontology, Bryant pays much attention to Bergson’s influence on Deleuze. In fact, Bryant presents Deleuze as ‘jumping out of the critical philosophy’ into an analysis of the being of time as a pure transcendental field.19 It is shown that critical thought ultimately reaches the point where it becomes indiscernible from speculative thought.20 There is certainly some truth to this claim. Although Deleuze’s transcendental philosophy in no way means a return to a pre-critical metaphysics that presupposes an inaccessible transcendent realm in principle, he does outline a metaphysics of immanence. As Deleuze contends we have the means to penetrate the realm of the sub-representative (DI 115/161), to explore virtual Ideas (DR 194/251), to live and to experience the pure past (cf. B 122/55, note 16/1) and even to create fragments of the pure past in art (cf. the Proustian example of the initself of Combray (DR 85/115 and 122/160)). However, in our book, we have refrained from labelling this Deleuzian metaphysics with the term ‘ontology’ and rather subsumed it under the title of Deleuze’s transcendental philosophy. This choice of terms is not merely a matter of taste. We believe that the underlying problem of Deleuze’s 8

Introduction early philosophy is not so much the question of ‘what is there?’ but rather ‘what are the real conditions of (experience, thought, consciousness, subjectivity, objects, and so on)?’ This approach searching for the real conditions of genesis is best described as Deleuze’s transcendental viewpoint. Another major work in this field is Christian Kerslake’s Immanence and the Vertigo of Philosophy: From Kant to Deleuze published in 2009. Unlike Levi Bryant, Kerslake proposes a more aesthetic and existential reading of the transcendental conditions of thought. The transcendental Ideas that provoke thought and make it enter into ‘psychic repetition’ are real problematic experiences beneath the mystifications of everyday (‘ideological’) reality, such as birth, death, sexual difference and so on.21 The Ideas or ‘real problems’ are necessarily unconscious but can be realised in various ways: ‘they may be treated from the perspective of knowledge claims, but they can also be given indirect presentation in art, theatre, literature, music and cinema.’22 Kerslake reads Deleuze’s transcendental empiricism as a ‘direct continuation of the Kantian turn’,23 as a project of ‘metacritique’ begun by the post-Kantians Maimon, Schelling, Novalis and Hölderlin.24 In a footnote, Kerslake makes it clear that his study is only concerned with Deleuze’s philosophy in the works of 1953 to 1968.25 In fact, the major reference point for his study is Deleuze’s very early and newly discovered lecture series ‘What Is Grounding?’ (Qu’est-ce que fonder?), held at the Lycée Louis le Grand from 1956 to 1957.26 In this lecture course ‘Deleuze “enacts a repetition of the Kantian enterprise”, working through the premises of Kantian, post-Kantian, and Heideggerian existential approaches to “self-­grounding” in philosophy’.27 On this basis, Kerlake argues that Deleuze’s ‘real questions and problems emerge from within the post-Kantian tradition of philosophy’.28 It is certainly a great achievement to have set out the relation of Deleuze’s project to that of the post-Kantians, but the danger is that Deleuze’s philosophical questions and problems are not evaluated in their own right. Indeed, Kerslake neglects the originality and radical openness of Deleuze’s investigations by identifying them with the post-Kantian project. ‘The main claim of this book is that the philosophical work of Gilles Deleuze represents the latest flowering of the project, begun in the immediate wake of Kant’s Critique of Pure Reason, to complete consistently the “Copernican revolution” in philosophy.’29 This strong claim leads Kerslake in some cases to 9

conditions of thought: deleuze and transcendental ideas a bizarre reading of Deleuze, as if Deleuze’s philosophy only served to amend transcendental philosophy and to solve Kantian and postKantian problems. According to Kerslake, ‘Deleuze rebaptises the faculty of reason as the faculty of “thought” ’,30 but Kerslake thereby ignores the fundamental differences between Deleuze’s conception of non-representational, nomadic and creative thought and the role of reason in Kant’s epistemology which comes down to securing the coherent employment of the understanding and the production of systematic theoretical knowledge. In Kant’s practical philosophy reason appears as the sole legislative power. Is it by analogy with this Kantian autonomy of reason that Kerslake finds the conception of an autonomy of thought in Deleuze? Kerslake contends that if thought ‘distrusts “common sense”, and instead seeks autonomy, it must then learn how to regulate itself’31 and it is for this reason that ‘Deleuze develops this model of a free, self-grounding generation of the relations of a system of faculties’.32 We would argue, by contrast, that Deleuze’s genetic model of the transcendent exercise of the faculties by no means relies on autonomy and self-regulation, but rather on heteronomy.33 Deleuze repeatedly insists that we are forced to think and that it is a violent experience which even takes from us the power to say ‘I’. Kerslake’s attempt to align Deleuze’s project with post-Kantian philosophy, in particular German Idealism, also leads him to discover a new subject in Deleuze’s philosophy. As is well known, Fichte, Schelling and Hegel all searched for an unconditioned, selfgrounding principle of subjectivity that would provide a ground for our conscious experience. Kerslake presents Deleuze’s philosophy as an extension of Schelling’s metaphysical empiricism: We will present Deleuze’s philosophy of immanence as caught between two poles, represented by the late Fichte on the one hand, and the ‘Absolutes’ of Wronski and the late Schelling on the other. Insofar as his metacritical, systematic approach remains valid, we will argue that Deleuze’s final ‘resubjectification’ of Life [in ‘Immanence: A Life’] signals his arrival at the same point as Wronski and the later Schelling, who ended up positing the existence of subjectivity within a ‘primordially living . . . actual being’, a ‘being that is preceded by no other and is ­therefore the oldest of all beings’. [Schelling, The Ages of the World]34

Kerlake’s claim that there is a ‘resubjectification’ of life in Deleuze’s last essay ‘Immanence: A Life’, first published in 1995, seems peculiar in the light of Deleuze’s own claim that he talks about 10

Introduction an indefinite, impersonal life, precisely a life accompanied by the ­indefinite article.35 Kerslake’s study is valuable for the information it provides on the metaphysical origins of Kantianism, on the evolution of Kant’s critical philosophy starting from his Inaugural Dissertation, and on the projects and endeavours of various post-Kantian philosophers. However, in this mass of detail the reader risks losing track of its relevance to Deleuze: Kerslake’s identification of Deleuze as the inheritor of the project of post-Kantian philosophy loses sight of what radically differentiates Deleuze from this philosophy. The most recent study in the field of Deleuze’s transcendental empiricism was released in November 2009. Anne Sauvagnargues’ book Deleuze: L’Empirisme transcendantal analyses Deleuze’s transcendental philosophy better and more deeply than any prior commentator. Sauvagnargues both covers Deleuze’s many philosophical and literary sources and offers a comprehensive and convincing account of Deleuze’s transcendental empiricism. Our book has benefited considerably from this excellent study, which ought to be an important reference point for Deleuzian scholars. However, our own project differs from Sauvagnargues’ book in that it examines many topics in much greater detail. For instance, our analysis of Salomon Maimon’s philosophy provides insights into his critique of Kant, his own philosophical system and background information about the early phase of Leibniz’s and Newton’s differential calculus, all of which is covered by Sauvagnargues but not explained in any depth. On the other hand, Sauvagnargues covers a much wider range of Deleuze’s sources: apart from Kant, Proust, Bergson, Nietzsche and Maimon, she also deals with Spinoza and Simondon, and in particular devotes more time to exploring the material or bodily aspects of transcendental empiricism. Since our project focuses rather on the transcendental conditions of thought and the critique of the illusionary effects of the dogmatic Image of thought, the aspect of material nature does not play a large role. However, anyone who wishes to have a broader picture of Deleuzian transcendental empiricism is recommended to consult Sauvagnargues’ seminal book. Throughout our study, Daniel Smith’s essays on Deleuze in relation to Kantian Ideas, Leibnizian principles and Maimonian differentials provided a very helpful source. 36 The recent collection of essays Deleuze’s Philosophical Lineage, edited by Graham Jones and Jon 11

conditions of thought: deleuze and transcendental ideas Roffe and published by Edinburgh University Press in 2009, also proved to be a helpful compendium, since it presents a series of thinkers (not only philosophers) that have been influential for Deleuze but whose thought is not necessarily widely known.37 Particularly important for this study has been Simon Duffy’s article on the mathematician Albert Lautman (1908–44) who provided Deleuze with a mathematical and dialectical model of problematic Ideas. This present study will examine the precise nature of Deleuzian transcendental conditions, in particular the transcendental conditions of thought, i.e. that which compels thought to transgress the established boundaries of representation. We will argue the following. (1) For Deleuze transcendental conditions need to be genetic. They have to account for the genesis of sensations and the variations of sense. It should be noted that Deleuze does not seek to give an account of the genesis of every particular given, here and now, but rather of a compound of sensations or a sign which can also mean a literary work, a painting, a thought.38 (2) The conditions must not be larger than what they condition. They are determined at the same time as they determine the conditioned. Borrowing a Nietzschean term, transcendental conditions are plastic in opposition to the invariant and abstract transcendental conditions of Kantian legacy. (3) The transcendental for Deleuze does not designate a first condition, a beginning or ground, but rather a ‘groundlessness’ or ‘universal ungrounding’. The ground is devoured so to speak by an ‘original depth’ which is to be conceived as a pure intensive ‘spatium’ (DR 230/296) or a differential multiplicity. (4) The multiplicity of differential relations is immanent to this world as its virtual half or dimension. (5) The Deleuzian transcendental conditions are further defined as Ideas or problems that we encounter in our unconscious and sub-representational mode of existence. They demand solutions, but the way in which they are actualised and answered in empirical terms and circumstances can never exhaust their ideal and problematic character. (6) Ideas or problems do not appeal to given, ready-made faculties that are already regulated within a harmonious accord. Rather, they transform those faculties forcing them to transgress their limits in a transcendent and paradoxical exercise. (7) The variations of Deleuzian transcendental conditions, which have been specified as differential Ideas or problems, must be thought of as unfolding outside historical linear time. Deleuze envisages a third synthesis of time in terms of Nietzsche’s eternal return and relates 12

Introduction it to a dissolved subject or fractured ‘I’ which is shown to be the ­correlate of the transcendental conditions of thought. The method of this study involves a close reading and interpretation of Deleuze’s texts from the 1960s, with occasional references to his later works. It will be noticed that we rarely make use of Deleuze’s The Logic of Sense although it was published in 1969 only one year after Difference and Repetition, and Deleuze was apparently working on their ideas simultaneously. However, it seems to us that they stand as two separate sources of his work, and each should be treated in its own right. While Difference and Repetition is centred on rethinking Kant’s transcendental, The Logic of Sense draws on the Stoic ontological distinction between bodies and incorporeal senseevents. Not only the terminology but also the whole philosophical framework of these two books differ considerably from each other. The aim of this study is to give a systematic reconstruction of what can count as a Deleuzian transcendental philosophy. The decision to focus on Nietzsche, Maimon and Bergson and to include thinkers such as the mathematicians Albert Lautman, Karl Weierstrass and Bernhard Riemann has been dictated to us by the very nature of the task of determining a transcendental which is conceived as a genetic and differential multiplicity with varying relations and located within an unconscious, virtual realm. Chapter 1 will examine what Deleuze understands by the expression ‘dogmatic Image of thought’ and why he rejects it. One of the main reasons for his rejection is the adherence of the dogmatic Image of thought to the model of representation, which operates through judgements on the basis of the identity of concepts, thereby excluding all the non-conceptual or pre-linguistic differences and repetitions that cannot be identified. The model of representation denies these differences and repetitions a concept of their own and dismisses the genetic and creative force that allows them to produce signs or senses that cannot be captured by logic. By means of a criticism of the dogmatic Image of thought, Deleuze opens the path to a detailed exploration of the transcendental as consisting of genetic, differential forces beneath the order of representation. Chapter 2 will focus on Deleuze’s demand for transcendental genetic conditions. This demand arises from a criticism of Kant’s extrinsic account of conditioning, which leaves a gap between the a priori concepts and given intuition. With recourse to Nietzsche’s ‘method of dramatisation’, Deleuze shows that the concepts or moral feelings operative in thought need to be related to a particular 13

conditions of thought: deleuze and transcendental ideas combination of forces that determines the sense and value of what we feel, say or think. The Kantian transcendental conditions, by contrast, are cut off from their genealogical origin and presented as pure a priori givens. This is why they are too large (general or abstract) with regard to what they condition. On the other hand, Kantian transcendental conditions are also still too similar to the psychological conditions governing the empirical cases of recognition. Kant simply traces the transcendental from the empirical and projects the newly discovered transcendental backwards as the transcendental ground of recognition. We will argue that in search of transcendental conditions that are not only genetic but also unconditioned themselves, that is heterogeneous to the series of conditioned conditions, Deleuze finds what he requires in Maimon’s concept of ‘differentials of consciousness’. For Maimon, the sub-conscious manifold of genetic differential elements serves as an explanatory principle for the manner in which real experience arises. Chapter 3 will take up the theme of problematic Ideas as it is laid out in Kant’s Critique of Pure Reason and Critique of the Power of Judgment. We will explore the way in which Ideas count as problems ‘without solution’ (CPR A 328/B 384) and how they are capable of animating our cognitive faculties to transcend their boundaries and thereby elude determining judgements. In this context, Kant’s model of the experience of the sublime will play an important role. The last part of this chapter will investigate how Deleuze develops Kant’s notion of Ideas into his own theory of Ideas, and analyse the structure, internal operations and the movement of actualisation of Deleuzian Ideas. In the elaboration of his ‘dialectics of Ideas’ Deleuze is inspired by the philosopher and mathematician Albert Lautman whose ideas will be addressed in this chapter. After having specified the transcendental conditions of thought as genetic and differential Ideas endowed with a problematic character and located within a virtual realm, we will then in Chapter 4 examine the way in which the transcendental conditions are related to a split subject. We will follow Deleuze’s reading of Kant according to which Kant’s invention of the pure and empty form of time not only breaks with the ancient circular model of time, but also introduces a fracture in the ‘I’ that will compel the subject to confront itself as an Other. Deleuze will explain the genesis as well as the fracture of the subject by his theory of time captured in the three syntheses of time in Difference and Repetition. We will argue that the third synthesis of time, i.e. Nietzsche’s eternal return, is the necessary prerequisite for 14

Introduction opening up the subject and referring it to the realm of Ideas. We will illustrate this relation by looking at how Deleuze makes use of Pierre Klossowski’s account of Nietzsche as a thinker of the eternal return. On the basis of these four chapters, we hope to offer a comprehensive account of Deleuze’s transformation of transcendental philosophy as it is usually conceived. By doing this, we aim to convince the reader of the originality and critical power of Deleuze’s own conception of the transcendental.

Notes   1.   2.   3.   4.   5.   6.

Cf. NP 1/1, 89–90/102, 91/104 and 106/121. Kant, Critique of Pure Reason, B xv; hereafter cited as CPR. Kant, Critique of the Power of Judgment, 5: 363; hereafter cited as CJ. Franks, All or Nothing, p. 204. See DR 139/182, 275/353 and also PS 97/189. See also DR 159/206, NP 1/2, 104/118, 110/125 and B 16/5. In Chapter 1 in the discussion of the seventh postulate of the dogmatic Image of thought, we will show in what way the determination of a problem and its conditions releases a necessary force that urges us all the way down to the very end of the problem’s necessary implications.   7. It should be noted that Deleuze explicitly exempts Hume’s empiricist philosophy from this charge. In his early book on Hume, Empiricism and Subjectivity, Deleuze attempts to show that subjectivity in Hume does not have the characteristics of a pre-existing subject. On the contrary, empirical subjectivity is determined as an effect of principles transcending and affecting the mind: ‘it is in effect an impression of reflection. The mind having been affected by the principles, turns now into a subject’ (ES 26/8).   8. Patton, Deleuze: A Critical Reader, p. 3.   9. Zourabichvili, ‘Une philosophie de l’événement’, p. 14. Cf. Deleuze’s definition of ‘free indirect discourse’: ‘there are no clear, distinctive contours; what comes first is not an insertion of variously individuated statements, or an interlocking of different subjects of enunciation, but a collective assemblage (agencement collectif) resulting in the determination of relative subjectification proceedings, or assignations of individuality and their shifting distributions within discourse. Indirect discourse is not explained by the distinction between subjects; rather, it is the assemblage (agencement), as it freely appears in this discourse, that explains all the voices present within a single voice’ (ATP 80/101). 10. In fact, the emphasis on internal difference can also be found in some other of Deleuze’s early writings, in particular in the context of Bergson’s concept of duration or non-numerical, qualitative multiplicity; see B 15

conditions of thought: deleuze and transcendental ideas 42/36 and DI 32–51/43–72. See also PS 41/54: ‘But what is an absolute, ultimate difference? Not an empirical difference between two things or two objects, always extrinsic. [. . .] In this regard, Proust is Leibnizian.’ 11. This comment is made when Deleuze criticises Kant for leaving concepts and intuition external to one another: ‘in this sense there is still too much empiricism in the Critique’ (DR 170/221). Deleuze blames Kant’s transcendental philosophy for not being transcendental enough. 12. Rölli, Philosophie des transzendentalen Empirismus, p. 10 and p. 34. 13. Ibid., p. 70. Unfortunately, Daniel Smith’s dissertation The Concept of ‘Difference’ in the Philosophy of Gilles Deleuze, accepted by the University of Chicago (Illinois) in March 1997, is not available to us. 14. Bryant, Difference and Givenness, p. 11. 15. Ibid., pp. 8–9, 46, 194, 242. 16. Ibid., p. 28. 17. Ibid., p. 63. 18. Ibid., p. 12. 19. Ibid., p. 181. 20. Ibid., p. 183. 21. Kerslake, Immanence and the Vertigo of Philosophy, p. 91. 22. Ibid., p. 4. 23. Ibid., p. 5. 24. Ibid., p. 7. 25. Ibid., p. 42, note 8. 26. The manuscript of the lecture course, recorded by Pierre Lefebvre, is available online at . 27. Kerslake, Immanence and the Vertigo of Philosophy, p. 3. 28. Ibid., p. 3. 29. Ibid., p. 5. 30. Ibid., p. 83. 31. Ibid., p. 84. 32. Ibid., p. 81. 33. Cf. Sauvagnargues, Deleuze: L’Empirisme transcendantal, p. 84. 34. Kerslake, Immanence and the Vertigo of Philosophy, pp. 212–13. 35. Using the example of Charles Dickens’ story Our Mutual Friend, Deleuze shows that ‘the life of the individual gives way to an impersonal and yet singular life that releases a pure event freed from the accidents of internal and external life, that is, from the subjectivity and objectivity of what happens’. See Deleuze, ‘Immanence: A Life’, p. 28. 36. To name only a few of his essays that were particularly important for us, these are (1) ‘Deleuze’s Theory of Sensation: Overcoming the Kantian Duality’, (2) ‘Deleuze, Kant, and the Theory of Immanent Ideas’, (3) ‘Genesis and Difference: Deleuze, Maimon, and the PostKantian Reading of Leibniz’. 16

Introduction 37. See, for instance, the following essays in this volume: (1) Simon Duffy, ‘Albert Lautman’, pp. 356–79; (2) Graham Jones, ‘Solomon Maimon’, pp. 104–29; (3) Melissa McMahon, ‘Immanuel Kant’, pp. 87–103; (4) Daniel Smith, ‘G. W. F. Leibniz’, pp. 44–66. 38. Levi Bryant calls them ‘topological’ or ‘morphological essences’, describing such an essence as ‘a possible world, a system of appearances, a way of being’. As examples he refers to the style of an author (the worlds of Proust, Joyce or Kafka), the unique patterns of seashells or the migration patterns of birds (cf. Bryant, Difference and Givenness, p. 66). In our view, his examples seem to be too close to a structuralist viewpoint. A painting by Francis Bacon, for instance, captures intensive forces or dynamisms that do not belong to the world of appearances but to an intensive depth, which is made visible in the vibration of colours and deformation of bodies. Thus Bacon adds a vertical layer, that is a dynamic, intensive and temporal dimension to the merely horizontal structure of the ‘good form’ of conventional representation. Deleuze makes use of the term ‘sign’ to refer to this dynamic or genetic structure. We prefer the term ‘sign’ to Bryant’s term of ‘morphological essence’, in order to elude the classical philosophical notions of essence and appearance, already laden with meaning.

17

1

The Dogmatic Image of Thought

The image of thought is a recurrent theme in Deleuze’s philosophy: it appears already in his writings on Nietzsche (1962) and Proust (1964), and is then fully laid out in his magnum opus Difference and Repetition (1968). At first sight, it might seem peculiar to talk about an ‘image’ of thought, for it seems that the realm of images or the imaginary is opposed to the realm of thought or the intelligible. Is the expression ‘image of thought’ not a contradiction in terms? Must we not distinguish carefully between the imaginary and thought, or in fact between the imaginary and the real? In one of his early essays Deleuze remarks: We are used to, almost conditioned to a certain distinction or correlation between the real and the imaginary. All of our thought maintains a dialectical play between these two notions. Even when classical philosophy speaks of pure intelligence or understanding, it is still a matter of a faculty defined by its aptitude to grasp the depths of the real (le réel en son fond), the real ‘in truth’, the real as such, in opposition to, but also in relation to the power of imagination. (DI 171/239)1

Thus in the classical tradition of epistemology, the understanding is understood as the faculty of thought capable of grasping the real or the true essence, while the faculty of imagination grasps nothing on its own because it produces only an endless series of varying images or representations. The imagination is powerless with regard to the recognition of true essences. This classical binary model of thought and imagination is still preserved in the psychoanalytic tradition. For instance, Deleuze criticises Freudianism for differentiating between ‘the reality principle with its power to disappoint, [and] the pleasure principle with its hallucinatory power of satisfaction’ (DI 171/240), since it reinscribes the binary model between the real and the imaginary. Deleuze further asserts that the methods of Jung and Bachelard also endorse this model. Psychoanalysis is consigned to the analysis of the imaginary, which ‘is defined by games of 18

The Dogmatic Image of Thought mirroring, of duplication, of reversed identification and projection, always in the mode of the double’ (DI 172/241).2 Suffice here the example of the distinction between the real father and the variety of father-images. On the whole, the psychoanalytic tradition uses the term image or imaginary to refer to deceptive representations that disguise and conceal the thought of the real and thereby disable the subject through fixations which are produced by the unconscious ­mechanisms of imagination. The binary model of the real and the imaginary even extends itself into socio-political theory in the distinction between real men and their real relations versus ideologies and imaginary relations. In fact, the notion of ideology suggests the existence of some brute reality which is concealed, distorted or oppressed by the grip of an image. For this reason, Deleuze takes a highly critical stance toward the notion of ideology understood as some repressive idea or image to which we submit.3 In sum, Deleuze rejects the simple binary model of the real and the imaginary. This brings us back to the initial question as to how to understand the meaning of the term ‘image of thought’. Deleuze does not take something real as a starting point, such as a natural capacity to think which is then obstructed and distorted by a deceptive image. Rather, for Deleuze, there is an intertwining of thought and image. Phrased more precisely, thought itself is produced by an image that acts like a machine which is coding thoughts in accordance with some normative form. As Claire Parnet explains in Dialogues, co-authored with Deleuze: ‘Images’ here doesn’t refer to ideology but to a whole organisation which effectively trains thought to operate according to the norms of an established order or power, and moreover, installs in it an apparatus of power, sets it up as an apparatus of power itself. (D 23/31)

Thus for Deleuze, a critique of the Image of thought cannot simply mean to unveil the true essence of thought by wiping out some false image. Instead, the Image of thought has to be considered as a productive machine or apparatus of power: we have to examine its mechanisms that produce thought according to certain axes or rules and make it serve some preconceived ends. Although in his early work Deleuze has not yet found the concepts of ‘machine’, ‘coding’ and ‘apparatus of power’, he does speak of the Image of thought as an established order (i.e. the order of representation) and analyses it in terms of a series of postulates that determine what it means to think and what the ultimate goals of thought are. These postulates 19

conditions of thought: deleuze and transcendental ideas need not operate visibly; more often they remain unconscious forming implicit subjective presuppositions, which are essentially pre-philosophical or non-philosophical in nature. This means that they are already at work when we start to think, although we may not always be aware of it. Why is it that Deleuze speaks of a single Image of thought? To be sure, throughout the history of philosophy there have been ‘variant forms’ (DR 131/172) of the image of thought. Thus the Greek image of thought manifest in Plato certainly differs from the modern Cartesian image of thought. Again, rationalists hold to a different form of image of thought than empiricists. Despite the various forms of images of thought pertaining to each philosopher or style of philosophy, there are, according to Deleuze, some features that are repeated and can be regarded as variations within a single movement. They form ‘a single Image in general’ (DR 132/172) – ‘image’ written with a majuscule – which Deleuze specifies as a ‘dogmatic, orthodox or moral image’ (DR 131/172). This Image is particularly detrimental, inasmuch as it obstructs the genesis of a thought that eludes the requirements of representation and that is capable of calling forth an absolute, wholly unpredictable and new, future. ‘In effect, thought is covered over [se recouvre] by an “image” made up of postulates which distort [dénaturent] both its operation and its genesis’ (DR 265/341). One of the main features of the dogmatic Image of thought is the privileging of identity over difference. More precisely, the nature of difference is distorted by the ‘four illusions of representation’ (DR 270/346): identity, resemblance, opposition and analogy. In particular, identity is preserved in the identity of the thinking subject, which serves as the principle for the production of abstract concepts or universals subsuming the diversity of the sensible under the identity of the concept. Thus differences in the sensible are cancelled in favour of resemblances and covered over by the identity of qualities or the quantity of extension. Opposite predicates divide the diversity of the sensible in a binary manner into mutually exclusive properties and by attributing only one property of a pair of opposites to each thing, determine this thing in accordance with the ideal of complete determination. Furthermore, there are certain determinable concepts (categories or genera of Being), which distribute Being in analogy with the relation between large genera and their species. In summary, not only is the world of the sensible denatured by 20

The Dogmatic Image of Thought being covered with a conceptual net of identical concepts, but also the nature of difference itself is distorted. Difference is treated as a default of identity and lacks a concept in its own right. Difference is either difference without a concept, concerning only external relations between individuals (being outside one another), or it is reduced to a merely conceptual difference (specific difference, generic difference), which allows the identity of a concept to subsist. As Deleuze says, there is conceptual difference, but no concept of difference (cf. DR 27/40–1). The task will be to establish a concept of difference and to restore difference to being and thought. Difference in being operates as the individuating force of nature, while difference in thought implies the fracture of the thinking subject, which is the necessary genetic condition for the ‘genitality of thinking’ (DR 266/342). Deleuze insists that thinking is not an innate faculty given by nature and conditioned by ready-made concepts rooted in our mind. Thinking must be engendered in thought, but to engender thinking in thought does not mean to follow a safe and secure method leading up to truth. Rather, thinking arises through the encounter with something that forces it to think. Thinking occurs by chance and through constraint.

Deleuze’s Critique of the Dogmatic Image of Thought Deleuze’s rejection of the dogmatic Image of thought is motivated by its deeply conservative and moral character. It is conservative because it distributes our experience according to ‘sedentary’ and fixed determinations. The language of ‘territories’ is particularly notable in Kant. Thus Kant wants to secure a territory for the exercise of our faculties of cognition and defend it against the invasion of the sceptics, ‘a kind of nomads who abhor all permanent cultivation of the soil’ (CPR A ix). Kant also distances himself from the ‘battlefield’ of metaphysics: ‘on this battlefield no combatant has ever gained the least bit of ground, nor has any been able to base any lasting possession on his victory’ (CPR B xv). Kant relegates the acquisition of knowledge and truth to a specific legislating faculty (the faculty of understanding), which prescribes to each of the remaining faculties a well-defined function in conformity with the overall interest. Deleuze calls this harmonious collaboration of the faculties under the ­legislation of the understanding the logical ‘common sense’. 21

conditions of thought: deleuze and transcendental ideas According to Kant, however, the greatest threat to the legitimate use of our faculties comes not from external forces but from reason itself. This is because reason finds within itself Ideas which cannot be applied to anything in our experience, but which reason is tempted to use for the determination of metaphysical objects (the soul, the world and God) in order to satisfy our ‘metaphysical need’ (CPR B 21). Therefore reason entices the understanding to an illegitimate use of its a priori concepts and thus gives rise to transcendental illusions. According to Kant, internal illusions are natural and unavoidable (CPR A 298/B 354–5), but their illusionary effect could be defused through a critique of reason itself. This means that reason takes over the chairmanship within the project of an immanent critique. It is the site of a ‘true court of justice’ (CPR A 751/B 779); it is simultaneously both the judge and the accused. Kant’s language invoking  the ‘court’, the ‘judge’, ‘legislation’ and ‘laws’ explicitly points to the moral character inherent in the dogmatic Image of thought. According to Deleuze, the entire doctrine of judgement, which implies the institution of a tribunal and the claim to power, i.e. the power to judge, ‘merges [se confond] with the psychology of the priest’ (CC 127/159). A moral or theological form is inscribed even in judgements of knowledge, inasmuch as their universal predicates lay claim to validity at all times and places. Judgements of knowledge enter into a relation with infinity and eternity, as they consider the existing reality in the name of higher concepts and values (sub specie aeternitatis, so to speak).4 This is why Kant never actually invented ‘a true critique of judgment’ (CC 126/158). For Kant, the exercise of the cognitive faculties is subject to universal laws, which should guarantee their ‘proper use’ and prevent the faculties from transgressing their limits and evolving freely. Variance, deviation, transgression – all these processes which are vital for creativity and novelty in thought are judged and punished, since they undermine the privileged identities of concepts. The logical common sense only produces an orthodox thought, which confirms what already exists, i.e. prejudged identities, prevalent opinions (doxa) and established values. ‘The form of recognition has never sanctioned anything but the recognisable and the recognised; form will never inspire anything but conformities’ (DR 134/176). The ideal of reason and truth to which Kant is devoted only conceals the work of established forces, in particular the state with its territorial claims, imposition of law and order, adherence to ‘higher’ interests and values, and the church with its moral authority. 22

The Dogmatic Image of Thought Kant claims to be beholden to the requirements of truth and reason; but beneath these requirements of reason are forces that aren’t so reasonable at all: the state, religion, all the current values.5

The conservative and moral character of the dogmatic Image of thought can be demonstrated not only with regard to Kant, but also with regard to other ‘state philosophers’ from Plato to Hegel. Against this background, Deleuze calls for a more radical critique than that of Kant and ‘a new image of thought – or rather, a liberation of thought from those images which imprison it’ (DR xvi–xvii). Philosophy is inseparable from ‘critique’. Only, there are two ways of going about it. On the one hand, you criticize ‘false applications’: false morality, false knowledge, false religions, etc. This is how Kant, for instance, thinks of his famous ‘Critique’: ideal knowledge, true morality, and faith come out perfectly intact. On the other hand, you have this other family of philosophers who subject true morality, true faith, and ideal knowledge to comprehensive criticism, in the pursuit of something else, as a function of a new image of thought. As long as we’re content with criticizing the ‘false’, we’re not bothering anyone (true critique is the criticism of true forms, not false contents. You don’t criticize capitalism or imperialism by denouncing their ‘mistakes’). (DI 138/191)6

A radical critique, according to Deleuze, does not simply affect the false contents of thought, i.e. errors or misguided opinions. The whole ‘form’ of thought has to be overthrown, which certainly implies a very disturbing and unsettling process. Deleuze demands that the philosophical logos has to be replaced by a ‘nomad nomos’ (DR 36/54); the ‘sedentary’ and fixed determinations imposed on thought by representation have to be dissolved in favour of ‘a completely other distribution which must be called nomadic, a nomad nomos, without property, enclosure or measure’ (DR 36/54). However, Deleuze’s nomads are not a people of sceptics. His philosophy is not a scepticism but an attempt for a renewed transcendental philosophy, which he himself named ‘transcendental empiricism’ (DR 144/187, 56/79–80). On the Necessity of Thought Like Kant, Deleuze is interested in the necessity of thought, that is in a thought that imposes itself and leaves no choice for the thinker. This necessity has commonly been called ‘truth’, the paradigm of which has long been mathematics with its method of deduction. 23

conditions of thought: deleuze and transcendental ideas Kant seeks to ground our knowledge of the exterior world on principles that are the result of a completely a priori deduction. To this end, he interiorises the relation between thought and the exterior world and he does so by making the truth of our statements of knowledge formally depend on transcendental subjective principles abstracted from our empirical acts of recognition (cf. DR 135/176–7). However, in this way the necessity of thought eludes us, because we have done nothing but closed thought upon itself in a fatal circularity.7 Deleuze will not cease accusing Kant of having traced the so-called transcendental structures from the empirical acts of a psychological consciousness. He particularly points to Kant’s three syntheses of apprehension, reproduction and recognition in the Transcendental Deduction of the pure concepts of the understanding of the first edition of the Critique of Pure Reason. Contrary to Heidegger and Hegel, Deleuze brings the third synthesis of recognition into focus, in which the manifold of intuition is subsumed under the concept of the identity of the object. Kant finds ‘that our thought of the relation of all cognition to its object carries something of necessity with it’, in short our cognitions ‘must have that unity that constitutes the concept of an object’ (CPR A 104–5). For Kant, the identity of the concept of an object as well as the unity of consciousness (the ‘transcendental unity of apperception’) are transcendental requirements. In Deleuze’s view, these transcendental conditions are directly traced from the empirical conditions of the synthesis of recognition: ‘In order to hide this all too obvious ­procedure, Kant suppressed this text in the second edition. Although it is better hidden, the tracing method, with all its “psychologism”, nevertheless subsists’ (DR 135/177). The fatal circularity of this philosophical ‘proof’ consists in Kant’s attempt to ground the ­necessity of thought on transcendental principles, which he had previously abstracted from our empirical objective thought, that is from mere doxa.8 Kant’s transcendental conditions only allow for possible experience, which is always already delineated and prejudged by the a priori concepts of the understanding. In fact, concepts only ever designate possibilities. They lack the claws of absolute necessity – in other words, of an original violence inflicted upon thought; the claws of a strangeness or an enmity which alone would awaken thought from its natural stupor or eternal possibility: there is only involuntary thought, aroused but constrained within thought, and all the more absolutely necessary for being born, illegitimately, of ­fortuitousness in the world. (DR 139/181) 24

The Dogmatic Image of Thought If Deleuze calls his philosophy ‘transcendental empiricism’, then he uses the term transcendental in an entirely modified meaning. The necessity of thought cannot be encountered by closing thought upon itself. Rather, thought must be opened up to the outside world that has to be conceived as a true exterior. The term ‘empiricism’ in Deleuze’s ‘transcendental empiricism’ means restoring exteriority to the world, as well as the concrete diversity and plenitude of the sens­ ible. Whatever forces us to think comes from this outside. It imposes itself upon us and intrudes as involuntary thought. According to Deleuze, our thought is not an innate faculty characterised by ‘categorial spontaneity’. Instead, thought is marked by a passivity or affectivity, which brings it in direct contact with the outside.9 Its principle is thus not autonomy, but rather heteronomy. But what precisely forces us to think? What produces the absolute necessity of an act of thought or a passion to think? Already in his early book on Proust, Deleuze states that it is the encounter with a ‘sign’ that forcibly engenders thought. What forces us to think is the sign. The sign is the object of an encounter, but it is precisely the contingency of the encounter that guarantees the necessity of what leads us to think. The act of thinking does not proceed from a simple natural possibility; on the contrary, it is the only true creation. Creation is the genesis of the act of thinking within thought itself. This genesis implicates something that does violence to thought, which wrests it from its natural stupor and its merely abstract possibilities. (PS 97/189–90)

A sign is material and intensive in nature. In Proust and Signs, Deleuze  distinguishes different types of signs, all of which have a more or less violent effect on the person sensitive to them. The violent impression triggers an involuntary exercise of the faculties of cognition, no longer bound by the laws of common sense. Deleuze develops this theory of signs in Difference and Repetition, in particular by elaborating its link to Kantian Ideas. Deleuze defines sensible signs as the bearers of Ideas or problems (DR 140/182). In his appropriation of Kant, Ideas or problems become the transcendental, genetic conditions of thought, which carry our faculties of cognition to their ‘nth power’ or ‘transcendent exercise’. ‘Transcendence’ in this case does not indicate a passage to a transcendent world, to metaphysics, but a confrontation with the limit, an opening to the outside world and an immediate relation with exterior forces. The ‘exteriority of thought’ is distinguished from the form of interiority of thought, 25

conditions of thought: deleuze and transcendental ideas which closes thought upon itself.10 Deleuze aims to substitute for the Kantian transcendental conditions of knowledge qua representation transcendental, genetic conditions of the emergence of thought and the production of the real (DR 154/200, 170/221).11 An Alternative Image of Thought? It is important to note that the term ‘image of thought’ does not necessarily connote something noxious or detrimental to thought. It first of all means that philosophy always relates to some kind of pre-philosophical or non-philosophical presuppositions. In his book Nietzsche and Philosophy, Deleuze spells out that thinking always depends on forces that take hold on thought. The theory of thought depends on a typology of forces. And once again a typology begins with a topology. Thinking depends on certain coordinates. We have the truths that we deserve depending on the place we are carrying our existence to, the hour we watch over and the element that we frequent. [. . .] Every truth is truth of an element, of a time and a place. (NP 110/125, translation modified, D. V.)

This means that we have to take the lives of thinkers into consideration, or rather – in order to get rid of ‘personalist’ references (NP xi) – the socio-historical milieu, the composition of forces, in which thought is born. We have to ask: ‘Who speaks?’ ‘Where?’ ‘When?’ ‘How?’ ‘In which case?’ ‘From what point of view?’ Traditionally, the legitimate philosophical question has been Plato’s question: ‘What is . . .?’ (ti estin?), which asks for the essence of things, that is for what is valid at all times and places, for instance ‘What is justice?’ ‘What is courage?’ ‘What is beauty?’ Deleuze suggests other forms of question which relate thought to the psychosocial and historical conditions taking hold of the thinker hic et nunc. A thought that pretends to ascend to the Idea or essence of things by following the ‘What is?’ question in dialogue with others and submitting only to the requirements of reason, presupposes precisely a dogmatic Image of thought. According to this Image, thought has a natural affinity to truth. One assumes that thought either possesses truth in terms of innate Ideas or formally contains truth in terms of a priori concepts and Ideas of reason that serve as guiding rules. One believes that if thought is based on a method and regulated by self-imposed rules of reason, it cannot go wrong. It is of a good and upright nature. Any deception that can befall man is due to 26

The Dogmatic Image of Thought forces external to reason; they come from outside, for instance from the body, the senses or our passions, or they result from a poorly educated faculty of judgement. According to the dogmatic Image of thought, all these forces that divert thought from its proper use count as ‘error’. Error is the negative of thought, but since error amounts only to an empirical fact, it can easily be averted. One has only to submit oneself to a methodological discipline, that is to the guidance of reason and understanding. In the case of an earnest commitment to reason and understanding, that is under the condition of the good will of the thinker, thought will naturally follow the path to truth. In his book on Nietzsche and also in his book on Proust, Deleuze opposes this dogmatic Image of thought, which has its roots in the ancient Greek image of the philosopher as the friend or lover of wisdom, with a new image of thought. The general features of this new image can be summarised in several interrelated postulates: (1) The philosopher is not the friend or lover of wisdom, but rather the jealous lover, the lover to be found in Proust’s In Search of Lost Time, who receives the signs emitted by his beloved and who senses the unknown, dark regions in which dwell the effective forces that act upon thought and force him to create (cf. PS 97–8/190). Philosophy means an apprenticeship to signs: ‘One must be endowed for the signs, ready to encounter them, one must open oneself to their violence’ (PS 101/194). (2) There is no natural affinity of thought to truth that could actively be played out by a truthful thinker endowed with a good will. On the contrary, thought is characterised by its capacity for being affected, that is its receptivity to sensible signs or intensive forces that communicate a violence and wrest thought from its natural stupor. (3) The act of thought is not determined by methods which would allow us to follow pre-existent lines of thought – a roadmap of reason. Rather, the genesis of the act of thought occurs as an involuntary adventure, under the conditions of ‘chance’ and ‘constraint’ (PS 16/23). The thinker has to undergo a process of formation of thought, a violent training (‘culture’ or ‘paideïa’), which brings the whole unconscious of the thinker into play (NP 108/124). (4) What the thinker needs to extract from the encounter with signs is the problem or Idea that it poses to the thinker. Philosophy thus means an act of creation. (5) Unlike error, which is merely an empirical fact, there are more profound enemies of thought, such as stupidity, clichés, baseness and opinion. These forces arise within thought itself, that is they belong to the transcendental structure of thought as such and are therefore difficult to combat (cf. NP 105/120). (6) 27

conditions of thought: deleuze and transcendental ideas Finally, the philosopher has an essential relation to time: he is a ‘thinker of the future’ attracting forces of the future, forces yet to come (NP xiii). He is always untimely in the sense that he acts against the reactive forces of the present world, which are a hindrance to life and its active plastic force, that is the force of metamorphoses and transformations.12 This implies that the philosopher subject cannot be identified with a substantial, well-constituted and identical subject (the Cartesian Cogito) unaffected by the condition of time. This list of postulates is not supposed to be exhaustive. It is meant to give a first impression of the new image of thought which Deleuze proposes and which points in the direction of a genetic, problematic alternative that calls for apprenticeship. We now need to address an inevitable objection that arises in connection with Deleuze’s claim in Difference and Repetition that he seeks a thought without image. In this book Deleuze explicitly sets himself the task of discovering ‘a thought without Image, even at the cost of the greatest destructions and the greatest demoralisations’ (DR 132/173). He compares this revolution in thought to that already accomplished by non-­ representative art: ‘The theory of thought is like painting: it needs that revolution which took art from representation to abstraction. This is the aim of a theory of thought without image’ (DR 276/354).13 How can we make sense of this paradox? Has Deleuze simply changed his mind between writing the books on Nietzsche and Proust and writing Difference and Repetition? This seems improbable given that in Logic of Sense, Deleuze insists that thought necessarily presupposes a non-philosophical, intuitive ground on which it develops (LS 127/152). Again, roughly twenty years later in What Is Philosophy?, Deleuze comes back to the idea of a relation between thought and a non-philosophical image of thought that is its presupposition. Here Deleuze even considers whether it is not the case that every great philosopher draws up a new image of thought (WP 51/52), or even whether a single philosopher cannot sustain several philosophies or images of thought during his life. Jean-Clet Martin indeed interprets Deleuze to be now claiming that a new image of thought emerges whenever thought encounters a problem and is forced to create concepts and determine a case of solution.14 This confusing proliferation of images of thought in What Is Philosophy? seems to be in outright contradiction to his demand for a thought without image in Difference and Repetition. Are the two claims simply inconsistent with one another? The tension which subsists with regard to Deleuze’s radical 28

The Dogmatic Image of Thought demand for a thought without image is due to the fact that in Difference and Repetition Deleuze first and foremost challenges the particular dogmatic Image of thought. This does not mean, however, that Deleuze renounces every presupposition of thought. On the contrary, even in Difference and Repetition, Deleuze stipulates transcendental conditions of thought, which, as one could argue, already form a new image of thought. Yet, in spite of the demand for a thought without image, Deleuze does not fall prey to an internal contradiction. This is because this new image of thought is precisely an ‘image of a thought without image’, since it compels the philosopher to engender thought always anew, and thus commits him to a ‘philosophical commencement and recommencement’ (DR 167/217). By determining the transcendental as ‘not larger’ than what it conditions, i.e. as not consisting of abstract universal principles but of principles that are ‘plastic’ and changing, Deleuze obliges each philosopher to determine for himself the transcendental conditions of the problem he deals with and to generate concepts in relation to the problem and its conditions. Every treatment of a problem and every act of creation of concepts thus require the erection of a new image of thought, that is a plane of composition, on which the problem and the concepts are laid out. Hence this ‘image of a thought without image’ is an image, which does not simply presuppose itself and the natural exercise of the faculty of thought (cf. DR 139/182), but which forces the philosopher to engender the act of thinking within thought. Therefore, despite a certain tension on a superficial level, we do not find a contradiction between the demand for a thought without image in Difference and Repetition and the frequent appeals to a new image of thought in Deleuze’s other works.15 Rather, Difference and Repetition functions to prepare the way for those later texts in which Deleuze once again directly addresses the question of a new image of thought. This is also why Deleuze can consistently declare in the Preface to the English edition of Difference and Repetition: It is therefore the third chapter [‘The Image of Thought’] which now seems to me the most necessary and the most concrete, and which serves to introduce subsequent books up to and including the research undertaken with Guattari where we invoked a vegetal model of thought: the rhizome in opposition to the tree, a rhizome-thought instead of an ­arborescent thought. (DR xvii)

The rhizome and the tree are two conceptions that Deleuze often uses in order to indicate two very different ways of thinking.16 While 29

conditions of thought: deleuze and transcendental ideas the rhizome grows from the middle and proliferates in an endless number of ways, the tree is rooted in a primary unity, from there drawing lines which go from one point to another – lines which might bifurcate but only according to the principles of a binary logic. While the rhizome operates in accordance with the conjunction ‘and . . . and . . . and’ (et . . . et . . . et), the model of the tree is based on the verb ‘to be’ (être), attempting to implant the logic of representation in being. While the vegetal model of thought or rhizome implies variations of the axes and orientations along which thought develops, the model of the tree subordinates being to an exhaustive set of fixed categories. While the model of the rhizome always constructs decentred, pluralist systems, the model of the tree erects its system around a centre, that is a central unity (even if this unity is synthetic), and builds from there a hierarchy of terms and pre-established relations. The vegetal model of thought or rhizome is a product of the combined forces of Deleuze and Guattari, and in A Thousand Plateaus they not only explicate it but also put it into practice. In effect, the problem of the image of thought has been a major concern of Deleuze throughout his work, including the books he co-authored with Guattari.17 However, the struggle against the particular dogmatic Image of thought is most clearly laid out in Difference and Repetition. It is in the third chapter that Deleuze explains in every detail what is at stake in the assumption of the dogmatic Image. While in Nietzsche and Philosophy, Deleuze summarises the dogmatic Image of thought in three essential theses, in Difference and Repetition he lists eight postulates. In the remaining part of this chapter, we will go through each of these eight postulates in turn, and in so doing deal with some further important issues that could not be covered in this introductory section. Thus we will have before us a comprehensive account of what is at stake in Deleuze’s criticism of the dogmatic Image of thought when we turn to the examination of the precise nature of Deleuze’s notion of the transcendental in subsequent chapters.

The Eight Postulates of the Dogmatic Image of Thought Cogitatio natura universalis The first postulate which Deleuze identifies in his criticism of the dogmatic Image of thought is what he calls Cogitatio natura universalis, that is the assumption of a universally distributed, natural capacity 30

The Dogmatic Image of Thought for thinking, together with a good will on the part of the thinker and an upright nature of thought. It is assumed that in order to start thinking it suffices to exercise one’s natural capacity, which is good in itself, and to be guided by a thirst for knowledge and truth. As such, even the ‘simple man’ can attain higher truths on the premise that he scrutinises the grounds of whatever knowledge he believes he has. Otherwise any knowledge just counts as opinion, that is mere doxa. A very illuminating text in this respect is Descartes’ dialogue The Search After Truth, in which he opposes the character Eudoxos, a simple, uneducated man who dislikes learning from books and rather trusts in his own natural power of thought, to Epistemon, an educated man, who draws all his knowledge from books. Eudoxos practises the method of universal doubt, which Descartes has become famous for. The first step is to discard all prejudices and inherited propositions of knowledge. Thought is to be released from its content,  that is from the mesh of concepts that depend on one another. What needs to be found is one originary concept, from which all other concepts can be derived. For Descartes, this is the Cogito, which consists of the three components ‘I doubt’, ‘I think’ and ‘I am’. Yet, in order to arrive at this ultimate truth, Descartes has to appeal to an intuitive certainty of one’s own existence, that is to a pre-philosophical or non-philosophical experience of one’s empirical and concrete being. Hence he presupposes that everybody knows what it means to think, what it means to say ‘I’ and how it feels to exist. According to Deleuze, ‘everybody knows, no one can deny, is the form of representation and the discourse of the representative’ (DR 130/170). The one endowed with a Cogitatio natura universalis is elevated to being the representative of rational discourse. Outside this discourse of representatives there is no audible or comprehensible speech, only ‘noise’. This implies that the person who denies knowing what everybody knows, who fails to think and talk reasonably in line with rational discourse, and who poses disturbing ­questions challenging the current value/belief system, is not represented in the discourse of representatives. Instead, such a person of ill will is excluded from representation. The discourse of the representatives casts out all of those who do not conform to the way everybody thinks and behaves. However, through the method of exclusion the discourse of the representatives creates its own condition of failure. It creates points of resistance that might trigger revolutionary (‘deterritorialising’) processes. The real danger comes from the excluded who returns to subvert and disorganise the order 31

conditions of thought: deleuze and transcendental ideas of representation. In other words, someone who is not integrated, ‘who neither allows himself to be represented nor wishes to represent anything’ (DR 130/171), carries the potential for a revolutionary struggle, a struggle for liberation: The forces of repression always need a Self that can be assigned, they need determinate individuals on which to exercise their power. When we become the least bit fluid, when we slip away from the assignable Self, when there is no longer any person on whom God can exercise his power or by whom He can be replaced, the police lose it. (DI 138/191)18

Thus, for Deleuze, it is not a particular class of society or an exclusive, revolutionary elite that produce disorganising or ‘deterritorialising’ effects. On the contrary, Deleuze cites the ‘young people today’ that practise ‘many and various forms of non-integration, the different forms of refusal’ who are perhaps the bearer of a revolutionary struggle (DI 138/191).19 In any case, it is the excluded people who manifest best the necessary modesty and ill will, not managing to know what everybody knows and denying what everybody is supposed to recognise. Deleuze believes that the presupposition of a Cogitatio natura universalis is a hindrance not only to philosophy but also to political thought. One might assume that the philosopher is best qualified to resist the presupposition of a Cogitatio natura universalis. Is he not the one who proceeds with the greatest ‘disinterest’, in pursuit of the pure form of knowledge and truth? Is he not the one who refuses to affirm the particular contents of what everybody knows (doxa)? But in fact the philosopher still holds firm to the ‘form of representation or recognition in general’ (DR 131/171): the form of what is generally recognised and represented as universally valid. However, such a thought will only lead to an affirmation of the represented order and values, and exclude the elements which can initiate a radical new beginning. ‘Common Sense’ and ‘Good Sense’ The second postulate can be summarised as the assumption of common sense and good sense. Deleuze uses ‘common sense’ and ‘good sense’ as specific technical terms. By ‘common sense’ he does not simply mean a common human understanding confirming a set of opinions that people have in common and agree upon. Instead, Deleuze uses the term ‘common sense’ (or sensus communis) in the 32

The Dogmatic Image of Thought way Kant defines it in the Critique of the Power of Judgment (CJ §20 and §40). In the Aristotelian tradition ‘common sense’ is defined as an inner mental faculty that recognises in the given manifold of sensory data, supplied by the external senses, the identity of one common object. Kant differs from this tradition in that he does not assume one inner faculty or special ‘sense’ but rather ‘a communal sense, i.e., a faculty for judging that in its reflection takes account (a priori) of everyone’s else’s way of representing in thought’ (CJ 5: 293). This communal sense is the effect of an a priori accord of our cognitive faculties (imagination, understanding and reason), which must be presupposed as the subjective condition for all ‘communicability’. That is to say, this a priori accord of our faculties makes experiential knowledge, the representation of the moral law or the feeling of pleasure universal and communicable in principle. There are at least three different forms of common sense or ‘different proportions’ (CJ 5: 238) of the faculties depending on the interest of reason they serve. These are respectively: the logical common sense which is directed toward the recognition of objects, the moral common sense which aims at the representation of a pure form, i.e. the moral law, and the aesthetic common sense which is ‘the effect of the free play of our cognitive faculties’ (CJ 5: 238). In each case, the specific ‘proportion’ or the relations that pertain between the faculties are of a different kind. For example, in the logical common sense the understanding is the legislating faculty, which provides pure concepts or categories for determining the general form of objectivity. It forces the faculty of imagination to conform its empirical synthesis to the intellectual synthesis of the formal unspecified object in general. Reason, on the other hand, thinks the formal completeness or totality of the pure concepts of the understanding through transcendent Ideas, and posits a focal point or focus imaginarius outside experience, which procures for the use of the pure concepts ‘the greatest unity alongside the greatest extension’ (CPR A 644/B 672). Such is, according to Kant, the relation between our active cognitive faculties in the ‘logical common sense’. Deleuze’s use of the term ‘good sense’ refers back to Descartes who defined it as a capacity for thought, which he considers of all things in the world the most equally distributed.20 Good sense is required in the recognition of one and the same object, which may be seen, touched, remembered, imagined or conceived. In his famous example of the piece of wax, it is the faculty of thought that identifies the same 33

conditions of thought: deleuze and transcendental ideas piece of wax despite all the sensuous alterations it has undergone and all the imagined changes of its shape and magnitude. Now it might seem that ‘common sense’ and ‘good sense’ mean the same thing: a collaboration of faculties with the aim to relate their data to one and the same object. But Deleuze distinguishes them in that ‘common sense’ guarantees the transcendental unity of an unspecified object in general, while ‘good sense’ accounts for the empirical unity of this or that particular determined object. For while common sense is the norm of identity from the point of view of the pure Self and the form of the unspecified object which corresponds to it, good sense is the norm of distribution from the point of view of the empirical selves and the objects qualified as this or that kind of thing (which is why it is considered to be universally distributed). Good sense determines the contribution of the faculties in each case, while common sense contributes the form of the Same. (DR 133–4/175)

Common sense and good sense complement one another: ‘together they constitute the two halves of the doxa’ (DR 134/175), that is the transcendental form and empirical unity of the objects of our experiential propositions. Although it is true that philosophers have always opposed particular doxa, Deleuze insists that they nevertheless always maintained the form of the doxa. They held firm to the concept of identity, that is the formal identity of the subject and the object, and they invoked the idea of harmony that is deployed in the collaboration of the faculties in the model of recognition. That is to say, for the recognition of an object the faculties are supposed to enter into a harmonious relationship, to form harmonious proportions. Deleuze criticises Kant for not having offered in his first two Critiques any explanation for the way in which this harmonious a priori accord of faculties arises. Kant rather introduces ‘common sense’ like ‘a supreme finalist and theological principle’ (KCP 20/35). With respect to the harmony between the two faculties, sensibility and understanding, in an experiential cognition, Kant says he can provide as to their origin ‘no further ground than our divine creator’.21 The Model of Recognition The model of recognition is the third postulate of the dogmatic Image of thought. The role of recognition has already been addressed in the discussion of the previous two postulates, which only testifies 34

The Dogmatic Image of Thought to the interrelatedness of the postulates with one another. Deleuze nevertheless makes the model of recognition a postulate of its own, and highlights two important points of criticism. First, he criticises the modelling of thought upon everyday acts of recognition, as if the destiny of thought were at stake in these acts and as if to recognise were to think (cf. DR 135/176). Philosophers have chosen the most banal and puerile examples for demonstrating the faculty of judgement in our acts of recognition: ‘this is a table’, ‘this is a piece of wax’, ‘Good morning, Theaetetus’. According to Deleuze, Plato’s aporetic dialogue Theaetetus is ‘the first great theory of common sense, of recognition, representation and error as their correlate’ (DR 149/194). From the very first, error is explained by a confusion of the data supplied by the inferior senses. If, for instance, I confusedly map the present object of my sight onto another object of my memory – as in the case of ‘Good morning, Theaetetus’ when it is Theodorus who passes by – I make a faulty judgement. Deleuze also raises a second objection against the model of recognition. It is not only the banality and insignificance of our daily acts of recognition that discredit it as a model of thinking. The model of recognition is not as harmless as it might seem. Recognition reaffirms established values: conventional, social and moral values. In so far as the practical finality of recognition lies in the ‘established values’, then on this model the whole image of thought as Cogitatio natura bears witness to a disturbing complacency. (DR 135/177)

The real danger of the model of recognition lies therefore in its complacency, in its unquestioned support of established values and institutions. Philosophers believed that on the basis of reason and understanding one could establish a model of recognition valid for all times and places, and did not see that even ‘formal’ criteria of recognition evolved in a historical and socio-political context. By maintaining the form of recognition (i.e. the form of knowledge and truth), philosophers have ensured that ‘thought “rediscovers” the State, rediscovers “the Church” and rediscovers all the current values’ (DR 136/177). However, with considerable debt to Nietzsche, Deleuze defends a different and critical conception of philosophy: We require a genesis of reason itself, and also a genesis of the understanding and its categories: what are the forces of reason and of the understanding? What is the will which hides and expresses itself in reason? What stands behind reason, in reason itself? (NP 91/104) 35

conditions of thought: deleuze and transcendental ideas Kant’s immanent critique of reason by reason itself does not satisfy the demands of a radical critique. Kant denounces false claims to knowledge and also a false morality but he leaves the domains of knowledge, morality and religion intact. The higher interests of reason (true knowledge, true morality, true religion) remain sacred. Therefore his critique is not as revolutionary as he maintains. We are told that we are free when we obey the demands of reason, since it is we who are giving the orders. In this way, reason persuades us to continue being docile (NP 92/106). Kant simply installed the priest and legislator within us (NP 93/106) and thus the power of the state and the church remain unchallenged. By contrast, a philosophy understood as a radical critique in the Nietzschean-Deleuzian sense questions the established powers and current values. In effect, ­philosophy should upset the established order: Philosophy does not serve the State or the Church, who have other ­concerns. It serves no established power. The use of philosophy is to sadden. A philosophy that saddens no one, that annoys no one, is not a philosophy. (NP 106/120)

The Postulate of Representation The fourth postulate, the postulate of representation, is a key target in Difference and Repetition. Deleuze retraces the model of representation through the philosophies of Plato, Aristotle, the neo-Platonists, Descartes, Leibniz, Kant and Hegel. In what follows we will focus primarily on Deleuze’s position with respect to Plato and Aristotle. There are two reasons for this priority: Deleuze demonstrates that for Plato the world of representation is essentially a ‘moral vision of the world’ (DR 127/166). Later in history, this moral origin of the world of representation will be more or less forgotten (DR 265/341), but since it is precisely the moral motivation that inspires Deleuze’s critique, his interpretation of Plato is of central importance. However, the Platonic cosmos still lacks the categories of representation, which will be fully deployed only with Aristotle. Aristotle provides the classificatory concepts according to which Being is distributed in determinable forms (genera of Being or categories) and further divided up by fixed determinations (specific differences). The Aristotelian philosophy of categories takes judgement as its operative tool. Judgement fulfils both requirements of representation: ‘distribution which it ensures by the partition of concepts; and hierarchisation, 36

The Dogmatic Image of Thought which it ensures by the measuring of subjects’ (DR 33/50). That is, the order of representation privileges those subjects which it considers endowed with a ‘good sense’ and thus better capable of exercising judgement than others. (For instance, in the days of Aristotle, these were free adult men, aristocrats and citizens of the Greek ‘polis’.) The logic of representation and the function of judgement are both complicit in the dogmatic Image of thought. Let us begin with Deleuze’s discussion of Plato. The Platonic theory of Ideas introduces a distinction between the model and the copy, between the Idea and the proper representations of the Idea. The Idea is defined as being identical with itself. That is to say, the form of the Same applies to Ideas and to Ideas only, because the Idea of justice is nothing other than just, the Idea of courage nothing other than courageous, and so on. The copies, on the other hand, are those instances which claim to participate in the Idea, that is which claim to have acquired the quality of being just, or being courageous, and so on. According to Deleuze, the problem at the heart of Plato’s phil­ osophy is to find a method for distinguishing the true claimants from the false pretenders. Plato’s method of division is therefore a method of selection.22 The selected claimants or proper representations are those which bear an internal resemblance to the Ideas, i.e. the ultimate things in themselves or models. This means that the true copies are in the essential respects the same as the model. Their difference is only secondary, or in other words: it is a mere ‘conceptual difference’, a difference that remains subordinated to the prior concepts of identity, resemblance and similitude. Apart from the true copies or proper representations there are also those which fail the test of the copy and the requirements of the model. These are the false pretenders or simulacra, which only simulate participation in the quality of the Idea. They produce an external effect of resemblance (DR 128/167) but in fact they are based on dissimilitude, perversion and disparateness. Their element is ‘free, internal differences’ which are not subject to the structure of representation. That is to say, in the world of simulacra, the Same and the Similar do not pre-exist; the concept of difference is not inscribed in a prior concept of identity. Plato realises that simulacra pose a real threat to the logic of representation. That is to say, simulacra are not just degraded copies, that is copies of copies. Instead, they possess a positive power (LS 262/302) to subvert and overturn the very idea of a model and its privileged position in relation to the copy. This is why Plato introduces a qualitative distinction between the good copies and the bad 37

conditions of thought: deleuze and transcendental ideas simulacra and seeks to banish or exorcise the latter.23 As Deleuze concludes: ‘the will to eliminate simulacra or phantasms has no motivation apart from the moral’ (DR 265/341). The ‘representative theology’ (DR 265/341) tolerates no one who threatens the affirmed hierarchies of the model and the copy, the original Idea and the derived representation, the ground and the grounded. In sum, the order of representation is characterised by the determination of hierarchies, fixed distributions and the exclusion of simulacra, that is the subordination of difference to the Identical, the Same or the Similar. According to Deleuze, philosophy or the theory of thought needs a revolution, which will lead to the abandonment of representation. In fact, modern works of art have already completed that revolution which took the tradition of realist or representational art to abstraction. ‘Aesthetic modernity provides Deleuze with one example of a world in which difference has free reign. He suggests that modernity is defined by the power of the simulacrum.’24 In overturning Platonism, that is in liberating simulacra from the Platonic order of representation, the imposed hierarchy of the original and the copy, the true and the false, or the good and the bad, Deleuze sees an escape for the theory of thought. But while there is still an escape route in Plato, in Aristotle the order of representation is deployed much more rigorously. With Aristotle, the logic of representation gains a new methodological approach and new conceptual tools. Aristotle rejects Plato’s dialectic method of division, which operates by selection among rivals, by testing and authenticating the claims of participation in Ideas. The method of division is a bad and illegitimate syllogism according to Aristotle, since it lacks the required middle term (DR 59/83; LS 254/293). That is to say, for determining the relation between the determinable (Idea or concept in general) and determined objects (individual claimants), some mediation is needed. In Aristotle, determination proceeds through the mediating concept of species. Aristotle’s method is one of continuous specification from the highest genera down to the lowest, indivisible infimae species. Deleuze’s critique of the logic of representation applies to Aristotle much more than to Plato. According to Deleuze, the logic of representation does not allow for an absolute concept of difference, of difference in itself. In the Platonic cosmos, there remains at least the displaced realm of simulacra, where we find no prior identity, no internal resemblance, where difference has become the ultimate 38

The Dogmatic Image of Thought element in which the identity of any concept in general is dissolved. In Aristotle by contrast the conception of difference is only relative, which is to say that difference always operates in relation to the supposed identity of a concept. This can best be seen by the example of ‘specific differences’: species are said to differ only within the identity of the genus. Given the genus ‘animal’, for instance, we can distinguish ‘terrestrial animal’ and ‘aquatic animal’.25 These are specific differences in the form of contraries (not contradictions, since these two determinations do not necessarily include a logical contradiction but they nevertheless divide the genus into different species through their real opposition).26 Specific differences are predicates, though predicates of a peculiar kind: the specific difference is attributed to the species thereby constituting it, and at the same time specific difference preserves that which it differentiates (DR 31/47).27 This means that the specific difference is inscribed within the identity of a generic concept, in this case the genus ‘animal’. For Aristotle, specific difference is maximal (megiste¯) and perfect (teleios). It is of all kinds of differences the best example. Generic difference, on the one hand, is too large, as it holds between categories that have nothing in common; difference between individual substances or little species, on the other hand, is too small, since the smallest indivisible objects or little species (atomon, adiaphoron or eidos) do not enter into relationships of contrariety. Their determination proceeds not so much by the opposition of predicates (contraries) but by the perception of resemblances, which presupposes continuity of sensible intuition in the world of representation. At first sight it seems that generic differences, which hold between categories, can be assimilated to specific differences because they are also said in relation to a unique term. However, this unique term is not a genus, that is a collective, explicit and distinct unity. The categories are related to Being, which is a confused unity, since it has no distinguishing marks, no content of its own. Rather than being divided, Being is distributed to the terms – that is the genera, the differentia of a genus, the sub-genera, the specific differences, the species, the individual differences and the individual substances – which is to say that Being is said of all of these terms but in different senses. In fact, there is a hierarchy of senses, since some things (substances) possess being in a primary sense, while other things (non-substances) only possess it in a secondary sense. Being is thus said in many ways, what Aristotle calls a pros hen equivocity. The Greek term pros hen, which literally means ‘in relation to’, expresses 39

conditions of thought: deleuze and transcendental ideas the fact that, although there are various senses of Being, they are all related to a single central sense. Aristotle maintains a ‘quasiidentity’ of Being by judging Being in analogy with the identity of a genus. Yet Aristotle explicitly states that Being is not a genus. When ­reconstructed, the argument goes as follows: 1. If something is a genus, then it cannot attribute itself to its specific differences [Aristotle, Topics, VI, 6, 144a].28 2. Being can be said of its differentia (because we can say that generic or categorial differences are, just as we can say that specific ­differences are). 3. Being is not a genus. This argument, however, implicitly presupposes that the generic or categorial differences of Being are similar to specific differences, which ultimately allows Aristotle to conclude that Being is not a genus. According to Deleuze, Aristotle borrows an argument from the nature of specific difference in order to conclude that ‘generic differences are of another nature’ (DR 32/49). However, one should note that Aristotle does not actually conclude that generic differences are of an utterly different nature than specific differences. It is rather Deleuze who wants to argue for the different nature of generic differences. What argument does he put forward to support his claim? Obviously, he cannot argue that (1) if Being were a genus, its differences would be assimilable to specific differences (DR 34/51), (2) Being is not a genus; therefore generic differences are not assimilable to specific differences. Deleuze seems to suggest this line of argument (cf. DR 34/51), but in any case, this argument would be invalid (p→q, ¬p, therefore ¬q). Thus Deleuze has to find other means to argue for the different nature of generic and specific differences. He makes the following distinction: 1. The pros hen relation of the categories to Being is a relation of interiority: ‘it is on its own account that each [category] has unity and being, by virtue of its own nature’ (DR 309/50, note 5/1; see also DR 33/49). 2. A genus is determinable only by specific differences from without (DR 34/51; italics are mine, D. V.). From (1) and (2) it follows that the relation of generic differences to Being differs from the relation of specific differences to a genus. Deleuze’s intentions are clear. He wants to show that, in Aristotle, there are 40

The Dogmatic Image of Thought two ‘Logoi’, differing in nature but intermingled with one another: the logos of Species, [. . .] which rests upon the condition of the identity or univocity of concepts in general taken as genera; and the logos of Genera, [. . .] which is free of that condition and operates both in the equivocity of Being and in the diversity of the most general concepts. (DR 32–3/49)

Given these two Logoi, Deleuze wonders whether we must not recognise here ‘a kind of fracture introduced into thought, one which will not cease to widen in another atmosphere (non-Aristotelian)’ (DR 33/49). In order to maintain the coherence of his philosophy of representation, Aristotle bases it on relations of analogy: the model of representation requires that the identity of the concept of Being, although it is only a confused and distributive unity, is analogous to the identity of the genus. Deleuze concedes that Aristotle himself did not speak of analogy with respect to Being (DR 308/50, note 5/1), but Deleuze finds support for his claim in the scholastics, who translated the Aristotelian pros hen as ‘analogy of proportionality’ (DR 309/50, note 5/1). With the example of Aristotle, Deleuze attempts to show that neither specific difference nor generic difference delivers an absolute concept of difference. Instead difference is fully subjected to the requirements of representation: it is subordinated to identity, in the form of the undetermined concept [Being]; analogy, in the relation between ultimate determinable concepts [genera or categories]; opposition, in the relation between determinations within concepts [specific differences as contrary predicates]; resemblance, in the determined object [individual substance] of the concept itself. (DR 29/44–5)

Deleuze calls the quartet of identity, analogy, opposition and resemblance ‘the necessarily quadripartite character of representation’ (DR 34–5/52), whereby representation is specified here as ‘organic ­representation’. By ‘organic representation’ Deleuze refers to a world of representation, in which Being is distributed and divided up according to fixed and proportional determinations. Deleuze compares this world to a ‘sedentary space’ (DR 36/54) with limited territories and defined properties. These sedentary structures of representation correspond to our faculty of judgement and its concomitants of common sense and good sense. Another fundamental feature of Aristotle’s philosophy of representation is the privilege he gives to specific difference. Difference operates mainly in the middle 41

conditions of thought: deleuze and transcendental ideas regions of genus and species, that is equidistant from the boundaries of the large and the small (DR 38/56). It measures and divides up the average forms (DR 42/61), while excluding the extreme. Differences which are too large (generic differences) are made analogous with specific differences (despite their different nature), while differences which are too small (individual differences) are neglected as differences without a concept. ‘Organic representation’ is characterised by keeping difference within the limits of the large and the small, and by inscribing it within concepts in general. However, Deleuze identifies a second type of representation, which he calls ‘orgiastic’ or ‘infinite representation’ (cf. DR 42/61). With Leibniz on the one hand and Hegel on the other, representation is rendered infinite: difference is drawn into an infinite movement to the moment at which difference either vanishes (Leibniz) or reaches its absolute maximum in contradiction (Hegel). The two limits of organic representation, i.e. the small and the large, are pushed towards the infinite, the infinitely small or the infinitely large. The introduction of the infinite into representation, Deleuze explains, renders the determined object independent of the genus as the ultimate determinable concept and of the species as the determination within the concept, by relating it instead to a ground (DR 43/62–3). This ground is completely indeterminate: differences remain unidentifiable and the distinction of forms is dissolved. The ground in ‘orgiastic representation’ equals ‘a completely undifferenciated abyss, a universal lack of difference, an indifferent black nothingness’ (DR 276/354). In the case of Leibniz, the ground is the infinite continuity of the universe, which is itself contained in finite particular Selves considered as essences (monads). In the case of Hegel, particular Selves are only determinations of a pure Self, that is a ‘Self’ enveloped by the infinite self-movement of a universal ground. In both cases, however, the determined is referred to an infinite and indeterminate ground, which must be said to engender finite determinations or to make difference. This means, though, that the concept of difference has not become absolute, but on the contrary is included in this infinite and indeterminate ground. The logic of infinite representation depends on a sufficient reason or a foundation. While this foundation is not the identical itself, it is nevertheless a way of taking the principle of identity particularly seriously, giving it an infinite value and rendering it coextensive with the whole, and in this manner allowing it to reign over existence itself. (DR 49/70) 42

The Dogmatic Image of Thought The point is that in the last resort infinite representation does not free itself from the principle of identity as a presupposition of representation. (DR 49/70)

Deleuze rejects both types of representation, since both finite and infinite representation (organic and orgiastic representation) suffer from the same defect, that of subordinating difference to identity (whether this is the identity of a common genus or the identity of an infinite and founding principle). The Concept of Error The fifth postulate of the dogmatic Image of thought is the postulate of the negative, or of error. As we have seen, the dogmatic Image supposes that thought is naturally oriented towards truth. It further subjects thought to common sense and good sense, as well as to the model of recognition and the requirements of representation. Is there anything that can divert thought from its proper path? There is of course the possibility of error, for instance a false act of recognition, which results from a failure of good sense. That is to say, in the determination of a particular object the collaboration of our inferior faculties might be confused, insofar as they erroneously relate something perceived and something remembered to one and the same object, although the contents should have been distributed to different objects. However, in this case the form of the common sense still remains integral and intact (DR 149/193). The error amounts to a simple fact that can easily be corrected. Errors that we commit due to a failure of good sense, absent-mindedness or a poorly educated faculty of judgement cannot endanger the in-principle good nature of thought. Philosophers have been aware that there are more serious threats besides error. Plato’s notion of ignorance or forgetting, the Stoic notion of stultitia (a hybrid of stupidity and madness), Spinoza’s notion of superstition, Kantian transcendental illusion or Schopenhauer’s notion of vulgarity – all these concepts testify to other dangers: amnesia, delirium, stupidity, madness, malevolence or baseness. Yet these dangers have mostly been treated as external forces, threatening thought from outside. The effect of these forces on thought is still regarded as error. ‘Error is the infinite movement that gathers together the whole of the negative’ (WP 52/53). Only Kant realised that the real threat for thought comes from within, from pure reason itself. Transcendental illusion arises if reason is left 43

conditions of thought: deleuze and transcendental ideas ‘in the state of nature’ (CPR A 751/B 779): then reason makes assertions which go beyond the conditions of all possible experience and claims their objective truth. However, the in-principle good nature of reason is not called into question. Kant even goes as far as putting the blame entirely on the faculty of judgement, such as to underline the good nature of our faculty of thought.29 Contrary to the view that thought possesses a good nature and an affinity to truth, Deleuze argues that none such presupposition can be made in principle. Moreover, even a discourse, which is entirely made up of truths, can be a symptom of stupidity and a base way of thinking. Stupidity is not error or a tissue of errors. There are imbecile thoughts, imbecile discourses, that are made up entirely of truths; but these truths are base, they are those of a base, heavy and leaden soul. (NP 105/120)

Thus stupidity and baseness express themselves even in true discourse.  But what precisely does Deleuze mean by base truths? A base truth is nothing but a plain and exact recognition, a proposition that is  detached from its context of living thought and from the problem it is supposed to answer. For instance, in his book on Hume, Empiricism and Subjectivity, Deleuze criticises the discourse that accuses Hume of a psychological atomism of perception: ‘ “Hume has pulverized the given.” But what does one think has been explained by this? Does one believe something important has been said?’ (ES 105–6/118–19). A proposition only makes sense if it is related to a problem or set of problems that haunted the philosopher. The highest art of thought is to pose problems and to develop these problems all the way down, to the very end, of their necessary implications (cf. ES 106/119). It is at this point that a ‘base way of thinking’ is separated from a ‘noble way of thinking’, that we can distinguish stupid and irrelevant remarks from the critical and creative activity of posing problems. However, even the posing of problems can be threatened by stupidity, namely in the case of badly posed or inexistent problems.30 Teachers already know that errors or falsehoods are rarely found in homework (except in those exercises where a fixed result must be produced, or propositions must be translated one by one). Rather, what is more frequently found – and worse – are nonsensical sentences, remarks without interest or importance, banalities mistaken for profundities, ordinary ‘points’ confused with singular points, badly posed or distorted problems – all heavy with dangers, yet the fate of us all. (DR 153/198) 44

The Dogmatic Image of Thought According to Deleuze, stupidity and baseness are far more devastating than error can ever be. The danger that pervades thought from inside is not error or falsehood, but stupidity. Stupid thoughts affect us all; they are ‘structures of thought as such’ (DR 151/196). They are not simply external forces that act on thought accidently, such as traits of character or an imbecile culture of society. Stupidity and baseness belong to thought by right. This means that the relation of thought and stupidity poses a ‘transcendental problem’ (DR 151/196). The important question is: what is the transcendental significance of stupidity? Deleuze claims that stupidity is not only ‘the greatest weakness of thought, but also the source of its highest power in that which forces it to think’ (DR 275/353). The reason for this is that he sees stupidity and its allies first and foremost as forces. Force is not understood as a blind and brutal drive which seeks to destroy and dominate. Forces are rather impersonal flows of energies or intensities, and their effects totally depend on the way they are compounded within a particular field. As such they can either inhibit and prevent critical thought or, on the contrary, increase the critical power. Take for instance Deleuze’s example of the two types of idiots in philosophy and literature: On the one hand, there is Descartes’ idiot (Eudoxos) who doubts particular opinions and prejudices but maintains the form of rational discourse; on the other hand, there is Dostoyevsky’s idiot, who tentatively calls the form of rational discourse itself into question. This new Russian idiot rejects the ‘truths of reason’ or the ‘truths of history’ and exercises a ‘critical aggressivity’.31 The old idiot wanted indubitable truths at which he could arrive by himself: in the meantime he would doubt everything, even that 3 1 2 5 5; he would doubt every truth of Nature. The new idiot has no wish for indubitable truths; he will never be ‘resigned’ to the fact that 3 1 2 5 5 and wills the absurd – this is not the same image of thought. The old idiot wanted truth, but the new idiot wants to turn the absurd into the highest power of thought – in other words, to create. The old idiot wanted to be accountable only to reason, but the new idiot, closer to Job than to Socrates, wants account to be taken of ‘every victim of History’ – these are not the same concepts. The new idiot will never accept the truths of History. The old idiot wanted, by himself, to account for what was or was not comprehensible, what was or was not rational, what was lost or saved; but the new idiot wants the lost, the incomprehensible, and the absurd to be restored to him. This is most certainly not the same persona; a mutation has taken place. And yet a slender thread links the two idiots, 45

conditions of thought: deleuze and transcendental ideas as if the first had to lose reason so that the second rediscovers what the other, in winning it, had lost in advance: Descartes goes mad in Russia? (WP 62–3/61)

In this quotation on the old and the new idiot (Descartes’ idiot and Dostoyevsky’s idiot), Deleuze distinguishes two different conceptual personae (personnages conceptuels), two different images of thought and two divergent series of concepts. A conceptual persona, for Deleuze, is the subject of enunciation of a philosophy; it is the one who speaks and invents concepts once the philosopher-subject ceased to say ‘I’ and turned into his conceptual persona. This is not to say that the conceptual persona functioned as a representative of the philosopher. On the contrary, the philosopher literally becomes his conceptual persona(e). Thus is the case with Nietzsche who at the end of his life even signed his letters with ‘Dionysus’ or ‘the Crucified’. But Deleuze cites many more examples of conceptual personae such as Plato’s Socrates, Kant’s figure of the judge or, precisely, Descartes’ idiot.32 Descartes’ idiot (Eudoxos) is the ‘private thinker’, in opposition to the public teacher or learned man (Epistemon) who operates with scholastic definitions and established truths. The private thinker rejects all knowledge that is passed on to him, pretending to know nothing, and strives to think for himself by means of strict methods procured by reason. It is the private thinker, i.e. Descartes’ idiot, who launches the Cogito as a first principle. However, the Cartesian Cogito does not yet think: ‘it only has the possibility of thinking, and remains stupid at the heart of that possibility’ (DR 276/354). What it lacks is the necessity of thought, the contact with the exterior, since it is closed upon itself in an indefinite regress: I think that I think that I think . . .33 As Deleuze says, ‘thought remains stupid so long as nothing forces it to think’ (DR 275/353). Dostoyevsky’s idiot is a new type of private thinker, though ‘private thinker’ ‘is not a satisfactory expression, because it exaggerates interiority, when it is a question of outside thought’.34 This new idiot rejects ‘method’ and the Cogitatio natura universalis; he constantly produces ‘counterthoughts’ (contre-pensées) questioning the importance of abstract, rational truths and the reign of so-called ‘truths of history’ interpreted by the power of an established order.35 The new idiot ‘wants the absurd, the lost and the incomprehensible to be restored to him’ (WP 63/61) – is this not the quest for a world of simulacra liberated from a world of representation? 46

The Dogmatic Image of Thought It seems that the new idiot indeed relates to another image of thought, which differs from the dogmatic Image. The ‘slender thread’ (WP 63/61), which links the old and the new idiot, is the programme of a ‘private thinker’ launching himself into critical thought. But the critical thought of Descartes’ idiot remains captured in the dogmatic Image, whereas Dostoyevsky’s idiot is pushed to a more radical critique, turning ‘the absurd into the highest power of thought’ (WP 62/61) and thereby creating new values. Coming back to the question of the transcendental nature of stupidity, we see now that stupidity can be taken in two senses. On the one hand, it amounts to the greatest weakness of thought when it entangles us in a ‘perpetual confusion with regard to the important and the unimportant, the ordinary and the singular’ (DR 190/245). We take banalities, simple acts of recognition and opinions for truths, and are incapable of evaluating the truths and values that are proclaimed by the powers of an established order. On the other hand, stupidity as the highest power of thought is the refusal of knowing what everybody knows. In this sense it becomes a transcendental condition for critical thought. The conceptual persona of the idiot is a thinker, who has no wish to know what everybody knows, who struggles against opinion (doxa) (Descartes’ idiot) and even against the rational form of discourse (Dostoyevsky’s idiot). With Dostoyevsky’s idiot, madness or delirium becomes a critical force, which precisely turns against stupidity in the first sense, i.e. the reign of base truths and petty values. Perhaps one could say that stupidity in the first sense also has a transcendental significance, inasmuch as it incites critical thought: Is it not also the existence of stupidity which forces it to think, precisely the fact that it does not think so long as nothing forces it to do so? Recall Heidegger’s statement: ‘What gives us most cause for thought is the fact that we do not yet think.’ (DR 275/353)36

Stupidity or Heidegger’s ‘idle chatter’, the thoughts of what ‘they’ (man) think provoke the acts of the philosophical idiot, i.e. of critical thought. The Postulate of Designation With the sixth postulate, the postulate of designation, Deleuze challenges both the traditional conceptions of sense and truth and 47

conditions of thought: deleuze and transcendental ideas the relation that has been identified between them. In the light of Frege’s account of sense and truth, it becomes apparent how we commonly distinguish sense and truth as two separate dimensions of the proposition where sense subsists only in a formal relation to the other. By contrast, Kant’s account of sense works quite differently insofar as sense becomes the superior transcendental condition of possibility of truth. However, Deleuze argues that both accounts define sense as merely the form of possibility of truth and as such sense remains an extrinsic condition, not capable of founding truth in terms of an intrinsic genesis. Deleuze demands a new conception of sense which is distinct from that of Frege and Kant. According to Deleuze, sense has to be conceived as both the effect and the intrinsic genetic element of an extra-propositional, differential structure (the problem). His point of view has affinities with the structuralist tradition but it is certainly not the same. Let us first begin with Frege’s account of sense and truth. In his famous essay ‘On Sense and Reference’ (1892), Gottlob Frege introduces the following phraseology: ‘A proper name (word, sign, sign combination, expression) expresses its sense, stands for or designates its reference.’37 He goes on to examine what the sense of a sign and what its reference is. According to him, the reference of a sign is the definite object that the sign designates, while the sense of a sign contains the ‘mode of presentation’ of the object. There can be different modes of presentation for the same object. As such there are also different signs for the same object, that is signs with different senses but with the same reference. Frege’s most famous example is that of the ‘morning star’ and the ‘evening star’, which are two signs with different senses yet referring to the same planet Venus. Now, Frege treats propositions in a similar way. Propositions have two dimensions, the dimension of expression and the dimension of designation or reference. The sense that a proposition expresses is the thought contained in the proposition. ‘Thought’ is understood as the ‘objective content, which is capable of being the common property of several thinkers’, no matter what language they speak and regardless of the desires and beliefs they individually connect with this thought.38 The reference of a proposition is generally determined by inquiring after the reference of its components. Considering cases in which components of the proposition have no reference, Frege discovers that the lack of reference of a part of the proposition has no bearing upon the sense of the whole proposition but it leaves the question of its reference in abeyance. He cites the 48

The Dogmatic Image of Thought example: ‘Odysseus was set ashore at Ithaca while sound asleep.’39 Poetry or fiction provides plenty of these examples, that is propositions that contain proper names without a reference. However, as Frege states, it is only in works of art that we are satisfied with the dimension of sense and do not seek to advance to the question of reference, but in other cases we press on: ‘It is the striving for truth that drives us always to advance from the sense to the reference.’40 The dimension of reference is the locus where the question of the truth and falsity of a proposition, that is its truth-value, is decided. This is why Frege says that the reference of a proposition, if it has one, ‘is either the True or the False’.41 Given this linkage between the truth-value and the reference of a proposition, there results a strangely detached relation between sense and the question of truth and falsity. As Frege remarks: The truth-value of a sentence ‘must remain unchanged when a part of the sentence is replaced by an expression having the same reference’.42 That is to say, although the sense of a proposition might be altered by the substitution of one expression by another, the truth-value of the whole proposition remains the same, provided that the substituted expression has the same reference as the one it replaces. In other words, truth and falsity remain to some extent unaffected by sense. On the other hand a proposition with no sense cannot be true and in this respect the requirement of sense is a necessary condition for a proposition to be true. Sense is a ‘condition of truth’ insofar as it contains a number of logical conditions, which define a grammatically well-formed expression. But sense is by no means a sufficient ground for truth: there are propositions, which make perfect sense from the point of view of their form of expression, but that are nonetheless false. An example would be the proposition ‘A decahedron is a regular geometrical figure.’ It is impossible to find a referent for the whole proposition (decahedrons are non-regular), but still the proposition contains a thought that makes sense and could mistakenly be regarded as true. Thus, in grasping the sense of a proposition, one cannot be assured of its truth-value. The question of truth and falsity is decided only with regard to the dimension of reference, ­independently from the dimension of sense. Deleuze’s objection to these conceptions of sense and truth and their relation with one another is twofold: having discovered sense as the condition of truth, the relation of the condition to the conditioned is on the one hand too loose and on the other hand too intimate. Let us unfold Deleuze’s position step by step. 49

conditions of thought: deleuze and transcendental ideas The relation between the condition and the conditioned is too loose because both terms of the relation remain more or less independent from one another. While sense is indifferent to what it conditions, the conditioned itself, that is truth, remains unaffected by the condition, which is supposed to render it possible. Sense is only the formal condition of possibility of truth (LS 18/29). That is to say, it can only determine the logical conditions under which a proposition would be true. It cannot exclude the case of false propositions that make sense. As Deleuze says: sense retains ‘an extension larger than that which is conditioned, sense does not ground truth without also allowing the possibility of error’ (DR 153/199). Thus Frege’s conception of sense cannot materially account for the truth-value of a proposition. In order to determine the truth-value of a proposition, we have to turn to the dimension of reference. There is in fact no way to pass from sense to reference, i.e. the truth-value. One can certainly deduce from one proposition further propositions by means of grammatical transformation rules or semantic implications of concepts, distributed within the original proposition. For instance, given the proposition that a person X is a widower, we can conclude from this that X is a man, that X was married, and that the wife of X has died. However, in inferring these further propositions we remain on the same level, the level of signification, and never cross over to the level of denotation or truth. In effect, ‘signification can never exercise its role of last foundation, since it presupposes an irreducible denotation’ (LS 18/29). Hence, although sense is discovered as a condition of truth, it amounts only to a formal condition of possibility for a proposition to be true. The second part of Deleuze’s objection actually follows from the first. In making sense the condition of truth, an essential step was made to establish a ground for a ‘critique’ of truth. However, the critical project is doomed to fail not only because the ground remains larger than the grounded (first objection), but also because  the ground is thought in the image of the grounded.43 The condition resembles the conditioned from the point of view of its logical form. That is to say, the conditioned or those propositions that we hold to be true (for example, scientific propositions describing objective states of affairs) already display the logical form of identity of the concept as well as logical forms of the relations of concepts with one another. We then extract the logical forms of the propositional facts and stipulate them as the formal conditions of possibility for a proposition being true in relation to an objective state of affairs. This 50

The Dogmatic Image of Thought strategy becomes even more apparent in the case of Kant, which we will now turn to. As is well known, Kant draws the ‘clue to the discovery of all pure concepts of the understanding’ (CPR A 76/B 102) from the Aristotelian table of logical forms of judgement. He recognises the importance of the logical forms as the formal condition of possibility for a proposition to be true. Thus Kant claims that ‘the formal aspect of all truth consists in agreement with the laws of the understanding’ (CPR A 294/B 350). This is to say that certain laws of the understanding, for example the principle of non-contradiction, must hold for all cognitions posed in propositional form. In this way, general logic provides a necessary formal criterion of truth.44 However, Kant goes much further than general logic can ever go. He explains that general logic only considers the logical form of our cognitions and their relation with one another, hence it abstracts from all content, that is from any relation of our cognitions to the object (CPR A 55/B 79). Transcendental logic, by contrast, has to do with pure concepts of the understanding insofar as they are related a priori to objects. Therefore transcendental logic provides a further criterion of truth: namely the requirement that pure concepts can be constructed in the formal intuition of space and time and thus be related to an object; for without the relation to a possible object of experience, a cognition will completely lose its content and hence all truth.45 This means, for example, that from the point of view of transcendental logic the proposition ‘A decahedron is a regular geometrical figure’ cannot be said to be false, but rather it makes no sense. Since it is impossible to construct a regular decahedron in space, the proposition cannot be related to a possible object of experience, hence it has no content, that is no sense. While the proposition can be said to have a sense from the point of view of general logic, transcendental logic dispels this proposition altogether. The same happens with a proposition like the following: ‘The width of Navidson’s house inside exceeds the width of the house as measured from the outside by a quarter of an inch.’46 From the point of view of formal logic, there is nothing wrong with this proposition. However, we are dealing with a transcendental impossibility: a house the interior of which is greater than its exterior is an impossible object. Not only can it not be constructed in space, it also contradicts the a priori condition of community. The category of community provides that the coordinated parts in an aggregate determine each other reciprocally. In the case of the house, in which the inside exceeds the outside, there is no reciprocal 51

conditions of thought: deleuze and transcendental ideas determination of parts. Thus the proposition cannot be related to a possible object of experience and therefore has no content, no sense. The same kind of transcendental impossibility applies in cases where something appears without any preceding cause, for instance the sudden apparition of an angel. Such a thing would also be no possible object of experience. Hence in the Kantian transcendental logic nothing escapes the transcendental conditions of sense. Anything that falls outside the transcendental scheme or structure, that is that which cannot be constructed in space and time, and ordered according to a priori conceptual rules, is not a possible object for us. To put it positively: whatever proposition we hold to be true, the referent of this proposition has to satisfy the transcendental conditions of sense. In this way, sense is made a superior condition of truth. Indeed, one could say that Kant’s transcendental philosophy is a logic of sense: he stipulates the transcendental conditions for something to have a sense, that is to be an object for us. Kant’s invention of transcendental logic has a revolutionary effect: truth is no longer simply a matter of adequation with an external state of affairs, as it is suggested from the point of view of an empirical consciousness. To put it differently, the Kantian invention of the transcendental contradicts the simple assumption that the locus of truth for a proposition is the dimension of designation or reference. The idea that (1) a proposition is true, if and only if what is said or expressed applies to the designated object or state of affairs it refers to, and that (2) a successful reference makes a proposition true, while an unsuccessful reference makes a proposition false, grounds a conception of truth which presupposes the existence of a reality exterior to sense. Kant’s revolutionary move is to make truth dependent on sense, which is to say that a true cognition necessarily points beyond itself to an object or state of affairs that can no longer be posited in reality exterior to sense. However, for rendering sense a superior condition of truth, Kant has to pay a high price: namely that of interiorising the relation between cognitions and the manner in which they relate to objects or states of affairs. This means that for Kant the outside world is not truly exterior: it remains relative to the a priori conditions of the transcendental subject. Before we even become aware of an objective reality, thought has already prescribed a priori the objective validity of logical forms. Only by virtue of this a priori institution of logical forms as conditions of possibility of objective reality can we explain the possibility of necessary and true knowledge. This means that thought can acquire necessity and truth 52

The Dogmatic Image of Thought only to the extent that thought itself provides the ground. As Kant states, ‘we can cognize of things a priori only what we ourselves have put into them’ (CPR B xviii). This circularity in Kant’s account is of course intended. Thought is led in a circle and closed on itself. The question arises, however, as to whether this foundation that Kant provides is really convincing and fulfils its purpose. ‘One is perpetually referred from the conditioned to the condition, and also from the condition to the conditioned’ (LS 19/30). This is to say that the condition is nothing but the form of possibility of the conditioned, and the form of possibility is fabricated retroactively in the image of the conditioned. Consequently, the general form inscribed in the proposition of knowledge is irrefutable to the extent that it responds exactly to the a priori conditions, which render the proposition possible.47 In fact, Kant’s revolutionary achievement comes down to having invented a new form of possibility, that is of replacing the formal possibility with transcendental possibility (cf. LS 18/30). But it remains that Kant’s invention of the transcendental condition is an odd procedure since it involves rising from the conditioned to the condition, in order to think of the condition as the simple possibility of the conditioned. Here one rises to a foundation, but that which is founded remains what it was, independently of the operation which founded it and unaffected by it. (LS 18–19/30)

Deleuze’s twofold objection, as to the condition being larger than the conditioned and being thought in the image of the conditioned, is rooted in a critique that concerns much more than a linguistic analysis of sense and truth-values of a proposition. Deleuze is concerned with all those philosophers who claimed to have discovered a true beginning in philosophy, a ground for truth and necessity, but who in fact argued in a circle and closed thought on itself. Thought presupposes truth and necessity by projecting a first principle (Plato’s Ideas, Being, sufficient reason, the Cogito, the transcendental I and its forms, a first proposition of consciousness, etc.) back to a fictitious original point from where philosophy can begin. According to Deleuze, the ‘true beginning’ in philosophy has to refer truth to a ground that is truly groundless (un véritable sans-fond, DR 154/200), an absolute ‘outside’ that resists being interiorised. Thought enters into a relation with pure difference, or in other words, with a differential structure consisting of divergent series of heterogeneous, nonsensical elements. In this differential structure inheres an intrinsic genetic power to produce sense and to ‘ground’ truth as the limit 53

conditions of thought: deleuze and transcendental ideas object of a genetic series of different senses (cf. DR 154/200). Sense is therefore not simply a formal condition of truth, its conceptual possibility fabricated retrospectively in the image of the conditioned, but a material and genetic principle of truth that is heterogeneous to what it conditions. Sense as the condition of truth ought to have an element of its own, distinct from the form of the conditioned. It ought to have something unconditioned capable of assuring a real genesis of denotation and of the other dimensions of the proposition. Thus the condition of truth would be defined no longer as the form of conceptual possibility, but rather as an ideational material or ‘stratum,’ that is to say, no longer as signification, but rather as sense. (LS 19/30)

For distinguishing these two understandings of sense, Deleuze refers to the former as ‘signification’ and to the latter as ‘sense’. That is to say, signification is the formal condition of truth, providing a number of conditions under which a proposition considered from the point of view of its logical form and conceptual implications ‘ “would be” true’ (LS 14/25). By contrast, sense, defined in Deleuze’s new way, provides the material condition, something unconditioned and ­heterogeneous, which accounts for the real genesis of truth. It should be noted, however, that Deleuze is not rejecting a whole tradition of linguistic analysis and philosophy of language. He is rather trying to complement it by adding a new dimension to the proposition, and calling this new dimension ‘sense’. The reason for this is that the dimension of signification is not sufficient to ground truth, and the dimension of designation or reference can ground truth only in rare cases, namely when the proposition is assumed to be ready-made and isolated from the context of living thought (DR 154/200). As Deleuze says, ‘there is only a single case where the designated stands alone and remains external to sense: precisely the case of those singular propositions arbitrarily detached from their context and employed as examples’ (DR 154/200). However, as soon as we place a proposition in the context of living thought, that is in relation to a problem, we will see how sense is engendered in the particular determination of the problem and its conditions and how this sense already implicates a truth which cannot be detached from the genesis of sense. For this reason, Deleuze claims that ‘we always have as much truth as we deserve in accordance with the sense of what we say. Sense is the genesis or the production of the true, and truth is only the empirical result of sense’ (DR 154/200). This is one of Deleuze’s central claims, which he repeats time and 54

The Dogmatic Image of Thought again on different occasions.48 It leads us to the important concept of the problem, which is the theme of the seventh postulate of the dogmatic Image of thought. For Deleuze, the ‘problem’ is a differential structure endowed with an intrinsic genetic power to generate sense. Although the problem can be incarnated in propositional form and in the empirical world, it belongs to an extra-propositional and subrepresentative realm. It is only in relation to a certain problem that a question becomes possible and a proposition acquires sense.49 Problems and Solutions The seventh postulate of the dogmatic Image of thought deals with our conception of problems and solutions. Deleuze’s main point of critique is that philosophers since Aristotle have misconstrued the nature of problems. They have fallen prey to a double illusion: a natural and a philosophical illusion. According to the natural illusion, philosophers are led to believe that problems can be traced from empirical propositions through a simple change in the phrasing. For instance, it is assumed that a declarative sentence in which a predicate, y, is attributed to a subject, x, can be turned into a problem by means of the interrogative form ‘Is y an attribute of x or not?’ In this way, Aristotle claims that ‘out of every proposition you will make a problem if you change the turn of phrase’.50 Thus the corresponding problem to the proposition ‘Man is a two-footed terrestrial animal’ would be ‘Is two-footed terrestrial animal the definition of man or not?’ The number of problems is therefore thought to equal the number of propositions that respond to them. The natural illusion makes us believe that to set and to solve a problem is the same procedure as interrogation and response. And since for every question, be it part of an examination, a quiz game, a crossword puzzle, a poll or government referendum, there is an answer ready at hand, we are certain that there is always an answer to a problem, that the solution pre-exists and is only waiting to be discovered by us. It is commonly assumed that a problem or question is nothing more than the expression of a subjective uncertainty, a temporary lack of knowledge which can be mended by a piece of information. In finding the answer, the question or problem is thought to disappear with the solution. According to Deleuze, such a concept of problem keeps us in a state of immaturity and dependence on those who actually pose the questions and set the problems. In fact, problems are not given 55

conditions of thought: deleuze and transcendental ideas ready-made; they have to be created. We remain slaves, ‘as long as we do not control the problems themselves, so long as we do not possess a right to the problems, to a participation in and management of the problems’ (DR 158/205–6). Thus the most important task is to construct the problem, to fully determine its conditions and to choose the terms in order to specify its sense. Once the problem is completely determined, a solution necessarily follows. However, there always remains the possibility of other determinations and other solutions. A problem is not dissolved or exhausted either with a single proposition or with a series of propositions. It does not disappear with a determinate response or a general solution comprising a series of particular responses. Although the problem never exists separately from its cases of solutions – that is to say, the problem ‘insists and persists in these solutions’ (DR 163/212) – it nonetheless has a being of its own (DR 269/345; LS 123/148). The being of the problematic is that of a positive virtual structure or complex of differential relations endowed with the genetic power to give rise to concomitant solutions. This virtual structure is never entirely captured in any given determination of its conditions and cases of solution. As Deleuze says, there is ‘a difference in kind between problems and propositions, an essential hiatus’ (DR 162/210). Deleuze defines the problem as being at once both transcendent and immanent in relation to its solutions. Transcendent, because it consists in a system of ideal liaisons or differential relations between genetic elements. Immanent, because these liaisons or relations are incarnated in the actual relations which do not resemble them and are defined by the field of solution. (DR 163/212)

Deleuze equates problems with Ideas, following the Kantian definition of transcendental Ideas as essentially problematic. According to Deleuze, Kant was without doubt the first to consider the problematic not as a fleeting, subjective moment in the mind of the thinking subject, but as an essential trait of the transcendental Idea, which functions as the ideal focus (focus imaginarius) or transcendental horizon for every empirical inquiry into the problem and its conditions (LS 54/70). Deleuze characterises problems as ideal ‘objectivities’, as Ideas-problems, which are made up of differential elements and relations (DR 267/343), as a structure constitutive of sense (LS 120/145). However, even in the case where philosophers have come to recognise the objectivity or irreducibility of problems and have brought 56

The Dogmatic Image of Thought to bear the question of truth or falsity on problems themselves, they have not succeeded in giving a satisfactory account of the truth of problems. According to Deleuze, they have fallen prey to a second illusion, i.e. the ‘philosophical illusion’ (DR 159/207). This implies that a problem is defined as true if and only if it is modelled upon the form of possibility of propositions. In other words, the truth of a problem depends upon its ‘logical possibility of finding a solution’ (DR 160/208). Aristotle, for instance, posed problems in terms of syllogisms and evaluated their ‘truth’ with respect to their logical ‘solvability’. According to Deleuze, the Aristotelian dialectic, conceived as the science or art of syllogisms, is a bad realisation of dialectic. First of all, the subject and premises of syllogisms are chosen with regard to ‘commonplaces’, that is mere opinions accepted by the majority of men. Furthermore, the logical form of the propositions is modelled upon the general form of empirical propositions. But Deleuze insists that as long as the criterion for the evaluation of problems is the extrinsic and variable form of possibility ‘we confuse sense with signification, we conceive of the condition only in the image of the conditioned’ (LS 122/147). What philosophy needs is the invention of a new dialectics, that is ‘dialectics as a superior calculus or ­combinatory’ of problems (DR 159/207). Deleuze suggests that a good dialectic first and foremost has to decide whether we deal with a badly posed or a well-formed problem. With a considerable debt to Bergson, Deleuze demands that the test of truth or falsity has to be applied to problems themselves (cf. B 15/3). The true and the false primarily qualify problems rather than their corresponding solutions. The question to ask here is: what is the criterion on which the truth or falsity of a problem depends? According to Deleuze, the criterion has to refer to an internal characteristic: it is the relation of the problem with its conditions which defines sense as the truth of the problem as such (LS 121/145). A false problem would be one whose conditions remain either insufficiently determined or overdetermined. But how do we pose a true problem? We have to determine its conditions and the distribution of singular and ordinary points (the important and the unimportant points) (DR 189/245). Admittedly, this remains a rather vague instruction. Let us therefore consider an example.51 Leibniz’s theory of monads has often been regarded as nonsensical, wholly arbitrary and nothing but a fantastic fairy tale.52 It has been rejected among other things on the grounds that it denies the reality of bodies and reduces any causal interaction or communication 57

conditions of thought: deleuze and transcendental ideas between monads to mere phenomena. But by simply insisting ‘Look, that’s not the way things are’, one has not achieved a refutation of Leibniz’s system. In fact, one has not even understood the sense of the Leibnizian theory of monads, for it finds its sense only in the subjacent problem that inspires it. Once we ‘forget’ the problem, we have before us no more than an abstract general solution, and since there is no longer anything to support that generality, there is nothing to prevent the solution from fragmenting into the particular propositions which constitute its cases. (DR 162/211)

Moreover, one understands nothing if one does not see that Leibniz opens up a problematic field which forces him to go all the way following the necessary implications of the questions and problems that he encounters. As Deleuze says in one of his lectures on Leibniz: he cannot stop.53 Leibniz’s constant deduction of principles and mad creation of concepts are not arbitrary efforts; they are necessitated by a continuous specification of the problematic field. Let us search for one of the initial problems or questions. It is certainly not the metaphysical question: ‘What is there?’ ‘What are the most basic components of reality?’ These ‘What is?’ questions lack the grip of necessity. They lead us nowhere. We will now extract what appears to us a true problem from his notes that he wrote prior to his letter to Arnauld from July 1686: I mean [. . .] that there is always something to be conceived in the subject which serves to explain why this predicate or event pertains to it, or why this has happened rather than not.54

Leibniz finds himself in a dilemma. He wants to believe that everything that has happened and that will ever happen to a subject has a reason (principle of sufficient reason). Because of theological concerns, it cannot be the case that God interferes ad libitum in the order of the universe. For Leibniz, God is not like a human being whose acts of resolution depend on particular circumstances. From the very first moment, God has foreseen and regulated the entire sequence of things for eternity, he does not act apart from this order of the universe that he has chosen. That is to say, nothing irregular happens in the world. But, on the other hand, whatever happens to a subject cannot follow with intrinsic necessity from its nature or essence. Only from mathematical concepts can it be said that the predicates contained in the concept necessarily follow by a simple analysis of the concept. Geometric demonstrations, for instance, yield necessary 58

The Dogmatic Image of Thought propositions whose contraries imply a contradiction and are therefore impossible. Such ‘truths of essence’, governed by the principle of non-contradiction, fall into the sphere of mathematics. Yet this doctrine of universal necessity cannot bear on ‘truths of existence’, for instance contingent truths that concern our life. For theological and moral reasons, Leibniz rejects (Spinozist) fatalism and wants to maintain a sense of the freedom of the subject. He achieves this by identifying a third option: yes, there is an intrinsic and necessary connection between the subject and all its past, present and future states. Indeed, the individual notion of each person contains all that has ever happened, is happening and will ever happen to him. However, in order to safeguard the notion of freedom, this necessity can only be ex hypothesi, that is the contrary of whatever happens must be possible.55 Leibniz’s response to the problem drives him to develop a general solution, which encompasses the theory of complete individual concepts, the theory of infinitely many possible worlds in the mind of God, and the notion of compossibility. Now we have to ask for the conditions under which the problematic field is determined. The lynchpin of the whole problematic field is the principle of reason: nihil est sine ratio (nothing is without reason). This means that nothing is or happens for which we could not find a reason why it is rather than is not, why it is so rather than otherwise. This is the popular formula of the logical principle that every truth is analytic. In every true proposition the predicate is included in the subject. Therefore every truth can be demonstrated a priori by means of an analysis of the subject term. In his seminal essay ‘On Leibniz’s Metaphysics’ (1902), Louis Couturat claims that ‘it is the entire Monadology which Leibniz thus progressively derives from the principle of reason’.56 The ‘metaphysical import of the ­principle’ is tremendous: He [Leibniz] derived from it the principle of indiscernibles and that other principle [. . .] that ‘there are no purely extrinsic characteristics (dénominations)’; then, step by step, the notion of the monad [. . .]; further, the pre-established harmony [. . .]; finally, the ideality of space and time and hence of movement and of bodies [. . .], and the immortality not only of souls, but of all substances.57

Taking the principle of reason (every truth is analytic) as the point of departure, Leibniz could count on the unreserved approval of his contemporaries, who, like him, received an education in Aristotelian and scholastic logic. However, the decisive step occurs, when Leibniz 59

conditions of thought: deleuze and transcendental ideas applied this principle equally to necessary truths of essence and contingent truths of existence. This means that Leibniz considered contingent truths not as synthetic, but as analytic. The sub-problem that then emerges concerns the question of how a predicate can be contained in the subject with the proposition being necessary only ex hypothesi (i.e. the contrary being possible). A solution to this problem finally came into sight thanks to Leibniz’s involvement with mathematics, in particular the infinitesimal calculus. ‘A new and unexpected light finally arose in a quarter where I least hoped for it – namely, out of mathematical considerations of the nature of the infinite.’58 Leibniz was now able to understand the nature of contingent truths: they differ from necessary truths as the infinite differs from the finite, or as irrational numbers differ from rational numbers. This means that contingent truths are indeed analytic, but the analysis of their terms is infinite and God alone can complete this infinite analysis. This is how Leibniz was able to secure both the notion of freedom and the notion of necessity. According to Leibniz, the true idea of free will does not exclude determinism, on the contrary, every free decision or act has its reasons in the individual nature of the subject. Yet, it is free to the extent that it is unpredictable and escapes any general law. Only God can foresee each decision or act with certainty and infallibility. Hence, the second most important condition of the Leibnizian problematic field is the condition of infinity or infinite analysis. As Leibniz repeats on several occasions: contingency is rooted in infinity.59 Having shown the importance of logic and mathematics for Leibniz’s metaphysical theses, we will not follow Leibniz any further in the elaboration of his metaphysical system. What has become apparent is that we cannot understand anything of Leibniz’s notion of the monad if we detach it from its context. Reading the Monadology is not sufficient, because the Monadology begins with the notion of the monad, but the monad itself derives from a continuous specification of a problematic field. As Couturat remarks, ‘the order followed by the Monadology is really the inverse of the order that is both logical and genetic’.60 Extracting the problem from a philosopher’s thought and determining the conditions and singular points that structure it is thus a challenging task. If the problem is well determined, then the solution necessarily follows from the differential problematic structure. It is not surprising that a change in the conditions will lead to different solutions. For instance, as soon as the principle of reason, that every true proposition is analytic, is no longer considered to hold 60

The Dogmatic Image of Thought for contingent truths, the specific Leibnizian problem disappears and his solution makes no sense any more. This happened with the Kantian determination of contingent truths as synthetic. Suddenly, the existence of purely extrinsic characteristics became possible. Thus two things could be the same with regard to their concepts but different with respect to their spatio-temporal relations. Not every external relation between things had to be expressed by an internal modification of the substance or essence of a thing. Hence Leibniz’s principle of indiscernibles, that for every concept there is one and only one thing, could not be upheld. Equally, the notion of the ‘windowless monad’ and the pre-established harmony between monads no longer made any sense. Subjects could now interact not only apparently but really on a physical level. The Postulate of Knowledge Let us proceed with the eighth postulate, the postulate of knowledge. While in the preceding paragraph we provided an example of a philosophical problem or problematic field with its conditions and concomitant solutions, Deleuze makes it clear that problems exist in various different fields – there are mathematical problems, problems in biology and physics, social, political and moral problems, problems in the arts, problems in our relationships and in everyday life. Deleuze’s very specific definition of the concept of ‘problem’ is accompanied by a whole new idea of ‘apprenticeship’ or ‘learning’ through the encounter with problems. In the dogmatic Image of thought, ‘learning’ is considered as just an intermediary passage from ignorance to knowledge under the guidance of methods. The desired result of the process is the acquisition of knowledge which, when it is achieved, settles the whole question or problem. For Deleuze, on the other hand, ‘learning’ is not to be equated with an empirical, psychological process, but with a transcendental and unconscious activity. ‘Learning’, defined in this new way, involves two essential aspects: (1) the exploration of the problematic Idea, that is the relation of its differential elements and singular points; (2) the transcendent, unregulated exercise of the faculties triggered by the encounter with the Idea-problem (cf. DR 164/213, 194/251). Deleuze calls the deregulation and trespassing of the faculties beyond their proper domain their ‘transcendent’ exercise in opposition to their empirical exercise.61 ‘Transcendent’ is not taken to refer to objects outside the empirical world, but rather to something within the world, which, 61

conditions of thought: deleuze and transcendental ideas however, cannot be grasped by the empirical operation of the faculties being employed together in a ‘common sense’. In its transcendent exercise each faculty apprehends something which concerns it exclusively, which it alone is able to grasp, yet which is ungraspable from the point of view of its empirical exercise (DR 143/186). Let us look at these two essential aspects of ‘learning’ in greater detail. In order to illustrate what it means to explore a problematic Idea, Deleuze takes up Leibniz’s example of the sea and considers the case of learning to swim. The sea with its movement of waves incarnates the Idea with its differential relations and corresponding singularities, that is physical points at which, for instance, the wave breaks or a dangerous current is formed. Our body has to adjust itself within the system of waves and troughs of the sea. It has to find a way of complicity between its own distinctive points and the singular points of the objective Idea which make up the problematic field (cf. DR 165/214, 192/248). Our conscious acts are just the global outcome, derived from the differential relations of infinitely many minute physical points or excitations and infinitely many minute perceptions and actions of our biological bodies. The process of learning is in fact an unconscious, ‘involuntary adventure’ (DR 165/215): entering into the differential relations of a problematic Idea is like being thrown into the ocean. No method can guide us safely through the differential, problematic field. Before we even start to think and act consciously, we have already undergone a ‘process of formation of thought’, a violent ‘training which brings the whole unconscious of the thinker into play’ (NP 108/124). Thought does not need a method but a paideïa, a formation, a culture. Method in general is a means by which we avoid going to a particular place, or by which we maintain the option of escaping from it (the thread of the labyrinth). (NP 110/126)62

Taking recourse to the Nietzschean concepts of paideïa and ‘culture’, Deleuze states that thinking is not just a natural exercise based on a good will and the application of method. Thinking is rather an extraordinary event, which explodes in thought itself under a constraint, a violent training. That which forces us to think is not an identifiable, recognisable object. In opposition to the process of recognition, which presupposes a common sense or the collaboration of all the faculties in relation to a supposed same object, the process of learning rather requires a disjointed and unregulated exercise of the faculties, such that each faculty communicates the violence it 62

The Dogmatic Image of Thought receives to the other faculties carrying them to their transcendent limit or ‘nth’ power. Arthur Rimbaud claims that the poet becomes clairvoyant only by undergoing a ‘deregulation of the senses’ (dérèglement de tous les sens), by experiencing all forms of love, of suffering and madness. The poet experiments with each and every poison to maintain nothing but the essence.63 According to Marcel Proust, it is in the dark regions that we discover truths that matter to us. The truths that intelligence grasps directly in the open light of day have something less profound, less necessary about them than those that life has communicated to us in spite of ourselves in an impression, a material impression because it has reached us through our senses, but whose spirit we can extract.64

For Deleuze, it is the fundamental encounter with an Idea-problem which sets our faculties into motion and raises each faculty to the level of its transcendent exercise. But how do we encounter an Ideaproblem which is, according to Deleuze, a ‘transcendental instance’ (DR 164/213)? We encounter it through ‘signs’, within a ‘symbolic field’ in which the problem expresses itself. As Deleuze says in his book Proust and Signs, ‘the signs mobilize, constrain a faculty: intelligence, memory, or imagination. This faculty, in its turn, mobilizes thought, forces it to conceive essences’ (PS 98–9/191). He continues: Everything that teaches us something emits signs; every act of learning is an interpretation of signs or hieroglyphs. Proust’s work is based not on the exposition of memory, but on the apprenticeship to signs. (PS 4/9)

The narrator in Proust’s In Search of Lost Time is confronted with many different signs: worldly signs (i.e. signs that society emits), signs of love, material signs (i.e. sensuous impressions or qualities) and essential signs of art. Although the narrator always feels that he ‘wastes’ his time in society or with love affairs instead of fulfilling his dream and starting a professional career as a writer, he gradually comes to realise that, in effect, he has been an apprentice all the time. It is through the violent encounter with signs that he is forced to think and forced to create. For instance, his love for Albertine and the jealousy she awakens within him force him to interpret all the enigmatic and deceptive signs she emits, to imagine all possible kinds of infidelity, danger or loss. He wants to penetrate the unknown world that revolves around her and from which he is excluded. But also the landscape in which they first met – the sea and beach in Balbec – is converted to signs and enveloped in her face and body. Her whole 63

conditions of thought: deleuze and transcendental ideas sensual appearance – the freshness of her face, her red cheeks, the little beauty patch and her soft fragrance – seem like material signs, which need to be deciphered. Like a work of art, Albertine triggers an inexhaustible, unlimited process of interpretation and thought, finally leading the narrator to an aesthetic production which he would have never been capable of without this love. He learns that the signs of love refer to a truth that is not restricted to the individual person, Albertine, but to all the past and future loves. The signs of love reveal a secret: the power of difference and repetition. The present love only repeats our past loves, and there is no end in this regress because there is no original first love. In a futural sense of the word, the present love also ‘repeats’ its end, the inevitable break-up, with every heated argument caused by jealousy. Every love affair is ‘a dispute of evidence’ (PS 117/143) and the jealous lover finds himself in ‘a delirium of signs’ (PS 122/150). His task is to decipher the ‘spiritual element’, the ‘essence’ or ‘truth’ out of the complex sensation. There is certainly a Platonic element in Proust. And Deleuze pays homage to Plato by granting that his theory of apprenticeship is an exception within the broader picture of the Image of thought. While the Image of thought models ‘learning’ on an empirical psychological process, and disparages it as a merely transitory stage in the acquisition of knowledge, Plato defined ‘learning’ as a ‘truly transcendental movement of the soul, irreducible as much to knowledge as to non-knowledge’ (DR 166/215–16). The transcendental conditions of thought are not drawn from innate, a priori forms but found in a process of reminiscence. Time is introduced into thought, though not in the form of the empirical time of a thinking subject. The object to be remembered, the memorandum, is not a contingent empirical content that was a former present and has become our past, but a transcendental Idea which has never been present but always past. The realm of Ideas eludes our empirical time and consciousness. However, Deleuze accuses Plato of a sleight of hand, because in the end Plato assimilates this transcendental memory to precisely the process of remembering on the part of an empirical psychological consciousness. Just as the empirical subject can remember events that happened to it in a former present, it is capable of remembering Ideas that it perceived in an original or mythical present. ‘Reminiscence is still a refuge for the recognition model, and Plato no less than Kant traces the operation of the transcendental memory from the outlines of its empirical exercise (we see this clearly in the account of the Phaedo)’ (DR 142/185). 64

The Dogmatic Image of Thought For Deleuze, the object of reminiscence, the memorandum, is that which can only be recalled, just as the material sign, the sentiendum, is that which can only be sensed or felt, and the cogitandum that which must be thought but is beyond recognition. Every faculty has its proper object that mobilises and pushes it to its transcendent limit – ‘as though the object of encounter, the sign, were the bearer of a problem’ (DR 140/182). In effect, the Idea-problem is already there in the sign, in an enveloped or involuted state. One must be sensitive to signs and open oneself to their violence (cf. PS 101/194). They are the problem-conditions for thought and pure creation. Deleuze’s definition of learning as an apprenticeship or interpretation of signs, which he first put forward in his book Proust and Signs, is still present in Difference and Repetition. But the traditional hermeneutic terminology (‘thinking subject’, ‘interpretation’, etc.) gives way to a terminology drawn from mathematics (‘differential relations’, ‘singularities’, etc.). Ideas-problems are, for instance, equated with Albert Lautman’s dialectical Ideas, which bear the urgency of problems and are prior to the discovery of solutions.65 Deleuze obviously wants to distance himself from a philosophy of the subject. Instead, he stresses the objectivity of Ideas and their ‘mindblowing’ effect, which takes from us the power to say ‘I’ (WP 55/55). The subject stays not intact, but is transformed in the extreme ­experience of learning. Deleuze’s criticism of the dogmatic Image of thought is an essential step in his project of transcendental philosophy, that is the project of finding the transcendental genetic and productive conditions of thought. It is first of all necessary to liberate thought from the constraints imposed upon it by a morally motivated order of representation and recognition. In this chapter, we have dealt with some characteristics of this order and also begun to sketch a new Deleuzian image of thought, that is an image that relates thought to a transcendental and genetic ground – or rather ‘ungrounding’ (effondement, DR 91/123) – of ‘pure differences’ or differential relations of problematic Ideas. The encounter with these problematic Ideas – be they experienced as material signs, as signs of art, as philosophical problems, or whatever – generate the act of thinking in thought as an involuntary and often violent adventure. Thought, if it is to conquer the new and not only proceed on the common path of already preestablished and prejudged categories and values, needs to rid itself of the dogmatic Image and discover its unconscious, sub-representative 65

conditions of thought: deleuze and transcendental ideas source. Pure difference or the differential is the model for a genetic and non-sensible element, which is fundamental to Deleuze’s renewal of the project of transcendental philosophy. In the following chapter, we will first look at Deleuze’s early book Nietzsche and Philosophy, in which his critical rethinking of the nature of the transcendental is already to be found, and then follow him in his engagement with Maimon’s criticism of the Kantian transcendental.

Notes   1. The essay ‘How Do We Recognize Structuralism?’ was presumably written in 1967 and first published in 1972.   2. Deleuze explicitly exempts Lacan from this criticism, since Lacan introduced a third term above and beyond the real and the imaginary: namely the order of the symbolic.   3. Deleuze’s critique of the notion of ideology is clearly expressed since his collaboration with Guattari in the 1970s and 1980s. In the 1972 interview with Catherine Backès-Clément, Guattari says: ‘we don’t have any time for concepts like ideology, which are really no help at all: there are no such things as ideologies’ (N 19/32). At several places in Anti-Oedipus ‘ideology’ is criticised as a confused and misleading notion. Deleuze and Guattari contend that ‘the concept of ideology is an execrable concept that hides the real problems, which are always of an organizational nature’ (AO 344/412). On their critique of psycho­ analysis as an ‘analysis of the subjective, as defined by ideology’, see AO 345/413. See also ATP 4/10: ‘there is no ideology and never has been.’   4. ‘Even the judgment of knowledge envelops an infinity of space, time, and experience that determines the existence of phenomena in space and time (“every time that . . .”). But the judgment of knowledge in this sense implies a prior moral and theological form, according to which a relation was established between existence and the infinite following an order of time: the existing being as having a debt to God’ (CC 127/159).   5. Deleuze, ‘Nietzsche’, p. 69. Cf. also NP 104/119.   6. See also NP 89–90/102: ‘There has never been a more conciliatory or respectful total critique. [. . .] Kant merely pushed a very old conception of critique to the limit, a conception which saw critique as a force which should be brought to bear on all claims to knowledge and truth, but not on knowledge and truth themselves; a force which should be brought to bear on all claims to morality but not on morality itself. Thus total critique turns into the politics of compromise: even before the battle the spheres of influence have already been shared out. Three 66

The Dogmatic Image of Thought ideals are distinguished: what can I know? what should I do? what can I hope for? Limits are drawn to each one, misuses and trespasses are denounced, but the uncritical character of each ideal remains at the heart of Kantianism like the worm in the fruit: true knowledge, true morality and true religion.’   7. Cf. Zourabichvili, ‘Une philosophie de l’événement’, pp. 22–3: ‘The failure of grounding is not alien to the fragility of this postulate [of the intimacy with the outside]. It is not surprising that the necessity eludes us, when we attempt to close thought upon itself’ (my translation, D. V.).   8. Cf. DR 274/351: ‘Is this not the most general characteristic of the ground – namely, that the circle which it organises is also the vicious circle of philosophical “proof”, in which representation must prove what proves it, just as for Kant the possibility of experience serves as the proof of its own proof?’ See also LS 19/30.   9. Cf. Sauvagnargues, Deleuze: L’Empirisme transcendantal, p. 84. 10. ‘But the form of exteriority of thought – the force that is always external to itself, or the final force, the nth power – is not at all another image in opposition to the image inspired by the State apparatus. It is, rather, a force that destroys both the image and its copies, the model and its reproductions, every possibility of subordinating thought to a model of the True, the Just, or the Right (Cartesian truth, Kantian just, Hegelian right, etc.).’ (ATP 377/467) 11. Deleuze thereby aligns himself with the philosopher Salomon Maimon, one of Kant’s early critics, who wanted to replace the transcendental conditions of possible experience with genetic conditions of real experience. Deleuze believes that this alternative approach to transcendental philosophy first put forward by Maimon is also taken up by a range of later philosophers (Schelling, Bergson, Nietzsche, Foucault) and even the film-maker Pasolini. See the following quotations: (1) ‘Thus it is not the conditions of all possible experience that must be reached, but the conditions of real experience. Schelling had already proposed this aim and defined philosophy as a superior empiricism: this formulation also applies to Bergsonism’ (DI 36/49). (2) ‘The Nietzschean and the Kantian conceptions of critique are opposed on five main points: 1. Genetic and plastic principles that give an account of the sense and value of beliefs, interpretations and evaluations rather than transcendental principles which are simple conditions for so-called facts [. . .]’ (NP 93/106–7). (3) ‘Foucault differs in certain fundamental respects from Kant: the conditions are those of real experience, and not of possible experience’ (F 60/67; the final phrase of this sentence is omitted from the English translation). (4) ‘If it is worth making a philosophical comparison, Pasolini might be called post-Kantian (the conditions of legitimacy are the conditions of reality itself), whilst Metz and his 67

conditions of thought: deleuze and transcendental ideas followers remain Kantians (bringing principle down to fact)’ (CIT 276/42–3, note 8/8). 12. As Nietzsche puts it, untimely thought means ‘acting counter to our time and thereby acting on our time and, let us hope, for the benefit of a time to come’ (Nietzsche, ‘On the Uses and Disadvantages of History for Life’, p. 60). It should be noted that the concept ‘untimely’ appears here in the context of Nietzsche’s discussion of the use of classical studies (philology and history), the above quotation being preceded by the words: ‘That much, however, I must concede to myself on account of my profession as a classicist: for I do not know what meaning classical studies could have for our time if they were not untimely.’ However, in ‘Schopenhauer as Educator’, Nietzsche also uses this concept with reference to philosophy, in which context it becomes significant for Deleuze (‘Schopenhauer as Educator’, pp. 133 and 145–6). 13. See also DR 167/217; for references from Deleuze’s later work, see ATP 377/467 and CC 82/106. 14. Martin, Variations, p. 157. 15. Arguing in a similar way, Zourabichvili says: ‘The oscillation of critique between the theme of a “thought without image” [. . .] and that of a “new image of thought” [. . .] indicates perhaps the moment in which Deleuze confronts the question in itself. In fact, this oscillation reflects the paradox of a transcendental philosophy, which in posing itself as immanent seeks the conditions that are “not larger than the conditioned” and that constitute a sort of “plastic” transcendental field [. . .]. Now, what is the worth of a theory that pretends to get by without an image, although it describes the conditions of an act of thinking? [. . .] In reality, the paradox is that the new image – the “rhizome” [. . .] – is the image of thought without image, an immanent thought that does not know in advance what thinking means’ (in ‘Une philosophie de l’événement’, pp. 63–4; my translation, D. V.). 16. Deleuze, ‘Rhizome (Introduction)’, in ATP 3–25/9–37. Deleuze also utilises the model of the rhizome to designate a creative ‘becoming’ of language in literature, which defies the language of the majority, its ordinary syntax and pre-existent semantic distribution: ‘Creative stuttering is what makes language grow from the middle, like grass; it is what makes language a rhizome instead of a tree, what puts language in a perpetual disequilibrium’ (CC 111/140). 17. Cf. Deleuze: ‘Because I believe that, besides multiplicities, the most important thing for me was the image of thought such as I tried to analyse it in Difference and Repetition, then in Proust and everywhere.’ See ‘Lettre-Préface à Jean-Clet Martin’, in Deux régimes de fous: textes et entretiens 1975–1995, ed. David Lapoujade (Paris: Editions de Minuit, 2003), p. 339; my translation, D. V. This passage is inadvertently omitted in the English translation. 68

The Dogmatic Image of Thought 18. In his book La Mésentente: politique et philosophie (Paris: Éditions Galilée, 1995), Jacques Rancière argues in a similar way. The revolutionary subject is not an identifiable subject captured by the order of representation (the ‘law of the police’ in Rancière’s terms). Rather the bearers of revolutionary struggle are processes of subjectification, that is dissolved subjects which elude all codes of representation and assemble and disassemble always anew. 19. This interview with Deleuze was conducted immediately prior to the student revolts in Paris which finally led to the general strike in May 1968. 20. Cf. the opening sentence of Part I of Descartes’ Discourse on the Method. 21. See Kant’s letter to Herz (26 May 1789). The translation of the letter appears in Appendix II of Maimon, Essay, p. 234. 22. For more on Plato’s method of division and the role of myth, see DR 59–64/82–9 and LS 253–66/292–307. 23. For Plato, the paradigms of those who only simulate or ‘mimic’ the wise are the Sophist and the ‘representational poets’, cf. Plato, Sophist 235a–236d and Republic, Book X, 601a–606d. 24. Patton, ‘Anti-Platonism and Art’, p. 154. 25. As Aristotle explains, ‘terrestrial’ and ‘aquatic’ are not simply denotations of locality but of quality. That is to say, a terrestrial animal does not become an aquatic animal when it is found in water, and vice versa. See Topics, Book VI, 6, 144b–145a, in The Complete Works, vol. I, p. 244. 26. Deleuze chooses as an example of specific differences the predicates ‘with feet’ and ‘with wings’ (DR 30/46). Although Aristotle indeed cites these predicates as specific differences (Topics, VI, 6, 143a–b, in The Complete Works, vol. I, pp. 241–2), they are (if provided in this conceptual couple) not the best example, since the predicates ‘with feet’ and ‘with wings’ are not contraries, i.e. not mutually exclusive in the object (for there are animals with wings and feet). The reason why ‘with feet’ is indeed a specific difference is because there exists the opposite predicate ‘without feet’ within the same genus (‘animal’). (As Aristotle explains, a genus can also be divided by a predicate and its negation as in the case of a length ‘with breadth’ and ‘without breadth’ (a line); Topics, VI, 6, 143b, in The Complete Works, vol. I, p. 242). 27. Cf. Aristotle, Topics, VI, 6, 145a, in The Complete Works, vol. I, p. 244: ‘The differentia seems rather to preserve that which it differentiates; and it is absolutely impossible for a thing to exist without its appropriate differentia – if there is nothing terrestrial, there will be no man. To speak generally, a thing cannot have as its differentia anything in respect of which it is subject to alteration.’ 28. Aristotle argues that a genus cannot attribute itself to its specific 69

conditions of thought: deleuze and transcendental ideas differences, but only to the objects that are determined by the specific differences. For instance, the genus ‘animal’ can be said of the human species but it cannot be attributed to the specific difference ‘rational’ (Topics, VI, 6, 144a, in The Complete Works, vol. I, p. 243). 29. ‘All errors of subreption are always to be ascribed to a defect in judgment, never to understanding or to reason’ (CPR A 643/B 671). 30. Deleuze agrees with Bergson that the true and the false are functions not so much of propositions that serve as solutions to problems, but first and foremost of problems themselves. He distinguishes false problems, that is inexistent or badly posed problems, from true problems, and compliments Bergson on having found a method (method of intuition) for the intrinsic determination of the value of problems (see B 15–21/3–11). 31. Zourabichvili remarks that Deleuze advocates a new, differential conception of violence, which describes an aggressive critical force necessary for philosophical thought. This critical aggressivity (agressivité critique) essentially differs from an aggressive thought that finds its sources in negation and turns stupidity into malevolence and cruelty. See Zourabichvili, ‘Une philosophie de l’événement’, pp. 34–5. 32. A detailed account of Deleuze’s definition of conceptual personae (as distinct from aesthetic figures and psychosocial types) can be found in WP, Chapter Three. 33. As Deleuze remarks, the Cogito is indeed a nonsensical proposition ‘to the extent that this proposition purports to state both itself and its sense’ (DR 276/353). According to Deleuze, this is precisely what defines a nonsense word (such as Lewis Caroll’s word ‘snark’ or the Stoic expression ‘blituri’) (DR 155/201), whereas any signifying word or proposition refers back to some other proposition or object whose sense it expresses. The Cogito has no other reference than its selfreference, that is to say, ‘the power of reiteration in indefinite regress (I think that I think that I think . . .)’ (DR 155/202). 34. This remark on the private thinker comes from a discussion of Nietzsche – see ATP 376/467. 35. Deleuze attributes the production of ‘counterthoughts’ to ‘private thinkers’ such as Kierkegaard, Nietzsche and Shestov (ATP 376/467). But this is true of Dostoyevsky’s idiot as well, whose way of thinking contrasts with the opinions and values of Russian society. 36. Cf. Heidegger, What Is Called Thinking?, p. 64. 37. Frege, ‘On Sense and Reference’, p. 27. 38. Ibid., p. 28. 39. Ibid. 40. Ibid., p. 29. 41. Ibid. 42. Ibid., p. 30. 70

The Dogmatic Image of Thought 43. See LS 105/128 and 123/149. 44. See also CPR A 59–60/B 84: ‘These criteria [of truth] concern only the form of truth, i.e., of thinking in general, and are to that extent entirely correct but not sufficient. For although a cognition may be in complete accord with logical form, i.e., not contradict itself, yet it can still always contradict the object. The merely logical criterion of truth, namely the agreement of a cognition with the general and formal laws of understanding and reason, is therefore certainly the conditio sine qua non and thus the negative condition of all truth; further, however, logic cannot go, and the error that concerns not form but content cannot be discovered by any touchstone of logic.’ 45. See CPR A 62/B 87; see also A 277/B 333 and B 149. 46. The example is taken from the novel House of Leaves (New York: Pantheon Books, 2000), written by Mark Z. Danielewski. 47. Cf. Lebrun: ‘ “Grounding”, in this sense, amounts simply to certifying in a good and proper way that the pretension to universality which is inscribed in my proposition turns up to be irrefutable because it responds precisely to the condition that is alone able to render it valid’ (in ‘Le transcendantal et son image’, p. 209; my translation, D. V.). 48. Cf. DR 159/206; NP 1/2, 104/118, 110/125; B 16/5. 49. Zourabichvili, ‘Une philosophie de l’événement’, p. 33: ‘It’s as a function of a certain problem that a question becomes possible and above all a proposition acquires sense. Sense is nothing but the relation of a proposition, not to the question that it answers, i.e. the sterile double, but to the problem outside which it has not sense’ (my translation, D. V.). 50. Aristotle, Topics, Book I, 4, 101b, in The Complete Works of Aristotle, vol. I, p. 169. 51. Zourabichvili demonstrates the art of posing problems with reference to Deleuze’s early book on Hume, in ‘Une philosophie de l’événement’, pp. 33–4. (For the reference to Deleuze, see ES 105–6/118–19). For further examples of problems defined in Deleuze’s manner, see Patton’s article ‘The World Seen From Within’ (1997). 52. Russell, for instance, admits that it was only when he read Leibniz’s Discourse on Metaphysics and the letters to Arnauld that he saw how Leibniz’s system could be deduced from a few simple premises. Before that: ‘I felt – as many others have felt – that the Monadology was a kind of fantastic fairy tale, coherent perhaps, but wholly arbitrary’ (in A Critical Exposition of the Philosophy of Leibniz, p. xvii). 53. Deleuze, Lecture Course on Leibniz, 15 April 1980. 54. See Leibniz’s preparatory remarks written prior to his letter to Arnauld (4/14 July 1686), in The Leibniz­–Arnauld Correspondence, p. 50. 55. Leibniz, Discourse on Metaphysics, p. 422. 71

conditions of thought: deleuze and transcendental ideas 56. Couturat, ‘On Leibniz’s Metaphysics’, p. 23. For a reference to Leibniz, see his letter to Arnauld (4/14 July 1686): ‘there must always be some basis for the connexion between the terms of a proposition, and it is to be found in their concepts. That is my great principle with which I believe all philosophers must agree, and of which one of the corollaries is the common axiom that there is a reason for everything that happens, and that one can always explain why a thing has worked out this way rather than that [. . .]. One sees that from the above-mentioned principle I draw surprising consequences, but it is only because one is not accustomed to pursue far enough the clearest knowledge’ (in The Leibniz–Arnauld Correspondence, pp. 63–4). 57. Couturat, ‘On Leibniz’s Metaphysics’, pp. 22–3. 58. Leibniz, ‘On Freedom’, p. 107. 59. Couturat, ‘On Leibniz’s Metaphysics’, p. 25. 60. Ibid., p. 23. 61. It is worth noting that Kant himself distinguishes between a transcendental use or rather misuse of the understanding that results from a failure of the faculty of judgement to restrict the application of categories to their ‘territory’, and transcendent principles that eliminate all lines of demarcation and attempt to seize a new territory beyond possible experience (CPR A 296/B 352–3). He opposes the latter to proper immanent principles of the understanding that are of merely empirical use. In a similar way, Deleuze opposes the transcendent exercise of the faculties to their empirical operation in recognition, but for Deleuze, in contrast to Kant, the transcendent refers to something unrecognisable (unthinkable, unimaginable, immemorial, imperceptible) within the world, not beyond it. 62. Deleuze is presumably referring to the ancient Greek myth of Theseus and the Minotaur. In Crete, King Minos had a labyrinth constructed to imprison the Minotaur, a bull-headed creature who devoured men for sustenance. Theseus volunteered to slay the monster, and Ariadne, the daughter of Minos, who had fallen in love with Theseus, provided him with a ball of thread allowing him to retrace his path. By means of this thread, Theseus, after having killed the Minotaur, eventually found his way out of the labyrinth. 63. Rimbaud, ‘Lettre à Paul Demeny du 15 mai 1871’, in Lettres du Voyant, p. 137: ‘The poet makes himself clairvoyant [voyant] through a long, immense and reasoned deregulation of all the senses [dérèglement de tous les sens]. He seeks all the forms of love, of suffering and madness; he exhausts on him all the poison, in order to save only the quintessence. Ineffable torture during which he needs all his faith, all superhuman force, during which he becomes amongst all the great invalid, the great criminal, the great accursed – and the supreme sage [Savant]!’ (My translation, D. V.) 72

The Dogmatic Image of Thought 64. Proust, A la recherche du temps perdu, p. 878. 65. See Chapter 3, this volume. For more details, see also Duffy, ‘Albert Lautman’, in Jones and Roffe (eds), Deleuze’s Philosophical Lineage, pp. 356–79, and Bowden, The Priority of Events, ch. 3, pp. 95–151.

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2

The Demand for Transcendental Genetic Conditions

As we have already mentioned, philosophy, for Deleuze, is inseparable from ‘critique’. He admires Kant for having brought a revolution to philosophy by means of his transcendental critique. The domain of the transcendental is not the domain of the transcendent. Kant undermines the traditional philosophical distinctions, in particular with his notion of ‘phenomenon’, which has a completely different meaning from the meaning that this term had acquired in the philosophical tradition. Since Plato, philosophers had distinguished the appearance of a thing from its metaphysical essence. They had opposed the ‘apparent world’ of sensuous, perishable and illusive appearances to the transcendent, ‘intelligible world’ of eternal and true essences. Kant replaces the disjunctive couple appearance/essence with the conjunctive couple of that which appears (Erscheinung) and its transcendental conditions of apparition. The Kantian phenomenon is no longer a deceptive simulacrum or an inferior copy related to an original essence, but an object of experience related to transcendental conditions which constitute it as a possible object for us, that is as having a sense or signification. This means that the dimension of signification takes the place of the metaphysical essence.1 Truth is no longer hidden in a metaphysical realm, unattainable in principle, but can be attained in experience on the premise that experiential cognition complies with the transcendental conditions of experience. Transcendental logic provides a necessary criterion for truth, namely the relation to an object (which is the dimension of signification). The problem with Kantian transcendental philosophy, however, is that Kant defines the transcendental conditions as pure a priori givens, without being able to account for the genesis of these a priori concepts themselves. Kant is first and foremost concerned with guaranteeing the universality and necessity of our objective experience, that is the necessary law-like interconnection of experiences 74

The Demand for Transcendental Genetic Conditions in synthetic judgements, and he does so by founding the objectivity of our experience on given, a priori concepts. Deleuze, as we have seen, argues that the foundation that Kant provides is very fragile. Kantian transcendental conditions suffer from a double defect. The first defect is that they are too far from the actual; that is why the signification they constitute is too abstract. They are only conditions of possible experience and not capable of generating real experience. In the second place, they are too close to the actual; that is why they are not truly transcendental. They are traced from the empirical and retrospectively presupposed as transcendental conditions. Deleuze demands that a transcendental philosophy has to account for the genesis of real experience instead of simply assuming conditions of the possibility of experience. A viewpoint of genesis has to be substituted for a viewpoint of conditioning. This demand for transcendental genetic conditions resonates in many of Deleuze’s books from the 1960s and explains his interest in post-Kantian philosophers such as Maimon, Nietzsche and Bergson. The viewpoint of genesis abandons the ‘high’ idea of foundation (cf. NP 2/2) and, instead, relates thought or the real to sub-representational, differential and immanent dynamisms of some kind, whether it is Maimon’s ‘differentials of consciousness’, Nietzsche’s will to power or Bergson’s virtual memory. In this chapter we will focus on Nietzsche’s and Maimon’s respective contributions to a critique of Kant, a critique that is brought to bear on the Kantian transcendental conditions themselves.

Deleuze’s Nietzsche Deleuze’s book Nietzsche and Philosophy, published in 1962, is symptomatic of a newly awakened interest in the study of Nietzsche, which reached its peak in France in the 1960s and 1970s. Before the Second World War, Nietzsche had been a rather marginal figure in French philosophy, and the reading of Nietzsche had been promoted mainly by very conservative circles that brought Nietzschean thoughts to bear on reactionary and elitist themes. A gradual shift of perspective finally evolved during the war years, thanks to a small group of philosophers, such as Georges Bataille, Jean Wahl, Jean Hyppolite and Georges Canguilhem, who met in the salon of Marcel Moré. Among those who frequented these philosophical reunions was the young Deleuze, at this time still a student in his final year at the Lycée Carnot.2 It was in the salon of Marcel Moré 75

conditions of thought: deleuze and transcendental ideas where he probably first came into contact with a new presentation of Nietzsche. Some of these philosophers later became his teachers at the University of the Sorbonne. Deleuze completed his diploma, the DES (diplôme d’études supérieures), on Hume under the direction of Jean Hyppolite and Georges Canguilhem. Deleuze’s investigations on Hume were later published in a book entitled Empiricism and Subjectivity (1953), which Deleuze dedicated to Jean Hyppolite in ‘sincere and respectful homage’. Though being a Hegelian himself, Jean Hyppolite encouraged diversity in philosophical investigations and thereby allowed a whole generation of students (Foucault and Derrida among others) to deviate from the French ‘official’ philosophy, which was very much influenced by Hegelian dialectic.3 This new generation developed a resistance to and increased criticism of Hegel’s philosophy. The study of Nietzsche played an important part in the rejection of the dialectical tradition. Dialectics had become discredited as a method of thought, for it aimed to achieve something positive by means of contradiction and negation. Contrary to the negative power of the dialectic, Nietzsche allowed conceiving a movement of thought, which proceeds by an affirmative play of ­differences and not by means of contradiction. Deleuze’s small volume on Nietzsche is indicative of this new reading of Nietzsche. Nevertheless, the Nietzsche it presents is unique to Deleuze, being more a transformation or extension of Nietzsche’s thought than a ‘faithful’ interpretation or commentary. Deleuze’s Nietzsche is important for this study mainly for two reasons: 1. Deleuze presents Nietzsche as an ‘inverted’ Kantian, who pushes the critique of traditional metaphysics to its limits by bringing it to bear on Kant’s critical philosophy itself. Nietzsche does not accept the ‘facts of reason’ (knowledge and morality)4 and instead demands a genetic account of the values of knowledge and morality, indeed the value of truth itself. 2. Nietzsche’s search for the genetic element, which generates the value of values, culminates in the theory of the ‘will to power’. Deleuze appropriates this theory and purges it almost entirely of anthropomorphic terms. Central to Deleuze’s interpretation is the assumption of a (non-dialectical) differential and genetic structure of active and reactive forces, which are distinguished by their quality, or difference in quantity. We will argue that Nietzsche’s will to power is the pre-form of a productive transcendental principle, which is mobile, plastic and changing. 76

The Demand for Transcendental Genetic Conditions Nietzsche and the Problem with Truth According to Deleuze, one of Nietzsche’s greatest achievements is having called the affinity between thought and truth into question.5 Thought is rather an ally of life or life forces to the extent that life poses problems, which set thought into motion, and thought shatters restrictions that are a hindrance to the exertion of life forces. Life would be the active force of thought, but thought would be the affirmative power of life. Both would go in the same direction, carrying each other along, smashing restrictions, matching each other step for step, in a burst of unparalleled creativity. Thinking would then mean ­discovering, inventing, new possibilities of life. (NP 101/115)

Thus thought and life both enter into a mutually enhancing relation, in which life makes thought active and thought in its turn invents new modes of being. By contrast, the search for truth, if truth is defined as a metaphysical value, is disconnected from the impetus of life forces. According to the metaphysical concept of truth, truth is conceived as something transcendent, invariant and universal, that is an unconditioned given for all times and places. As such, truth is placed outside the world, out of reach with regard to perspectival assessments, practical demands and transformative factors active within life. Furthermore, in the name of absolute truth, life is devalued and accused. The world we are living in is judged as erroneous, as mere appearance, while the truth lies beyond the sensible world in a transcendent realm. Nietzsche poses the question: ‘What in us really wants “truth”?’6 Searching for the origin of the will to truth, he wonders: who wants truth in the first place? What will and what type of forces want truth and for what reason? His genealogical approach differs considerably from the traditional concern regarding the essence of truth (‘What is truth?’). Nietzsche wants to know what the value of truth is. Why should truth be more valuable than untruth? ‘Why couldn’t the world that concerns us – be a fiction?’7 Not without pride Nietzsche compliments himself on being the first person to dare to pose this problem. For him, the will to truth itself becomes problematic. Hitherto, philosophers naturally claimed that truth belonged to thought in principle. They refrained from ‘relating truth to a concrete will of its own, to a type of forces, to a quality of the will to power’ (NP 95/108). According to Nietzsche, the striving for truth rests on a metaphysical faith or conviction 77

conditions of thought: deleuze and transcendental ideas that truth is worth more than appearance. This is an element of the Christian faith, and in fact Plato had already expressed this conviction.8 It seems obvious that the will to truth is not grounded on a calculus of utility, since appearance, deception, disguise, simulation or self-blinding have often proven much more favourable to life than truth. Thus the unconditional will to truth must come from another source. Nietzsche argues that it arises on moral grounds, since it expresses the will not to allow oneself to be deceived, or more concretely: ‘I will not deceive, not even myself!’9 Philosophers are mistrustful of this volatile, illusive and sensuous world, which they conceive as being deficient and guilty. They accuse the world because they cannot bear being deceived. ‘The blind rage with which the philosophers resist being deceived’ is the expression of a will to truth, that is the desire for a true world beyond the world of mere appearances.10 Philosophers search for truth in ‘the lap of Being, the intransitory, the hidden god, the “thing-in-itself” ’.11 Their metaphysical aspirations lead them to denounce the world they are living in and to diminish life in the name of higher, ‘superior’ values. The will to truth betrays a nihilistic will, which is hostile to life and destructive with regard to life’s most fundamental prerequisites. The ascetic ideal is a symptom of this will to nothingness: it implies a hatred of the material world, a horror of the senses, a fear of happiness and beauty, a condemnation of appearance and transience, and an annihilation of wishing and longing. However, we should note that asceticism is not necessarily negative and directed against life. As Nietzsche says in On the Genealogy of Morals, there is a kind of ‘cheerful asceticism of an animal become fledged and divine, floating above life rather than in repose’.12 The ascetic ideal can create the freedom and optimum conditions for thinking: ‘the most favourable preconditions of higher spirituality [Geistigkeit]’.13 It is thus indispensable for the philosopher or the philosophical animal (la bête philosophe).14 Moreover, it had a vital role as a precondition for the existence of philosophers: according to Nietzsche, it served the philosopher as a mask by giving him the appearance of an already established type of contemplative man, the priest or religious man in general. The philosopher had to play this part and believe in it himself in order to be accepted in the social milieu. Thus the ascetic ideal has had many functions and meanings. It is only noxious if it is the symptom of a nihilistic will and a will to truth. As we have already mentioned, philosophers from Plato onwards traditionally distinguished between a ‘real world’ and an ‘apparent 78

The Demand for Transcendental Genetic Conditions world’ and believed in truth as the highest value. They only differed in relation to the question whether the real world is attainable, unattainable for now or unattainable in principle. As such, Nietzsche summarises the occidental history of philosophy in a stunning short tale, which he calls ‘How the “Real World” at Last Became a Myth’.15 There he narrates the delusion and final dissolution of the ideal of the real world. It seems that with the demise of Christian religion, Kantian morality and ultimately the belief in science, the ideal of the real world loses every function. Nietzsche already foresees a new category of philosophers who doubt the value we ascribe to truth, truthfulness or altruism. It is a type of philosopher who is genuinely doubtful and suspicious: In bourgeois life ever-present suspicion may be considered a sign of ‘bad character’ and hence belong among things imprudent; [. . .] what should prevent us from being imprudent and saying: a philosopher has nothing less than a right to ‘bad character,’ as the being who has so far always been fooled best on earth; he has a duty to suspicion today, to squint maliciously out of every abyss of suspicion.16

The philosopher of the future dares to pose the problem of values and put the hierarchy of values into question. However, a proper critique will not simply lead to a destruction of established values or a mere reversal of the existing hierarchy of values. It is true that Nietzsche opts for re-evaluating appearance, the will to illusion, egoism and desire, but these values do not have an intrinsic meaning either. In order to determine the meaning of values, the philosopher needs to investigate the conditions and circumstances under which values grew up and developed. He has to ask ‘who makes this meaning?’ Deleuze calls this Nietzschean method the ‘method of dramatisation’. It consists in ‘relating a concept to the will to power in order to make it the symptom of a will without which it could not even be thought (nor the feeling experienced, nor the action undertaken)’ (NP 78/89). To dramatise a value means to relate it to the mouth that utters it and the ‘geohistorical’ milieu from which it originates. The philosopher of the future will have to test values constantly by evaluating their origin in ‘noble’ or ‘base’ ways of thinking. If one wants to object that ‘noble’ and ‘base’ are themselves values, and why should ‘noble’ be worth more than ‘base’, the answer is: ‘noble’ and ‘base’ are not values but modes of existence of those who evaluate and judge. These ways of being are symptoms or 79

conditions of thought: deleuze and transcendental ideas expressions of a particular will to power, which serves as a principle for a style of life as well as for a mode of thought. This is the crucial point; high and low, noble and base, are not values but represent the differential element from which the value of values ­themselves derives. (NP 2/2)

The will to power is precisely this differential element. In the following, we will mainly refer to Deleuze’s interpretation of the will to power, which relies heavily on Nietzsche’s physics of force. The theory of forces is only sketchily outlined in the unpublished fragments collected in the posthumous opus The Will to Power (1906), which suffered greatly under the distortions that were caused by Nietzsche’s sister. In the exposition that follows, we do not attempt a reading faithful to Nietzsche or consider his unpublished notes and books from a philological point of view. We will rather present the Nietzsche of Deleuze’s early book, Nietzsche and Philosophy (1962), that is ‘a rigorous and systematic thinker who constructed a philosophy of nature around the complex concept of will to power’.17 Nietzsche’s Will to Power The will to power is by no means a will that wants power and struggles for recognition. If power is understood as getting oneself recognised, then the will to power means nothing more than the confirmation and conservation of current values that serve as criteria for recognition. Such a will to power is conservative, not creative. It conforms to the model of representation, for it makes power an object of representation: power is represented in the money you have, the luxuries you enjoy, the honours you are endowed with or the reputation you hold. The mania for representing, for being represented, for getting oneself represented, for having representatives and representeds: this is the mania that is common to all slaves [. . .] The notion of representation poisons philosophy: it is the direct product of the slave and of the relations between slaves, it constitutes the worst, most mediocre and most base interpretation of power. (NP 81/92)

The will to power, understood as striving for recognition and having power represented, is the conception of the slave. It is important to note that ‘master’ and ‘slave’ do not designate sociological or 80

The Demand for Transcendental Genetic Conditions historical types of human beings. Rather they are used as epitomes of high or low, noble or base, ways of thinking and being; in Deleuze’s words we might say that the slave and the master or aristocrat ­function as ‘conceptual personae’.18 The slave is a negative and reactive type, a man of ressentiment. As Nietzsche says: the slave morality needs external stimuli in order to act at all – ‘its action is fundamentally reaction’.19 The eye of ressentiment is directed toward the aristocrat or master. The slave resents the master; he calls the master evil; and by negating him, he seeks to affirm himself: ‘You are evil, therefore I am good’. His thinking and reasoning is based on the principle of contradiction and negation. The ‘syllogism of the slave’ (NP 121/139) operates by a double negation: it begins by stating a negative (‘the master is evil’) and by opposing the master to himself (‘the master is the non-ego’). He assumes that the negation of a negation equals an affirmation. In fact, the slave is a ‘covert Hegelian’; he follows the logic of the dialectic.20 On the contrary, the master is an affirmative and active type. He is aware of himself as an ‘overflowing power’ which likes to bestow and share his wealth, not so much out of pity but rather out of an ‘excess of power’.21 The master labels himself as good. He actually creates values. These values are not negatives of already existing values. He creates values by determining what is good for him, that is what enhances his power and his capacity to act. By contrast, he labels ‘bad’ what diminishes his power and tries to separate it from what it can do. The slave is ‘bad’ in the value-positing eye of the master. However, ‘bad’ in the mouth of the master is by no means the same as ‘evil’ in the mouth of the slave. As Nietzsche explains: This ‘bad’ of noble origin and that ‘evil’ out of the cauldron of unsatisfied hatred – the former an after-production, a side issue, a contrasting shade, the latter on the contrary the original thing, the beginning, the distinctive deed in the conception of a slave morality – how different these words ‘bad’ and ‘evil’ are.22

Thus the slave creates the highly moralised notion of ‘evil’, which is born out of resentment and hatred, while the master only comes to this ‘bad’ of noble origin after a double affirmation: first he affirms himself, then he affirms his difference from the slave. The negative conclusion (‘the slave is bad’) is only the complementary shadow, which follows ‘from a triumphant affirmation of itself’.23 We should note that the master says not only ‘yes’ to himself 81

conditions of thought: deleuze and transcendental ideas but to the whole community of masters: ‘We noble ones, we good, beautiful, happy ones.’ The masters are capable of developing a ‘communal feeling’ which is based on a free play or competition of equal forces (agon).24 They respect each other and also respect their enemies, for they regard someone as an enemy only if he is worthy, that is equal in power. Thus the logic of the master is a logic of affirmation and difference. The negative, contradiction and opposition is of no importance in this logic. Characterised in this way, ‘master’ and ‘slave’ do not, as we have already mentioned, correspond to real characters, but rather to ideal types. According to Deleuze’s reading of Nietzsche, this distinction of master and slave amounts to a typology of forces. We have to reject a simplistic psychological or anthropomorphic interpretation. Here we must rid ourselves of all ‘personalist’ references. The one that . . . does not refer to an individual, to a person, but rather to an event, that is, to the forces in their various relationships in a proposition or a phen­ omenon, and to the genetic relationship which determines these forces (power). (NP xi)

The master stands for an active type of forces, that is forces of conquest and subjugation, while the slave stands for a reactive type of forces, that is forces of adaptation and regulation.25 Active and reactive forces do not simply differ with respect to quantity; rather they differ with respect to quality. Quality, so Deleuze says, is irreducible to quantity.26 Quality can be defined as a difference of quantity in relation to other forces. That is to say, a force is never isolated; a force is always in a relation of tension to all other forces. This relationship of difference with other forces makes each force singular, such that no two forces are equal. ‘Difference in quantity is the essence of force and of the relation of force to force’ (NP 43/49). Already in Beyond Good and Evil it becomes clear that Nietzsche rejects the theory of materialistic atomism and instead puts forward a physics of dynamic quanta or power-quanta, which he largely borrows from Boscovich. Roger Joseph Boscovich (1711–87) was a mathematician and physicist born in Ragusa, Dalmatia (present-day Dubrovnik in Croatia). He is the author of Philosophiae naturalis theoria (Theory of Natural Philosophy, 1758), in which he develops a dynamic interpretation of the world according to which phenomena are explained in terms of force instead of mass. Nietzsche cites him as the one who won the greatest triumph over the senses by renouncing ‘the belief in the last part of the earth that “stood fast” 82

The Demand for Transcendental Genetic Conditions – the belief in “substance”, in “matter”, in the earth-residuum, and particle-atom’.27 By following Boscovich, Nietzsche does not want to claim that our material world is a mere delusion, appearance or representation. Instead, he intends to find the genetic principle of it all, a more rudimentary world of forces and affects, which allows organic forms and functions to develop and differentiate. He assumes a ‘pre-form of life’, that is ‘a kind of instinctive life’, in which a will has an effect upon another will, such that all mechanical events can subsequently be interpreted as effects of the will.28 Denying continuity between forces and causality as a mechanistic principle, Nietzsche explains the relation between forces as the effect of a will to power which acts at a distance. The principle of action at a distance (actio in distans) means that the will to power does not operate as a mediator of their interaction; rather the will to power is the difference or distance which brings about the differentiation of forces separated in space. Suppose, finally, we succeeded in explaining our entire instinctive life as the development and ramification of one basic form of the will – namely, of the will to power, as my proposition has it; suppose all organic functions could be traced back to this will to power and one could also find in it the solution of the problem of procreation and nourishment – it is one problem – then one would have gained the right to determine all efficient force univocally as – will to power. The world viewed from inside, the world defined and determined according to its ‘intelligible character’ – it would be ‘will to power’ and nothing else.29

Hence, according to this ontology there are two ways of regarding the same world. The world as we know it consists of organic processes and definite entities (subjects and objects). The ‘inner world’, or the world on a micro-level, however, is nothing but the will to power, that is a differential complex of forces and discharges of force endowed with the potential of creation. The will to power is never unitary but multiple. According to Nietzsche, ‘there are treaty drafts of will (Willens-Punktuationen) that are constantly increasing and losing their power’.30 The composition of forces changes and new ‘centres’ and ‘nodes’ are formed. A new arrangement of forces is achieved by the interference of chance that brings new forces into relation and the effect of the will to power which is the differentiating and determining principle of this relation (cf. NP 53/60). The will to power is a necessary addition to the concept of force. According to Deleuze, there needs to be an ‘internal will’ (NP 51/57), an internal 83

conditions of thought: deleuze and transcendental ideas element without which the relations of forces would remain indeterminate. One of the key quotations that Deleuze considers to be essential for the interpretation of the will to power is the following: The victorious concept ‘force’, by means of which our physicists have created God and the world, still needs to be completed: an inner will must be ascribed to it, which I designate as ‘will to power’, i.e., as an insatiable desire to manifest power; or as the employment and exercise of power, as a creative drive, etc.31

However, the crucial part ‘an inner will must be ascribed to it’ is based on an error, that is a ‘correction’ that was made by Peter Gast who together with Nietzsche’s sister Elisabeth Förster-Nietzsche prepared Nietzsche’s handwritings for the print version. The original line goes ‘an inner world must be ascribed to it’. Deleuze could not have known of this error, since he used the French translation by Geneviève Bianquis (1935 and 1937), which relies on the Musarion edition, in which this error was not yet changed back to the original line.32 However, we do not believe that Deleuze’s argument depends substantially upon this typographical error. The main statement remains that ‘the world viewed from inside’ is nothing but the will to power.33 Deleuze’s interest in Nietzsche’s will to power arises in the context of the philosophical project of a radical critique. Taking up Nietzsche’s method of dramatisation, Deleuze wants to relate thought, that is our concepts and values, to the type of forces that stipulate their meaning. To dramatise a concept or value means to pose the question ‘Who speaks?’, that is to relate the concept or value to a will to power. It is important to grasp that in Deleuze’s reading of Nietzsche, the will to power is not a personal will, but an internal, genetic element which is capable of determining the relations of forces from a double point of view: ‘the reciprocal genesis of their difference in quantity and the absolute genesis of their respective qualities’ (NP 51/57). Deleuze draws on mathematical analysis and the formulation of the differential calculus to explain the issue. The will to power is added to force as the internal principle of the determination of its [the force’s] quality in a relation (x 1 dx) and as the internal principle of the quantitative determination of this relation itself (dy/dx). (NP 51/58)

The mathematical symbols dy and dx represent ‘differentials’, that is infinitely small values on the point of vanishing. The first 84

The Demand for Transcendental Genetic Conditions important point to notice is that the elements dx and dy do not represent quantities with assignable values, since they are smaller than any assignable value. Now, Deleuze describes two kinds of relations. (1) Given an arbitrary quantity x the synthesis of a differential dx is possible, which is in a variable relation to x. The synthesis of x and dx represents a quality, that is a difference of quantities that is not measurable. (2) The relation between the differentials dx and dy is slightly different: it relates two infinitely small variable quantities, which cannot be measured and are thus completely indeterminate when considered in isolation. Yet, through their relation (dy/dx) their values are reciprocally determined. Furthermore, it is important to note that the relations between dx and dy, and between dx and the variable x, are not relations which are external to their terms. Instead, the relations and elements are inseparable from each other. In other words, the relations are internal, that is included in each element. The crucial point, however, lies in the generative power of differentials. Given the ratio dy/dx, there is a procedure (called integration), which allows us to generate the primitive function, that is the function from which the ratio dy/dx is differentiated. This process of generation can be interpreted as involving a change of order: from the sub-representational differential order to the order of actual quantities and their relations, which are represented by the primitive function. Deleuze sees in the mathematical procedure of integration (the generation of primitive functions from differentials) a model to explain the nature of the transcendental in philosophy. He will conceive a kind of ‘transcendental function’, which by virtue of the reciprocal determination of its sub-representational differential elements, generates thought (concepts and values) and real experience alike.34 This will be the fundamental theme in Difference and Repetition, where Deleuze presents his transcendental empiricism. However, we can say that in Nietzsche and Philosophy, Deleuze’s demand for a transcendental genetic principle already finds an early expression in his reading of Nietzsche’s will to power. It is true that in Difference and Repetition, the model of differential calculus takes up a large part of Chapter Four, while in his book on Nietzsche, Deleuze deals only briefly with differential calculus, his remarks remaining only suggestive. Nevertheless, Deleuze does make use of the mathematical model of differentials, their internal relations and generative power to formulate Nietzsche’s theory of forces. According to Deleuze’s reading of Nietzsche, there exists a multiplicity of forces, which are related to one another through their differences and which constitute 85

conditions of thought: deleuze and transcendental ideas an inner, genealogical and differential element. Where force acts upon force, there is will to power. This is what the will to power is; the genealogical element of force, both differential and genetic. The will to power is the element from which derive both the quantitative difference of related forces and the quality that devolves into each force in this relation. The will to power here reveals its nature as the principle of the synthesis of forces. In this ­synthesis – which relates to time – forces pass through the same ­differences again or diversity is reproduced. (NP 50/56)35

We have not yet encountered the relation to time which is mentioned here. According to Deleuze, the temporal dimension is a necessary complement to the will to power. Using Nietzschean terminology, Deleuze equates this temporal dimension with the ‘eternal return’: the eternal return is a principle of selection, which puts the differential relations of forces to the test of time. Certain constellations of forces are fit to return, while others are expelled by the selection of the eternal return. What comes back is that which affirms difference and becoming; what is doomed to disappear is that which contradicts affirmation, that is nihilistic forms of the will to power, forces of reaction. The eternal return carries out the synthesis of forces and ensures ‘the reproduction of diversity at the heart of synthesis’ (NP 52/58), while the will to power is the differential and genetic principle of the synthesis of forces. They are both linked together like Nietzsche’s divine couple Ariadne/ Dionysus.36 The will to power is Dionysian becoming: it is the first affirmation, that is the creation of new values and possibilities of life, which render life light and active. But this first affirmation is in need of a second affirmation; that is to say, only as the object of a second affirmation can becoming affirm its being: ‘Dionysian becoming is being, eternity, but only insofar as the corresponding affirmation is itself affirmed’ (NP 187/215). Ariadne is this second affirmation. As Nietzsche says: ‘That everything recurs is the closest approximation of a world of becoming to a world of being’37 – this eternal recurrence is the wedding ring of Ariadne. It should be noted that the eternal return does not mean the reproduction of the same, but of diversity, of that which differs from itself and from other forces (NP 46/53). Identities are destroyed and abolished, and only becoming is affirmed (DR 41/59). In other words, identity in the eternal return does not describe the nature of that which returns but, on the contrary, the fact of returning for that 86

The Demand for Transcendental Genetic Conditions which differs. This is why the eternal return must be thought of as a synthesis; a synthesis of time and its dimensions, a synthesis of diversity and its reproduction, a synthesis of becoming and the being which is affirmed in becoming, a synthesis of double affirmation. (NP 48/55)

Much more can certainly be said on Deleuze’s interpretation of the eternal return. But since the theme of the eternal return will be taken up in Chapter 4 of this book, we will now focus here on the surprising formula of the will to power as a principle of the synthesis of forces. Deleuze’s explanation of the will to power as a principle of the synthesis of forces is a decisive move which puts Nietzsche explicitly in line with Kantianism. In fact, Deleuze believes that there is in Nietzsche, not only a Kantian heritage, but a half-avowed, half-hidden, rivalry [. . .]. Nietzsche seems to have thought (and to have found in the ‘eternal return’ and the ‘will to power’) a radical transformation of Kantianism, a re-invention of the critique which Kant betrayed at the same time as he conceived it, a resumption of the critical project on a new basis and with new concepts. (NP 52/59)

In the following section, we will shed light on this alleged Kantianism in Nietzsche. We will examine how Nietzsche overturned the Kantian account of transcendental conditions, which define what counts as an object for us and thus bestow sense or signification. Against the Kantian account, which remains one of external conditioning, Nietzsche proposes a principle of internal genesis. Nietzsche’s will to power generates the particular senses and values of phenomena by relating them to a complex of forces, to vital ­dynamisms immanent to the world. First Traces of a New Transcendental In the first edition of the Critique of Pure Reason, Kant describes three syntheses, which constitute the possibility of experience: the synthesis of apprehension in the intuition, the synthesis of reproduction in the imagination and the synthesis of recognition in the concept. These syntheses all culminate in the third synthesis of recognition, which yields the cognition of the form of an unspecified object as a correlate of the formal unity of consciousness (‘I think’). The task of the a priori concepts of the understanding is to bring about synthetic unity in the manifold of intuition. Kant’s transcendental concepts have thus the same function of providing unity as do Aristotle’s categories in the realm of logic: 87

conditions of thought: deleuze and transcendental ideas The same function that gives unity to the different representations in a judgment also gives unity to the mere synthesis of different representations in an intuition, which, expressed generally, is called the pure concept of the understanding. (CPR A 79/B 105)

However, since Kantian categories seek to capture the world of experience, Kant finds himself confronted with a particular difficulty: the manifold of intuition cannot be brought directly under the synthetic unity a priori. The synthetic unity a priori only applies to a unity of pure intuition (a pure unity of space and time). The intermediary of pure intuition is supposed to mediate between the particular (real experience) and the abstract, transcendental concept of an ­unspecified object, constitutive of the possibility of experience. It was the achievement of the post-Kantians to point out that the Kantian transcendental concepts cannot be applied to the diversity of real experience (neither directly nor through any mediation). Nietzsche is a post-Kantian in this sense. He criticises principles for being too large or too abstract in relation to what they condition. For instance, he condemns Schopenhauer’s metaphysical ‘will’, which is outside the order of space and time and which expresses itself in every phenomenon according to different degrees of objectification. This will is ‘a mere empty word’ because ‘one has eliminated the character of the will by subtracting from it its content’.38 Equally, the Kantian transcendental concepts are too abstract: the signification of the form of an unspecified object cannot be related to the senses and values of particular experiences. Contrary to Kant’s transcendental conditions, Nietzsche’s ‘will to power’ clings to real experience. The will to power wants this relation of forces, this quality of forces. This is why the will to power is not larger than what it conditions. Nietzsche introduces the concept of plasticity in order to express the intimate relation between the condition and the conditioned, which is one of internal genesis. The important thing to grasp is that the condition itself does not remain unaffected by what it conditions. In other words, it is determined at the same time that it determines. The will to power varies with the relations of forces that it produces and can therefore be called an immanent and ‘plastic’ principle: As plastic element it simultaneously determines and is determined, simultaneously qualifies and is qualified. What the will to power wills is a particular relation of forces, a particular quality of forces. And also a particular quality of power: affirming or denying. This complex, which varies in every case, forms a type to which given phenomena correspond. 88

The Demand for Transcendental Genetic Conditions All phenomena express relations of forces, qualities of forces and of power, nuances of these qualities, in short, a type of force and will. (NP 85/97)

Depending on the particular quality of the synthesis of forces that the will to power effectuates, the will to power is either affirmative or negative. This means that the synthesis of forces can result in a configuration in which the active forces prevail over the reactive forces, or else one in which the reactive forces form units and prevent the active forces from acting out. The quality of the first configuration is affirmative, whereas the triumph of the reactive forces is the symptom of a negative or nihilistic will to power. Another essential characteristic apart from the plasticity of the will to power is its creativity. The will to power produces the sense and value of phenomena. In other words, the will to power ‘interprets’ – it bestows a fresh interpretation by imposing a new purpose ‘through which any previous “meaning” or “purpose” are ­necessarily obscured or even obliterated’: Purposes and utilities are only signs that a will to power has become master of something less powerful and imposed upon it the character [Sinn] of a function; and the entire history of a ‘thing,’ an organ, a custom can in this way be a continuous sign-chain of ever new interpretations and adaptations, whose causes do not even have to be related to one another but, on the contrary, in some cases succeed and alternate with one another in a purely chance fashion.39

Things are signs or symptoms of relations of forces. Their history can be read as a ‘continuous sign-chain’ whereby the various chain links are the results of ‘combats’ between forces. These combats should not be read as combats-against, but rather combats-between forces.40 These are processes through which forces augment their power by appropriating other forces, which agree with them, thereby forming a new composition or intensive compound of forces. There is no final end, no ultimate goal to such processes; it is an infinite becoming. The evolution of a thing is therefore not a progress towards a goal but a succession of processes of attempted transformation, resistance and appropriation inflicted on the thing. ‘The form is fluid, but the “meaning” [Sinn] is even more so.’41 Hence the true essence of a thing is neither a transcendent intelligible being nor an abstract signification constituted by external transcendental conditions, but rather the outcome of an infinite process of sense-production. Truth is the limit object of a production 89

conditions of thought: deleuze and transcendental ideas of sense. We should mention, however, that the characterisation of truth as the limit of a genetic series, which constitutes sense, is already an addition that Deleuze introduces in Difference and Repetition and which is a result of his involvement with differential calculus as a technical model for internal genesis and creation (cf. DR 154/200). However, the concept of limit provides a helpful tool for the interpretation of Nietzsche, who defines truth as an infinite process and an active determination, that is as creation: ‘Truth’ is therefore not something there, that might be found or ­discovered – but something that must be created and that gives a name to a process, or rather to a will to overcome that has in itself no end.42

We have finally come to the point where we can consider Deleuze’s thesis of a peculiar Kantianism in Nietzsche. The Kantian transcendental conditions are supposed to function as principles of synthesis bringing unity to the manifold of intuition. The relation of transcendental concepts to intuition is essential, because otherwise the pure concepts would remain entirely empty, that is without content and hence without signification. However, the signification they constitute remains rather abstract, namely the signification of a possible object of experience. Now, Nietzsche’s will to power is supposed to function also as a principle of synthesis. However, the synthesis is not between concepts and intuition, but between active and reactive forces. The will to power is a creative principle: it creates the particular senses and values of phenomena. It is therefore a genetic principle of real experience, not of possible experience. The differences between Kant’s and Nietzsche’s accounts are perfectly obvious. While Kant adheres to a model of external conditioning, Nietzsche allows for a model of internal genesis. While Kant’s transcendental conditions are abstract, universal and invariant, Nietzsche’s will to power is plastic and changing. According to Deleuze, the will to power is ‘a good principle’: This is because it is an essentially plastic principle that is no wider than what it conditions, that changes itself with the conditioned and determines itself in each case along with what it determines. (NP 50/57)

The principle of the will to power constitutes a ‘superior empiricism’ (NP 50/57). Therefore it deserves to be called ‘transcendental’, provided that we accept a change in the meaning of the term ‘transcendental’. But why should Kant have the final definition and exclusive authority over his invention of the transcendental? According to 90

The Demand for Transcendental Genetic Conditions Deleuze, philosophical concepts are usurped and appropriated time and again in the history of philosophy. In fact the history of philosophy is completely without interest if it does not undertake to awaken a dormant concept and to play it again on a new stage, even if this comes at the price of turning it against itself. (WP 83/81)

In Difference and Repetition, Deleuze will call his philosophy a ‘transcendental empiricism’, and without doubt his transcendental incorporates the characteristics of Nietzsche’s plastic principle of the will to power. However, in Nietzsche and Philosophy, Deleuze still draws back from this appropriation of the term ‘transcendental’. He says that when he compared the will to power with a transcendental principle, his aim was to point out the difference from psychological determinations (NP 91/104). ‘Nevertheless, in Nietzsche, principles are never transcendental’ (NP 91/104). This means that there are irreducible differences between Nietzschean and Kantian principles. Yet, it can be said that Nietzsche paved the way for Deleuze’s transcendental, which will be further explored in the course of this book. As a final note to the first part of this chapter, we would like to point out two features that can be regarded as unfortunate with respect to Nietzsche’s concept of the will to power. The first is expressed by the temptation to interpret the will to power in terms of a personal, psychological will. Although Deleuze and, indeed, Nietzsche himself provide many reasons to abstain from this interpretation, there is still a need to clarify the ‘objectivity’ of the will to power as a transcendental and genetic principle. Deleuze will find an adequate solution in the Maimonian term of differential Ideas, which are defined as ‘objectivities’. The second difficulty with the concept of the will to power concerns the question of its status with regard to our conscious representations (concepts, senses and values of things). It seems that the will to power is necessarily sub-representative: it designates the ‘inner world’ of the world we see, remember, imagine and conceptualise. However, what is still lacking is an adequate expression to mark the heterogeneity and distinctness of the will to power from the world of actual objects and common values. In this regard, Bergson’s concept of the virtual will provide the terminological means to describe the ‘world as seen from inside’. In connection with the concept of Idea, we will thus gain the concept of virtual Ideas, which Deleuze 91

conditions of thought: deleuze and transcendental ideas will introduce as differential and genetic principles for the sense of ­phenomena, for values and concepts of thought.

Maimon’s Essay on Transcendental Philosophy Deleuze’s ambition to substitute for Kant’s account of external conditioning a model of internal genesis whose conditions are not larger than what they condition led him to appreciate the philosophy of Salomon Maimon (1753–1800). Maimon was the first philosopher ‘to pass from a transcendental philosophy to a genetic one’.43 Unfortunately, Maimon has been a rather marginalised figure in philosophy and his extensive philosophical work, which comprises several books, commentaries and journal articles, has been unduly neglected. Although Maimon’s astute mind and talents were acknowledged by prominent philosophers of his day (e.g. Kant and, in particular, Fichte), he never quite received the attention that he deserved.44 One reason might be the prevalent anti-Semitism in his time. Given his social background as an Eastern European Jew born into an impoverished family and his unusual career as a self-taught philosopher, Maimon had to face many prejudices.45 A further reason for being unduly neglected might be the intricacy and obscurity of his philosophical thought, which at least in part resulted from his unusual style of writing. As Gideon Freudenthal points out, Maimon was educated in the Talmudic tradition and was used to writing commentaries, a genre which essentially differs from the systematic form of philosophical discourse common in the western world.46 Samuel Atlas suggests that the grandeur and splendour of Fichte, Schelling and Hegel and their metaphysical systems simply overshadowed Maimon’s philosophical investigations.47 For these and maybe other reasons, Maimon has not received appropriate attention until this day. Deleuze is one of the few philosophers who did recognise Maimon’s achievements, although he does not dwell extensively on Maimon – in Difference and Repetition, he only devotes a few pages to him. However, Maimon’s name is mentioned explicitly in many of Deleuze’s books, essays and seminars, and traces of Maimon’s thought can be found throughout Deleuze’s work.48 Deleuze takes a particular interest in Maimon’s Essay on Transcendental Philosophy (1790), where Maimon laid out his criticism of Kant’s transcendental philosophy and suggestions as to how to improve it. Rejecting the Kantian viewpoint of external conditioning, Maimon develops 92

The Demand for Transcendental Genetic Conditions a model of internal genesis based on the concept of ‘differentials’, which he defined as ‘Ideas of the understanding’. Maimon’s theory of differentials is inspired by the mathematical model of differential calculus. Deleuze shares Maimon’s interest in the differential calculus, and he acknowledges that by means of the model of differential relations, a new concept of difference and of internal relation is thought. Maimon developed the concept of ‘intrinsic difference’ (already adumbrated in Leibniz), that is difference as a positive, internal quality, which does not merely result from external limitation or determination.49 This intrinsic difference is fundamental insofar as any difference (spatio-temporal, quantitative or qualitative) can be traced back to this kind of difference. As Nick Midgley says, Maimon is committed to a ‘univocity of difference’.50 To this extent, Maimon already paved the way for a philosophy of difference, where difference is conceived as the sufficient reason or genetic (material) principle of the real.51 Surprisingly, there hardly exists any scholarship on the Maimon– Deleuze nexus. In the last two years, only a few book chapters on this topic have been published by Graham Jones, Daniel Smith and Beth Lord respectively.52 In addition, the Maimon–Deleuze nexus is discussed briefly in the three monographs on Deleuze’s transcendental empiricism authored by Levi R. Bryant, by Christian Kerslake and by Anne Sauvagnargues.53 Maimon’s Challenge to the Kantian Categories Maimon’s rethinking of Kantian transcendental philosophy does not aim to dismantle it, but on the contrary, to improve it by introducing Leibnizian elements. Maimon seeks to overcome the Kantian dualities between understanding and sensibility, concept and intuition, and form and matter. Naturally, Kant himself could not approve of this project, which undermines his basic tenet of the heterogeneity of the two sources of human knowledge, receptive sensibility and active understanding, a tenet that he basically intended to ward off dogmatic idealism from his transcendental idealism. In The Critique of Pure Reason Kant issued an attack against Leibniz for treating sensibility and understanding as a single cognitive faculty that is distinguished only in terms of the clarity of the representation.54 Leibniz, he said, ‘conceded to sensibility no kind of intuition of its own, but rather sought everything in the understanding, even the empirical representation of objects, and left nothing for the senses 93

conditions of thought: deleuze and transcendental ideas but the contemptible occupation of confusing and upsetting the representations of the former’ (CPR A 276/B 332). Thus sensibility, for Leibniz, is just an inferior confused mode of cognition and not a special source of representations (CPR A 271/B 326). Consequently, Leibniz allowed only conceptual differences between things. While for Kant space and time are irreducible forms of sensible intuition, Leibniz defined them as ‘outer’ relations that have their ground in something absolutely internal (CPR A 285/B 341). That is, space and time must be reducible to inner conceptual determinations contained in the concepts of purely intelligible things. These intelligible things, or things in themselves, are entirely thought without any schema of sensibility (CPR A 286/B 342). Only a sort of non-sensible or intellectual intuition, that is ‘an entirely different intuition and an entirely different understanding than our own’ (CPR A 287/B 344) can have this immediate access to things in themselves. Although Kant does not state it explicitly at this point, he refers to the notion of an intuitive intellect, which does not require ‘schemas’ or ‘sensible images’ of space and time in order to represent objects. Instead, an intuitive intellect entertains a direct relationship with objects, in the sense that the very act of intuiting produces them at the same time (CPR B 139, B 145). After having read the Essay on Transcendental Philosophy, Kant responded to Maimon’s criticism with the accusation that Maimon assumed precisely such an intuitive intellect as ‘the originator [Urheber] not only of sensible forms but also of their matter, i.e. of objects’.55 For Kant, the idea of an intuitive intellect is absurd, ‘since we are acquainted with no sort of intuition other than our own sensible one and no other sort of concepts than the categories’ (CPR A 287/B 343). Kant insists that our human understanding is discursive and not intuitive. It relies on something given to the senses, that is a spatio-temporal manifold of intuition to which it can relate its categories. If we abstracted from sensibility, that is the manner in which objects are given to us, then our concepts of understanding would have no relation at all to any sort of object. ‘Without the data of sensibility they would be merely subjective forms of the unity of the understanding, but without any object’ (CPR A 287/B 343). For Kant, understanding and sensibility are two entirely different sources of representation, ‘which could judge about things with objective validity only in conjunction’ (CPR A 271/B 327). Therefore a special act of synthesis is required through which a manifold of intuition is united in accordance with the a priori representation of an object in 94

The Demand for Transcendental Genetic Conditions general. In Kant, this transcendental synthesis of apperception is the supreme principle of all use of our understanding. For Maimon, on the contrary, the conjunction of form and matter, or concept and intuition, in an a priori synthesis remains incomprehensible, given that they stem from completely independent and heterogeneous faculties. His sceptical challenge can be summarised in his doubts about Kant’s solution to the question quid juris?: by what right do a priori concepts apply to something given in intuition? Kant addresses this problem in the Transcendental Deduction, as well as in his chapter on the Schematism of the pure concepts of the understanding. In a first step (CPR §§15–21) he tries to prove the objective validity of the categories, that is their being necessary conditions for the possibility of objects in general.56 Kant argues that the categories are objectively valid because without them I would not have cognition of any objects at all, not even of my own mental state. In a second step (CPR §§24–6) Kant goes on to prove the objective reality of the categories. That is to say, Kant explains how it is possible that a priori concepts necessarily relate to intuition. He argues that a priori concepts are not applied to empirical intuition directly (as this would beg the question quid juris?), but to pure intuition, namely space and time. As pure intuition is given a priori, the question quid juris? appears to be solved. Kant concludes that the categories are applicable to actual or empirical objects through ‘schemas’ or a priori spatio-temporal marks of the object. Strictly speaking, the claim of objective reality of the categories includes two claims: (1) the capacity of pure concepts to be applied to real (i.e. given spatiotemporal, yet a priori) objects, and (2) through this mediation to actual objects of experience.57 Maimon’s rejoinder is very complex. He pursues several lines of attack. The focus of his objections, however, lies on the objective reality of the categories, whereas he is willing to admit their objective validity, at least to some extent. In reconstructing Kant’s argument for the objective validity of the categories, Maimon appeals to a regressive transcendental argument starting from accepted facts of knowledge, such as the one that Kant presents in the Prolegomena.58 Unfortunately, he does not take into account Kant’s attempt in the Critique of Pure Reason to put forth a progressive transcendental argument that proceeds from ground to grounded, that is without presupposing the fact of objective experience. The regressive ­transcendental argument can be reconstructed as follows:59 95

conditions of thought: deleuze and transcendental ideas 1. Without the objective validity of the categories, there would be no objective experience (that is a universal and necessary connection between distinct representations) for us. 2. But objective experience does exist. 3. So, the categories of the understanding are objectively valid.60 Since Maimon doubts the second premise, he cannot concede the objective validity of the categories. Thus he only grants a hypothetical validity: the categories are objectively valid if the fact of synthetic a priori judgements is true. Maimon’s qualms, however, begin with Kant’s claim of the objective reality of the categories.61 Maimon can be said to pursue an ‘external’ and an ‘internal’ approach to the problem. The external approach consists of taking sides with Hume and doubting that there are any facts of ‘objective experience’ defined as a universal and necessary interconnection between representations. At least, we cannot know of any such fact, since we have no justifiable criterion with which to determine whether a given manifold can be thought in a synthetic a priori unity, still less a criterion in which unity this manifold could be thought.62 That is to say, we lack any a priori or a posteriori criterion. For instance, in response to the question to which case does the synthetic a priori concept of causality apply, we are unable to provide an a priori criterion. It might appear that the irreversibility of a temporal sequence can provide a criterion for its objectivity, since in this case the succession of representations ensues in accordance with a necessary rule. But ‘irreversibility’, as Maimon argues, cannot be detected either a priori or a posteriori. Mere perception leaves the question of an objective, i.e. irreversible, order between the successive representations undetermined, since all our representations (subjective or objective as they may be) are equally apprehended in a successive order of before and after, and there is no means to decide which of them is just subjective and which of them objective. That is to say, we cannot go back in time and prove that the succession of our representations was merely arbitrary and could have been represented in a reversed order, although we might very well imagine such a thing. But ‘then this reversed order of succession must happen in another time than the preceding one so that in each time only one kind of succession can be actual’.63 Thus the irreversibility of a sequence, i.e. the claim that the reversed order of succession is impossible, can never be shown with regard to a 96

The Demand for Transcendental Genetic Conditions particular perception. As Hume has argued, there can in principle be no inference from the subjective order of sensations to an objective order of states of the world. This means, however, that the evidence of our sensory perceptions can testify at most to a constant conjunction between distinct representations, but never to a universal and necessary interconnection.64 Maimon concludes that we do not have any criterion for deciding whether a particular succession of representations occurs in conformity with a necessary rule. Furthermore, even if we could somehow make out an objective, irreversible order of succession, we would not know whether the determining rule is the a priori concept of causality which prescribes a unilateral determination (a relation of subordination) or, for instance, the a priori concept of community which prescribes a reciprocal determination (a relation of coordination). That is to say, it would remain undetermined under which concept the manifold of representations can be brought. However, this line of attack, which is based on the question quid facti? (‘Are there any synthetic a priori judgements in experience?’), cannot undermine the deduction of a priori concepts in Kant’s Critique, though it might well be a valid objection with regard to Kant’s Prolegomena. In the Prolegomena Kant presupposes the fact of necessary truths in mathematics and pure science and then goes on to infer the objective validity of the categories. In the Critique of Pure Reason, Kant also suggests the factual existence of a priori synthetic propositions with regard to mathematics and pure physics. He admits, however, that these facts of a priori synthetic propositions can only serve an illustrative purpose; they cannot contribute to the deduction, since the deduction has to take place on a transcendental level.65 Hence, Kant demands not the factual existence, but the possibility of the factual existence of objective experience, that is he attempts to show that the categories can be applied to intuition. In order to counter Kant’s deduction, Maimon has to prove that pure a priori concepts are incapable of determining intuition. This is the second line of attack pursued by Maimon. It can be called an ‘internal’ approach, since Maimon’s argument affects Kant’s proof of the objective reality of the categories from within. Maimon asks: ‘How can an a priori concept apply to an intuition even to an a priori intuition?’66 The crucial point of divergence between Maimon and Kant concerns the notion of pure intuition. As Midgley remarks 97

conditions of thought: deleuze and transcendental ideas in his Introduction to Maimon’s Essay: Maimon ‘claims that either there is no pure intuition, or to the extent that there is, it cannot fulfil the function Kant demands of it.’67 For Kant, the question concerning the possibility of the synthesis of a priori concepts and pure intuition does not arise, for both concepts and pure intuition are a priori. That is to say, pure intuition (time and space) does not simply belong to intuition; as the formal element of intuition it cannot be derived from anything given in perception and is therefore an a priori feature of cognition.68 It can thus fulfil the role of a mediating representation between intellectual concepts and sensible intuition. Maimon objects that inasmuch as pure intuition is still conceived as given (namely as formal intuition), the synthesis of concepts (thought relations) and intuition (given material) remains incomprehensible.69 His main concern, however, bears on the conception of pure intuition itself. The Problem with Pure Intuition According to Kant, pure intuition comprises not only space and time as ‘forms of intuition’ but also ‘formal intuition’.70 Kant claims that through a method of abstraction, it is possible to isolate and have access to the formal properties of an object given in intuition. First one needs to remove from the representation of an object everything that the understanding thinks about it through its concepts, and then all sensory content of empirical intuition. What remains is formal intuition, that is the extensive magnitude (extension and figure) of the determinate, represented object (CPR A 20–1/B 35). Kant argues that space and time have a content of their own, pure matter or extensive magnitude, which is logically independent of and ­irreducible to concepts and empirical intuition. The role of formal intuition is crucial for Kant’s purpose in the Transcendental Deduction. By means of ‘formal intuition’, Kant wants to explain how it is possible that a priori concepts relate to a posteriori intuitions. The significance of ‘formal intuition’ for Kant’s argument is underlined by the fact that he introduces the distinction between ‘forms of intuition’ and ‘formal intuition’ only in §26 of the Transcendental Deduction, where he seeks to prove the objective reality of the categories. There he wants to show that the categories are not only conditions of the possibility of experience, but are also valid a priori of all objects of experience. Kant argues: 98

The Demand for Transcendental Genetic Conditions 1. Space and time are not only forms of intuition but also formal intuitions. 2. Formal intuition contains a pure manifold that is combined in a unity (the unity of a determinate, extensive magnitude). 3. The unity of formal intuition presupposes a synthesis (a pure synthesis of apprehension), which neither belongs to the senses, nor to the understanding. 4. The pure synthesis of apprehension is performed by the faculty of imagination in agreement with the categories, that is in agreement with the synthesis of apperception. Consequently: 5. All synthesis, through which even perception itself becomes ­possible, stands under the categories (CPR B 161). This is how Kant attempts to show that the categories determine intuition, though not directly but through the mediation of formal intuition. In the case of mathematics, the formal intuition required is space, which is the determinable matter to be synthesised according to concepts. In transcendental metaphysics, the formal intuition, upon which the synthesising activity can act, is time. In his chapter on Schematism, Kant elaborates time as a ‘third thing’ or ‘mediating representation’ (CPR A 138/B 177), which renders the synthesis of a priori concepts and a posteriori intuition possible. The result of the synthesis of apperception, that is the synthesis under categories, is objective experience or ‘real objects’. Let us look, however, more closely at the synthesis of apprehension, that is the synthesis of the imagination, which brings about cognition (albeit raw and confused, cf. CPR A 77/B 103), that is a combination of a given manifold in one intuition. As we have already mentioned, if this manifold, which is brought into a unity, is pure space and time, the product of this synthesis is ‘formal intuition’. Maimon doubts that such a pure synthesis of apprehension can be conceived consistently. His main argument is that difference is a necessary feature of any synthesis (a synthesis being a ‘unity of difference’), that is to say without difference there can be no synthesis.71 In a first step, Maimon refutes Kant’s claim that we can conceive an empty uniform space (or time), that is an absolute, continuous and homogeneous spatial (or temporal) whole.72 According to Maimon, absolute space, absolute movement and the like are fictions or imaginary beings (ens imaginarium) produced by the faculty of imagination, which imagines something as absolute, although it exists only 99

conditions of thought: deleuze and transcendental ideas in relation to something else.73 Thus we can only imagine such a thing as an empty uniform space, because we unconsciously relate it to differentiated sensible representations, for instance a manifold of distinct objects. He provides the following example:74 a river can be imagined as a continuous and homogeneous body of water whose parts are indistinguishable. Yet Maimon insists that we can only represent it to ourselves as such, because we refer the water to distinct objects on the river’s bank. If there were no distinct objects, the parts of the river would be indistinguishable. Maimon resorts to Leibniz’s principle of indiscernibles, arguing that if there is nothing to distinguish parts or points quantitatively or qualitatively, these parts or points are identical. Hence the supposed extensive magnitude of a continuous and homogeneous field (the river, for example) would collapse and shrink to nothing.75 The representation of space as a continuous and homogeneous whole ‘lacks the diversity that is required to see things apart from one another’.76 Maimon’s example of the river shows that it is impossible to distinguish and identify ‘parts’ of an indeterminate, continuous and homogeneous whole, be it space or time.77 It follows that a synthesis of a pure spatiotemporal manifold, in which the elements are indistinguishable, is impossible. Kant simply assumes a pure manifold of space and of time, which can be synthesised to determinate and measurable extensive magnitudes (cf. CPR A 77/B 103). But how are we supposed to conceive a pure synthesis of homogeneous spatial or temporal parts that are indeed indistinguishable? The notion of formal intuition (allegedly being the result of a pure synthesis) looks suspiciously inconsistent. The Kantian pure synthesis of apprehension is a fiction just as the representation of an empty uniform space or time. Kant models the pure synthesis of imagination on an empirical synthesis of already spatially or temporally differentiated representations (for instance, the synthesis of a particular triangle from three given lines). He misses the point that a synthesis of a pure spatial or temporal manifold in one (formal) intuition is indeed impossible. But what if we assume for a moment that a synthesis of pure intuition is somehow possible. Kant admits that synthesis in general proceeds obscurely: Synthesis in general is [. . .] the mere effect of the imagination, of a blind though indispensable function of the soul, without which we would have no cognition at all, but of which we are seldom even conscious. (CPR A 78/B 103) 100

The Demand for Transcendental Genetic Conditions For Maimon, even if such an obscure synthesis occurs it cannot constitute a solution to the problem: the unity of a pure spatial or temporal manifold (i.e. formal intuition) would be given to the understanding but not produced by it.78 According to Kant, the unity that belongs to formal intuition is the product of a pure synthesis of apprehension, which belongs neither to the senses nor to the understanding. As Kant says, the unity of space and time ‘precedes all concepts’ (CPR B 161). Formal intuition is the product of a synthesising activity of the imagination, which is performed only in agreement with the categories, that is in agreement with the synthesis of apperception (i.e. the synthesis of the understanding). It still remains ‘to bring this synthesis to concepts [which] is a function that pertains to the understanding’ (CPR A 78/B 103). Therefore it seems as if the pure synthesis of the spatio-temporal manifold is given to the understanding qua synthesis, that is as a product of the imagination, before the understanding has intervened at all. Maimon objects that inasmuch as formal intuition is still conceived as given, the synthesis of pure concepts and intuition remains incomprehensible. The legitimacy or truth of the application of pure concepts to intuition has not been shown.79 Thus Maimon cannot agree with Kant’s solution to the problem quid juris? Kant tries to fill the gap between thought concepts and given intuition by the intermediary of formal intuition. But formal intuition cannot fulfil the function that Kant ascribes to it. Does Maimon’s criticism of formal intuition (as a synthesised whole from homogeneous spatio-temporal parts) compel him to reject the possibility of geometry and mathematical natural science? Both sciences depend upon the possibility of determining measurable spaces and times, and both claim a pure a priori status (that is to say, they allegedly abstract from empirical representation). Maimon denies these sciences a pure a priori status, but he does not deny them their possibility as sciences. Although they cannot claim apodictic certainty, they can nonetheless claim assertoric certainty (i.e. a high degree of subjective necessity, which approaches the idea of objective necessity).80 Maimon defines geometry and mathematical natural science as ‘real thought’, that is a creative thought which generates real objects or new determinations of objects through rules of construction. The crucial point is that Maimon envisages a new conception of synthesis, according to which synthesis is essentially genetic. Contrary to Kant’s view . . . 101

conditions of thought: deleuze and transcendental ideas the understanding does not subject something given a posteriori to its a priori rules; rather it lets it arise [läßt entstehen] in accordance with these rules (which I believe is the only way to answer the question quid juris? in a wholly satisfactory way).81

As we have seen, Kant assumes the pure synthesis of apprehension as already given to the understanding but not produced by it. The synthesis of apprehension acquires its objectivity, that is its objective significance or relation to an object, when it is brought under concepts (synthesis of apperception). This relation is one of subsumption or conditioning: the understanding subjects the activity of the imagination to its a priori rules. Maimon, by contrast, demands that the understanding itself produces the synthesis.82 The elements of synthesis must be wholly immanent within the understanding. In Maimon’s view, the question that Kant fails to solve is: ‘how can the understanding subject something (the given object) to its power (to its rules) that is not in its power?’83 This question would not come up if our understanding could produce objects out of itself according to its prescribed rules or conditions without needing to be given something from elsewhere.84

Maimon demands that both parts of the synthesis must equally be thought. Concepts and intuition, form and matter, must equally arise through an internal genesis from the understanding. The underlying idea is to dissolve the given into thought relations that precede any cognition of objects themselves.85 For instance, if we are able to conceive of space as a thought relation given prior to any extended objects, then we can eliminate space as determinable content, and the two parts of the synthesis, i.e. the determinable (space) and the determination (e.g. the determination ‘enclosed by three lines’), can be thought equally. The model that Maimon will use is that of differential calculus. In differential calculus, space is considered as a differential relation abstracted from all quantity, that is as an intensive magnitude (the quality of the quantum). In other words, extensive magnitude is reduced to its differential.86 From there Maimon develops the philosophical concept of ‘differentials’ as ‘real relations’, by means of which he will explain how the understanding produces, although in an obscure manner, space and time as extensive magnitudes. In the following section we will provide a short summary of the early phase of the calculus, in particular Leibniz’s differential calculus and Newton’s method of fluxions.

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The Demand for Transcendental Genetic Conditions The Mathematical Model of the Differential or Fluxional Calculus Leibniz and Newton are commonly said to be the founders of the differential calculus or calculus of fluxions, though it is more exact to say ‘that they gave to the infinitesimal procedures of their predecessors the algorithmic unity and precision necessary for further development’.87 Leibniz and Newton both benefited from the work of other mathematicians (such as Torricelli, Barrow, Wallis, Gregory and Fermat), but they were the first to establish a pragmatic set of universal rules for solving the problems under consideration. Apparently, Leibniz and Newton developed the rules of the calculus independently from one another, though there exists a large controversy accusing Leibniz of plagiarism.88 It is, however, plausible that both of them indulged in similar investigations, drawing on their common predecessors’ methods and applying these methods to their respective fields of study. While Newton was primarily interested in the physical phenomenon of movement and the rate of change of bodies in motion, Leibniz dealt with classical geometrical problems such as the problem of tangents and that of quadratures. Thus Newton’s calculus can be labelled as dynamic, inasmuch as Newton is concerned with the generation of variable quantities from points, lines and planes. He called the generated quantity a ‘fluent’ and the rate of change with which it varies a ‘fluxion’. For Newton, the fundamental problem of the calculus amounts to: the relation of quantities being given, to find the relation of the fluxions of these and conversely.89 Leibniz, by contrast, held a comparably static view of the calculus. He saw geometric quantities not so much as generated ‘fluents’, but rather as aggregates of infinitesimal elements.90 However, the algorithmic procedures, which both Newton and Leibniz codified, are very similar. More significantly, both men employed the idea of the infinitely small, a factor which enormously facilitated the operations required for the determination of gradients of curves or the computation of areas under curves. Yet it must be said that neither Newton nor Leibniz made a serious effort to clarify the conceptions they employed and to find exact logical definitions. They missed out on giving a clear interpretation of the meaning of the notion of the infinitely small. In the mathematical debate of their day, there was no consensus as to how to interpret the ontological status of differentials. This can clearly be seen with regard to the multitude of expressions that existed alongside one another 103

conditions of thought: deleuze and transcendental ideas and that contributed to a confusion of thought and metaphysical speculation. Differentials were designated as ‘ultimate differences’, ‘quantities smaller than any given quantity’, ‘qualitative’ or ‘relative zeros’, ‘ghosts of departed quantities’, ‘evanescent quantities’, ‘differences on the point of vanishing’ and ‘momentary increments’ or ‘­decrements of a flowing quantity’.91 With regard to Newton, the infinitely small is usually equated with his notion of ‘fluxions’. This is, however, not quite correct. As Carl Boyer points out, the infinitely small is rather what Newton designated as ‘evanescent increments,’ or ‘moments’ of a flowing quantity.92 The notion of fluxion is based upon some other idea, the idea of a limiting ratio of evanescent increments. A limiting ratio is defined as the limit of the ratio of two quantities decreasing until they approach zero. It is important to grasp here that fluxions were always considered as ratios. In this way, Newton tried to avoid dealing with the infinitely small, realising the lack of rigour involved in a naive view of infinitesimals: ‘I have sought to demonstrate that in the method of fluxions it is not necessary to introduce into geometry infinitely small figures.’93 Nevertheless, he could not completely expunge the infinitely small from his calculus, since the idea of the infinitely small enters in the form of the elements of his limiting or ‘ultimate ratios’. Thus, in the illustration of his method of fluxions, it becomes obvious that Newton could finally not elude the infinitesimal point of view that characterised seventeenth-century mathematical geometry. Leibniz, on the contrary, seems to have been less concerned with the notion of the infinitely small. He considers it a convenient fiction which allows the facilitation of mathematical operations. In Boyer’s words, ‘he felt that the calculus, as a modus operandi, brought its demonstrations with it.’94 This may be the reason why he did not believe it necessary to provide a clear and consistent account of the infinitely small, or what he calls ‘differentials’. In the beginning we see that Leibniz wavered in his attitude as to whether the differentials were to be regarded as quantities with assignable or with inassignable values (that is as merely very small quantities or quantities incomparably smaller than any given quantity). However, starting from the definition of differentials as finite quantities, he seems to have become more reckless with regard to the use of infinitesimal conceptions, since the success with which the infinitesimal procedures were met confirmed the validity of their use.95 In the following we will give a brief account of Leibniz’s differential calculus which 104

The Demand for Transcendental Genetic Conditions can serve as a basis for understanding the mathematical origin and use of the notion of differentials.96 In fact, it was Leibniz’s research on the theory of number sequences and his mathematical considerations on the nature of the infinite that led him to a discovery that was of great impact in the field of analytical geometry: the conception of infinite sequences of line segments, distinguished into ‘difference sequences’ and ‘sum sequences’. ‘Difference sequences’ comprise an ordered sequence of infinitely many terms with infinitely close values representing the continuous diminishing of a line segment. The differences between the terms of the sequence were considered infinitely or ‘incomparably’ small, that is smaller than any assignable interval and yet unequal to zero. In his letter to Varignon with a note on the ‘Justification of the infinitesimal calculus by that of ordinary algebra’ (1702), Leibniz also refers to differentials as ‘differences which are on the point of vanishing’. Hence in a mathematical context ‘differentials’ can be defined as these infinitely small differences between successive values of a continually diminishing quantity.97 What is the importance of the theory of infinite sequences of line segments for the study of curves? It was suddenly possible to interpret the curve as an infinite assemblage of infinitely small straight lines. In effect, this idea had already been developed by the ancient Greeks in an attempt to solve the problem of ‘squaring the circle’. According to the famous Archimedean-Eudoxan ‘method of exhaustion’ a polygon was inscribed inside a circle. By increasing the sides of the polygon to infinity, it was thought to approximate the curve and ultimately ‘exhaust’ its arc length. Thus a circle was considered an infinitangular polygon, whose sides are infinitely small and whose angles are infinitely many. In Leibnizian calculus this ancient method was put to use again. The line of the curve was thought of as identical with a broken line stretched toward the curve to infinity. The infinitely small straight segments of this broken line, if prolonged, were conceived as tangents to the curve, which could be determined by the ratio of the differences in the ordinates and abscissas as these become infinitely small. As Leibniz explains: . . . to find a tangent is to draw a straight line which joins two points of the curve which have an infinitely small distance, that is, the prolonged side of the infinitangular polygon which for us is the same as the curve.98

In terms of limit (although Leibniz did not use the term ‘limit’ explicitly), the tangent is the limit of a secant, which runs through 105

conditions of thought: deleuze and transcendental ideas two consecutive points of the curve and forms a ‘differential triangle’ with the appertaining abscissa and ordinate. As the second point of this secant approaches the first point, the chosen point of tangency, the gradient of the secant tends toward the gradient of the tangent. They coincide in intuition as the two points of the secant line become infinitely close to one another. This method of a ‘differential triangle’, which depends upon the fundamental relation between ordinates and abscissas, had in a sense already appeared in the works of previous mathematicians such as Torricelli, Fermat and Barrow, but it was Leibniz who developed this method for determining the differential relations of infinitesimals. He conceived two infinitely close points of the curve and expressed the infinitely small distance between them by means of infinitesimals, or infinitely small differences. In order to designate these infinitely small differences between two consecutive values of a variable, Leibniz adopted a characteristic notation, which has been maintained to the present day. Leibniz employed the symbol dx to designate the differences in the values of the abscissa x, and the symbol dy for the differences of the ordinate y, and defined dy as the quantity which is to dx as the ratio of the ordinate to the subtangent.99 By means of this notation, Leibniz codified the rules for determining the gradient of tangents or, in other words, the rate of change of a curve at the point where the tangent touches the curve. The overall procedure involving these rules for determining differences of infinitesimals and their quotient is called differentiation. Leibniz also codified a procedure for computing the area of a curvilinear figure by means of so-called ‘sum sequences’. The area under the curve was defined as an infinite sequence of sums of approximating rectangles whose sides are represented by the ordinates for infinitesimal intervals in the abscissas. This procedure is called integration and the sum of these infinitely thin rectangles the integral. A great discovery was made when Leibniz (and Newton) recognised the inverse relationship between differentiation and integration. They discovered the remarkable property that if a geometric quantity decreases continually until it vanishes, then that same quantity is the sum of all the successive differences. In other words, the differential of the integral equals the original quantity. This is now known as the fundamental theorem of the calculus, namely that the definite integral F(x) of the continuous function f(x) has a derivative which is this very same function, F’(x) 5 f(x).100 It should be noted, however, that the concepts of ‘function’ and ‘derivative’ were introduced only much later in the course of the nineteenth century, in the attempt to 106

The Demand for Transcendental Genetic Conditions liberate the calculus from geometric connotations and to provide a rigorous arithmetic foundation according to the standards of mathematics as a formal discipline (see the work of Augustin Cauchy, in particular his Cours d’analyse algébrique (1821), Résumé des leçons sur le calcul infinitesimal (1823) and Leçons sur le calcul différentiel (1829),101 and Karl Weierstrass, in particular his ­introductory ­lectures on analysis of 1859/60).102 Maimon’s Differentials of Consciousness Maimon was familiar with both Leibniz’s and Newton’s account of differential and fluxional calculus. Traces of both can be found in Maimon’s philosophical appropriation of the mathematical term of differential. For Maimon, the differential calculus provides a metaphysical explanation of the generation of quantities, not only mathematical quantities but also empirical quantities and their relations. He considers differentials as the genetic elements which cannot be given in intuition, but which are nonetheless real and generate perfectly determinate, extensive quantities. Maimon thereby draws on the fact that the ratio dy/dx expresses a finite quantity designated by a third term z, such that dy/dx equals z. Leibniz defined the term z as the gradient of the tangent to a curve at a single point. Thus, while z has a value that can be represented in intuition, the differential elements of the ratio dy/dx cannot be intuited. With respect to intuition differentials are equal to nothing, although their ratio dy/dx does not equal zero. Mapping the mathematical model of differential calculus onto transcendental philosophy, Maimon says: These differentials of objects are the so-called noumena; but the objects themselves arising from them are the phenomena. With respect to ­intuition 5 0, the differential of any such object in itself is dx 5 0, dy 5 0 etc.; however, their relations are not 5 0, but can rather be given ­determinately in the intuitions arising from them.103

Maimon calls the differentials noumena, at other times ‘Ideas’ or ‘limit concepts’ (Grenzbegriffe), thus alluding to Kant’s definition of noumenon but at the same time completely modifying its meaning. Kant openly admits that noumenon is a problematic concept (CPR A 254/B 309), that is a concept which, in spite of the fact that it contains no contradiction, can never be given a corresponding object in intuition. In principle, it can without contradiction be thought as designating a thing-in-itself independent of sensibility. Such a thing 107

conditions of thought: deleuze and transcendental ideas would be given to the pure understanding in a non-sensible or intellectual intuition. Yet Kant adds that we as human beings cannot comprehend the possibility of intellectual intuition, for the nature of our understanding is discursive and not intuitive. Thus the concept noumenon in its positive meaning, that is as designating a thing-initself, is inadmissible from an epistemological point of view, since no object can be determined for the concept. Nevertheless, Kant acknowledges that the concept of noumenon has an important use if taken in its negative sense as a ‘boundary concept’ (Grenzbegriff) (CPR A 255/B 310–11). As such it functions as ‘a boundary for given concepts, connected with other cognitions’ (CPR A 254/B 310). It does not designate a real object or given thing, but serves to provide unity or an objective ground, in relation to which other cognitions can be synthesised. The concept of noumenon in its negative sense has all the characteristics of the Kantian ‘transcendental Idea’ of reason; insofar as the Idea has no corresponding object in sensible intuition, it remains an empty form of thought but serves the understanding to be guided better and further in its cognition through concepts. When Maimon refers to differentials, he uses the Kantian terms ‘noumenon’,104 ‘limit concept’ (Grenzbegriff)105 or ‘Idea of reason’106 interchangeably. But he does not use them in the Kantian sense. This becomes apparent when he introduces the term ‘Ideas of the understanding’ in order to refer to differentials, defining them as ‘the infinitely small of every sensible intuition and of its forms, which provides the matter [Stoff] to explain the way that objects arise’.107 Ideas of the understanding are the material, genetic elements of an object (or as Maimon says, they provide the ‘material completeness of a concept, insofar as this completeness cannot be given in intuition’108), while Ideas of reason aim at the formal totality of a concept. Maimon dedicates a whole chapter to the end of opposing Ideas of reason and Ideas of the understanding,109 but unfortunately, in other parts of the Essay, Maimon fails to exercise care in distinguishing clearly between the two. Sometimes Maimon calls differentials ‘Ideas of reason’, but most of the time he refers to differentials as ‘Ideas of the understanding’. However, from the way Maimon puts differentials to use it becomes clear that they cannot be equated with Kantian Ideas of reason, i.e. empty forms of thought that have a merely regulative function in providing formal totality, but with Ideas of the understanding, that is with real objects (ens reale) or rather real relations.110 The crucial point is that differentials are nothing but reciprocal relations that precede any cognition of objects and even constitute 108

The Demand for Transcendental Genetic Conditions it.111 In this way Maimon seeks to eliminate the Kantian ‘sensation’, that is anything given to our consciousness through causal affection. The givenness of sensation always indicates a referential relation to something ‘outside’ consciousness. Maimon objects that we have no right to posit the origin of sensation outside of us. He demands a purely immanent account of cognition. According to this immanent account, sensation only plays a role insofar as it is itself regarded as a synthesis, whose elements must be thought as a pre- or subconscious manifold. In other words, every conscious perception (that is sensation or the perception of an object of experience) must ultimately be dissolved into its elements: a rational manifold or ‘differentials’. Arguing that differentials are nothing but pure relations or intellectual genetic rules, Maimon provides the following example taken from mathematics.112 Think of a right-angled triangle, one of whose catheti moves infinitely in the direction of the angle opposite to it, thereby remaining parallel to its original position. The triangle becomes infinitely smaller and its sides eventually disappear in intuition. Nevertheless, although the sides have disappeared completely and are reduced to their differentials, the relation still subsists. That is to say, the rule according to which a right-angled triangle can be generated still holds between the differentials or infinitely small sides. Leibniz and Newton were already referring to similar examples. Thus Leibniz claimed that the form of the triangle remained even after all quantity had been abstracted from it. While being reduced to zero, the evanescent quantity retains the character of that which is disappearing.113 Newton equally spoke of the ultimate forms of evanescent triangles.114 In order to think the transition from the finite to the infinite, Leibniz and Newton both invoked the idea of continuity or continuous motion. In the same way, Maimon conceives of a continuous transition from extensive quantities to the infinitely small, to the differential. However, we need to pay attention to Maimon’s characterisation of the differential. The differential is not a quantity in the common sense of the word, but a quality or intensive inner magnitude. Consequently, the intensive magnitude (the quality of the quantum) is in this case the differential of the extensive quantities, and the extensive quantities are the integral of the intensive magnitude.115

Maimon claims that quality can be conceived as abstracted from all quantity, and yet still as being instantiated in a relation of extensive quantities.116 He argues that the lawfulness of a relation 109

conditions of thought: deleuze and transcendental ideas essentially belongs to the qualitative elements, after extension has been removed.117 For instance, in the case of the evanescent rightangled triangle, the sides, although reduced to differentials, maintain the relation which is equal to √2:1:1. Maimon comments: So, it is not a relation of number to number, since I have assumed both to be infinitely small, omni dabili minora [smaller than anything given], and consequently it cannot be expressed by any number in relation to any unit, but only by the relation of one unit to another unit, i.e. this relation does not hold between the lines in so far as they are measurable, but merely in so far as they are determined by their quality (by their position). As a result, they are not extensive but intensive magnitudes.118

Maimon argues that pure relations do not hold between extensive quantities or numbers, but between differentials (i.e. qualities abstracted from all quantity). The ratio dy/dx gives a perfect example for the discovery of this new type of relations. As Maimon explains, dy/dx does not express an invariable numerical relation, like the relation of irrational magnitudes, but a ‘universal functional relation’. That is to say, ‘these magnitudes [dy and dx] stand in a universal functional relation to one another so that if one is determined, then the other is also determined’.119 The main characteristic of this universal functional relation seems to be, not so much  the variability of its differential elements, but first and foremost the fact that none  of the differentials can exist on its own outside the relation. Outside of the ratio itself, the terms dx and dy have no meaning. It is only in and through their reciprocal relation that they are determined. By contrast, if we consider the fraction 2⁄7, we notice that each of the quanta which make up the elements of the fraction can be conceived separately. A quantum has a completely indifferent existence apart from its ratio. This means that the relationship between quanta is not essential. Hegel noted later that an algebraic description of the fraction shows the same deficiency. In an algebraic formulation such as y/x 5 a, the ratio can be eliminated without loss by transforming the original formula into the expression y 5 ax.120 Hence only the ratio dy/dx expresses an essential or pure relationship, in which the relation is prior to its terms. As Deleuze remarks in his lecture on Spinoza, the infinitesimal calculus puts into play a new type of relation, the differential relation as pure relation. ‘The thought of relation as pure relation can only be made in reference to the infinite. This is one of the highly original moments of the ­seventeenth century.’121 110

The Demand for Transcendental Genetic Conditions Maimon’s reading of the differential calculus thus allows him to conceive of relations that are prior to their objects and even generate them. Conversely, every object must be resolvable into differential relations. For an infinite understanding, the given completely disappears. What appears as given to our finite understanding, that is sensation must be ordered in differential relations.122 As Bergman contends, ‘Not an iota of “given” sensation that is foreign to the understanding remains.’123 Hence, Maimon believes he has resolved the question quid juris?: the pure concepts of the understanding are not directly applied to intuition, but only to the limits of intuition, i.e. the real relations of differentials or Ideas of the understanding.124 In this way the understanding relates its concepts only to a rational manifold, which is entirely thought. Just as in higher mathematics we produce the relations of different magnitudes themselves from their differentials, so the understanding (admittedly in an obscure way) produces the real relations of qualities themselves from the real relations of their differentials. So, if we judge that fire melts wax, then this judgment does not relate to fire and wax as objects of intuition, but to their elements, which the understanding thinks in relation of cause and effect to one another. Namely, I hold that the understanding not only has a capacity [Vermögen] to think universal relations between determined objects of intuition, but also to determine objects by means of relations.125

Contrary to Kant, Maimon conceives of the understanding not only as a faculty of rules which needs to apply its a priori concepts to something given to it from outside, but as a genuinely creative faculty which creates the content in accordance with its a priori rules. The mathematical model of differential calculus is supposed to provide the proof of this creative capacity, which Maimon calls ‘real thought’. For Maimon, to create the world is to think the world, and therefore the thinker’s ideal is to engage in an ‘infinite progress through which what is thought is always increased, while the given is reduced to the infinitely small’.126 However, Maimon concedes that our understanding can probably never achieve this ideal goal due to its limitation. Our consciousness is incomplete, in other words ‘we start in the middle with our cognition of things and finish in the middle again’.127 Our consciousness is a consciousness of representation, and it reproduces only a part of the synthesis. The elements of the synthesis, that is the differentials, fall outside the order of representation since they are 111

conditions of thought: deleuze and transcendental ideas below the threshold of consciousness. They form a kind of primitive consciousness beyond the order of representation. Maimon defines the genetic differential elements as ‘presentations’ (Darstellungen). They do not represent anything, for in order to represent something they need to be related to a represented whole, an object. Thus differentials can ultimately only be grasped as determined in and through perceived objects (just as the differential is thought through its integral).128 According to Maimon, there is, in reality, a series of degrees of consciousness.129 Our consciousness of representation lies in the middle between two limits or limiting ideas: primitive consciousness and the consciousness of a complete synthesis. The consciousness of a complete synthesis is the superior limit of our conscious representations, which can never be attained because of the infinity that it involves. The consciousness of a complete synthesis possesses the complete concept of an object, that is it knows its relation to all possible objects.130 This idea of a higher consciousness is reminiscent of Leibniz’s idea of a divine intellect that knows the complete concept of an individual substance. However, Maimon does not conceive a divine or infinite intellect external to independent individual substances (Leibniz’s monads). Instead, he insists on the possible transition from the finite to the infinite, that is from our consciousness of representations to higher degrees of consciousness, or from our finite intellect to the infinite intellect. Only in this way can he give a truly internal, genetic account of objects of experience arising from unconscious differentials. As Bergman explains, Maimon deviates in this respect from Leibniz and comes close to Spinoza’s position. ‘To the extent that Maimon believes in an infinite understanding that created (thought) the world and in the identity of our limited understanding with this infinite understanding he is a disciple of Spinoza.’131 The immanent productivity of the infinite intellect, which makes it the material cause of the world, certainly is a Spinozistic element. Spinoza believed that all things are ‘modes’ of the infinite substance and wholly intelligible in the divine thought. Furthermore, Maimon’s claim that the human understanding is the same with the infinite understanding, ‘only in a limited way’, is also embraced by Spinoza.132 In this respect, Kant is right when he says in his letter to Herz that ‘Mr Maimon’s way of presenting things [Vorstellungsart] is in fact one and the same as Spinoza’s.’133 However, Maimon attempts to elude the charge of Spinozism in a footnote to the passage in which he claims the part-whole relation of the finite and infinite understanding: 112

The Demand for Transcendental Genetic Conditions Many readers will imagine they are catching a glimpse of Spinozism here. So in order to prevent all misunderstandings of this kind, I now want to explain myself once and for all: [. . .] our understanding is the schema for the idea of an infinite understanding. [. . .] So I differ from Kant merely in this: instead of the three ideas that he assumes, I assume a single idea (of an infinite understanding), and I ascribe objective reality to this idea (not, it is true, viewed in itself – for this is contrary to the nature of an idea – but only in so far as it acquires objective reality for us).134

In this remark Maimon distances himself from Spinozism, which in those days was condemned as atheist and politically radical thought. Instead of saying that the human understanding is a ‘mode’ of the infinite understanding, Maimon claims that the human understanding is the schema for the idea of an infinite understanding. According to Kant, the process of schematisation of an Idea proceeds by analogy. Thus seemingly Maimon only claims that the human understanding is like the infinite understanding, and he assumes the infinite understanding, i.e. God, as an idea which has objective reality for us (and not in itself as a metaphysical, all-embracing and constitutive reality). This conception of the human understanding as a schema for the idea of an infinite understanding seems a whole world away from an immanent ontology in which the finite understanding is part of the infinite intellect and participates in an immanent productivity. It must be said that this ambiguity subsists in Maimon’s philosophy. Perhaps one can say that, unlike Spinoza, Maimon does not posit an immanent ontology from the start, but rather projects it as the goal that we reach in our philosophical investigations if they are ‘carried through’ rigorously.135 His proposed solution to the quid juris? problem certainly brings him already on the road towards an immanent ontology.136

Deleuze and Maimon Deleuze’s interest in Maimon lies precisely in the fact that the subconscious mechanism of reciprocally determined differentials provides an explanation of the genesis of real experience, whereas the Kantian conditions of possible experience are ‘too general or too large for the real’ (DR 68/94). Kant’s transcendental philosophy may claim to be a philosophy of genesis, but ‘to be precise, there is no genesis of the phenomenon, but in fact there is a genesis of the intelligibility of phenomena’.137 Real experience only plays a role insofar as it is intelligible, that is it conforms with the conditions of possible experience. This means that real experience is reduced to that which can be represented 113

conditions of thought: deleuze and transcendental ideas within the transcendental conceptual framework (DR 56/79) and that what can be represented is decided in advance, namely solely identical objects with extensive sensible qualities. What is excluded from the Kantian account of objective experience is the flux of meaningless intensive sensations or micro-perceptions below the threshold of consciousness. According to Deleuze, Maimon paves the way for a ‘transcendental (differential and genetic) psychology of perception’ (FLB 89/118). This means that contrary to Kant’s transcendental conditions, which are abstracted from experiential cognitions and arbitrarily projected as conditions of possibility of experience, the Maimonian transcendental conditions designate genetic and differential mechanisms that generate perception or real experience. We should not be confused by Deleuze’s use of the term ‘transcendental psychology of perception’: he is not pursuing a psychology of the person or subject. Transcendental, differential and genetic conditions are objective structures or Ideas within a sub-representative, unconscious realm: an intersubjective differential unconscious or transcendental field. Furthermore, it has to be noted that Deleuze’s reading of Maimon stands squarely within Maimon’s own project. Maimon is undoubtedly committed to a form of rational dogmatism: he defines differentials of consciousness as Ideas of the understanding in order to give a purely immanent account of the understanding’s synthetic activity. His solution to the question quid juris? consists in filling the gap between given intuition and pure concepts by dissolving the given into reciprocally determined differentials which are entirely thought. Everything is thought, nothing is given. Deleuze adapts Maimon’s invention of differential and genetic Ideas to the Leibnizian notion of infinitely minute perceptions. This means that differential Ideas are not thought but sensed, although in an unconscious manner. Therefore Deleuze’s reading of Maimon owes much to his reading of Leibniz and to his very own interest in a differential unconscious. In the following, we will look at how Deleuze develops the notion of a differential unconscious taking as a point of departure the problem of the unconscious nature of differentials, or in other words the problem with the ‘unthought in thought’. The Problem with the ‘Unthought in Thought’ Maimon’s solution to the question quid juris?, by means of which he wanted to bridge the gap between what is given and what is purely 114

The Demand for Transcendental Genetic Conditions thought, is based on the premises that our finite understanding is continuous with an infinite understanding, and that some kind of original differential production takes place subconsciously from the point of view of our limited understanding. It seems that the original differential production must be assigned to the unconscious activity of an infinite understanding. Now a certain difficulty arises which in a way repeats the initial problem on the level of the infinite understanding. The conflict between the given and pure thought appears again. There is a ‘minimum of given (minimum de donné)’138 even in the infinite understanding, namely precisely the differential rule of production itself. In other words, the processes of differentiation cannot be reduced to pure thought. If pure thought proceeds according to the principle of reciprocal determination, if it is the nexus between differentials, there always remains a residue of something given. One is compelled to introduce a ‘given’, an ens reale, which is irreducible to the pure thought of the infinite understanding. Maimon recognises this difficulty, but seeks to resolve it ‘in the same way as with a finite understanding’: The given intuited by an infinite understanding is either an objectum reale, signifying something present in the infinite understanding, but not thought by it (this does not contradict its infinity, because this consists only in the ability to think everything that is thinkable and the given is by its nature not thinkable); or the given is a mere idea of the relation of the concepts to something outside it, which in itself is merely a modification of the understanding. In the latter case the actuality would not consist in something outside the understanding, but merely in this relation.139

Maimon’s response seems far from satisfying. What he suggests is that both can be the case. First, there can be something given to the infinite understanding (though it cannot have been given from outside). Second, this given can be conceived in analogy to an empirical representation consisting in the relation of a concept to some external object. However, as Maimon has explained elsewhere, the relation to something outside is illusory, since a representation is nothing but an internal modification of the understanding. ‘This “outside us” signifies something in whose representations we are not conscious of any spontaneity, i.e. something that (with respect to our consciousness) is purely passive and not active in us.’140 The problem with transposing this ‘solution’ to the infinite understanding is that with the acceptance of something given to the infinite 115

conditions of thought: deleuze and transcendental ideas understanding, we have reintroduced an unintelligible and ‘occult quality’.141 Maimon’s insistence that this ‘unthought’ in thought does not contradict the infinity of the infinite understanding appears not very persuasive and sounds rather like a capitulation to the problem. Maimon’s ‘solution’ is open to serious criticism, which is presented by Martial Guéroult from a Fichtean perspective. For a Fichtean, the claim that there is something given to thought, which cannot be brought to consciousness, is ‘dogmatic and contradictory’.142 There are two main reasons why our consciousness of representations can in principle never shed light on the original differential production. First, bringing differentials into our consciousness of representation would mean destroying their definition as ‘presentations’, i.e. something that neither represents anything nor can be represented. Second, if we define consciousness as a pure for-itself, that is not only as a consciousness-of-something but also as a lucid, transparent self-­consciousness, there can be nothing unthought in it. This residue would instantly dissolve by virtue of the capacity of consciousness to penetrate itself.143 Consequently, if one follows this line of argument, the manifold of differentials could only be outside consciousness, located in a non-consciousness. This position would imply a separation of the conditions of knowledge (forms of thought and the sensible given) from the conditions of existence (differentials or rules of production). In other words, the reason for knowing would be distinct from the reason for being. As a consequence of this distinction, the immanence of the subject of cognition would be undermined, since the constitutive elements of knowledge, i.e. the differentials, would be an extrinsic reality located in an objectified infinite understanding. The subject would actually be posterior to the reality of which it seeks to gain knowledge.144 The simple claim of immanence could not be a change for the better. Apparently, we would have to conclude that the infinite understanding was qualitatively distinct from the subject of cognition, which is bound by the limitation of our cognitive faculty. If we follow this argument to its ultimate consequence, Maimon would have only reinforced the Kantian dogmatism of the thing-in-itself: the occult character, which in Kant inhabited the thing-in-itself, would range over the whole of empirical experience.145 Jules Vuillemin, who endorses this line of argument, sees the lynchpin of Maimon’s reasoning in ‘the refusal to assign a full self-consciousness (conscience de soi) to consciousness. [. . .] Consciousness is still conceived outside self-consciousness and thus the whole of philosophy has become impossible, because truth escapes cognition.’146 116

The Demand for Transcendental Genetic Conditions We can assume that Deleuze was very well acquainted with this criticism of Maimon, in particular with the one issued by Guéroult. Indeed, it appears that Deleuze even discovered Maimon first and foremost through Guéroult’s books on Maimon and on Fichte, since almost every time when Deleuze mentions Maimon, he also refers to Guéroult.147 In response to this criticism of Maimon, Deleuze argues that the unconscious nature of differential Ideas has been completely misunderstood, for it is precisely the unconscious nature of differential Ideas that provides a solution to the problem of the ‘unthought in thought’. It is a mistake to believe that ‘the unconscious of a pure thought must be realised in an infinite understanding’ (DR 193/249). It is equally mistaken to condemn ‘the differentials [. . .] to the status of mere fictions unless they acquire the status of a fully actual reality in that infinite understanding’ (DR 193/249). The alternative between mere fictions and actual reality in an infinite understanding is simply false.148 According to Deleuze, the original differential production does not refer to an infinite understanding, but to differential psychic mechanisms in the unconscious of a finite self. Thus Deleuze eliminates the infinite understanding and restores the differential Ideas to a differential unconscious within finite thought. He says that ‘the infinite is taken here only as the presence of an unconscious in finite understanding, of something that cannot be thought in finite thought, of a nonself in the finite self’ (FLB 89/118). For Deleuze, there is no contradiction in the notion of something unthought in thought. True, this ‘occult quality’ differs in kind from clear and conscious thought. This is why it is located on a different plane that differs in kind from the order of representation. In other words, being of the order of presentations, it does not belong to our consciousness of representation but to a differential unconscious. How can this be reconciled with the claim of immanence of the differentials of consciousness?149 Deleuze sees a solution in a ‘transcendental (differential and genetic) psychology of perception’ (FLB 89/118). The unconscious is both the transcendental condition and the genetic origin of consciousness. This distinguishes precisely Maimon’s ‘transcendental’ from the Kantian method of external conditioning: ‘Maïmon restores an internal subjective method of genesis’ (FLB 89/118). Deleuze’s Notion of a Differential Unconscious Since Deleuze develops the conception of a differential unconscious with regard to Leibniz, we will in what follows mainly refer to his 117

conditions of thought: deleuze and transcendental ideas lectures and book on Leibniz. We will thereby attempt to make sense of Deleuze’s few explicit remarks on Maimon, on the assumption that his interpretation of Leibniz is also applicable to Maimon’s case. We believe this to be justified, because Deleuze seems simply to equate the conception of the unconscious of Leibniz with that of Maimon.150 For Deleuze, Maimon is the ‘first post-Kantian who returns to Leibniz’ (FLB 89/118) and draws all the consequences from the ‘Leibnizian reinterpretation of the calculus’ (DR 170/221). Deleuze does not hesitate to identify Maimon’s differentials of consciousness with Leibniz’s ‘minute perceptions’.151 He probably did not know Maimon’s letter to Kant dated 20 September 1791, in which Maimon sharply criticises Leibniz’s theory of minute perceptions.152 According to Maimon, the conception of obscure representations that fall below the threshold of consciousness can only be of use in anthropology, that is a doctrine that deals with human beings insofar as they are endowed with a body. Obscure representations are modifications of the body, and not of the soul or pure consciousness. Maimon’s rationalistic commitments actually forbid equating his differentials of consciousness with Leibniz’s obscure representations. For Maimon, differentials of consciousness are the object of a transcendental critique of cognition that is concerned with genetic, intellectual relations or laws. Thus it is important to note that Deleuze ‘sensualises’ Maimon’s differentials of consciousness by interpreting them as unconscious ‘micro-perceptions’.153 It is true that Maimon occasionally refers to differentials as ‘differentials of sensations’. In fact, Maimon states: Sensibility thus provides the differentials to a determined consciousness; out of them, the imagination produces a finite (determined) object of intuition; out of the relations of these different differentials, which are its objects, the understanding produces the relation of the sensible objects arising from them.154

But it should be noted that Maimon refers here simply to what he calls a ‘subjective order’, namely how it presents itself to our consciousness of representation.155 By contrast, the ‘objective order’, which is established by a true critique of our cognition, dispenses with sensibility or intuition altogether. It only deals with Ideas and concepts.156 With regard to the objective order, there are first and foremost the ‘Ideas of the understanding’ that provide the non-intuitive, intellectual matter, that is the manifold of differential relations. On the basis 118

The Demand for Transcendental Genetic Conditions of these Ideas, the faculty of understanding determines real objects and the relations between them. The faculty of reason provides Ideas of formal totality, in order to coordinate the acts of the understanding so that a maximum of unity prevails among its concepts. Thus, from the point of view of a true critique, empirical perceptions must ultimately be resolved into Ideas of the understanding.157 However, Deleuze not only modifies the historical Maimon by characterising differentials as Leibnizian minute perceptions, he also reinterprets Leibniz insofar as he defines minute perceptions not only as smaller than conscious perceptions but as different in kind. This characteristic, i.e. their difference in kind, is drawn from mathematical considerations of differentials as intensive qualities in contrast to extensive quantities, which make up the terms of the primitive function. Deleuze’s redefined conception of differentials, drawn both from Maimon and Leibniz, paves the way for a transcendental philosophy of perception which eludes a mere empirical psychology or ‘anthropology’. After these preceding remarks we will now outline Deleuze’s conception of a differential unconscious that he attributes equally to Leibniz and to Maimon. The theory of a differential unconscious is based on two claims: a metaphysical claim, according to which the infinite world is contained within a finite consciousness or monad; and a psychological claim, according to which every conscious perception implies an infinity of tiny, obscure perceptions (FLB 87/116). The common structure of both is that ‘something finite consists of an infinity under a certain relation’.158 The fact that the mind is finite and the world infinite explains the darkness and obscurity of the mind, its depths. The mind bathes in an unconscious that consists of infinitely minute perceptions lacking an object, ‘that is, hallucinatory microperceptions’ (FLB 86/115). They are the ‘representatives’ (FLB 86/115) or rather ‘presentations’ of the world. The world exists only in these presentations; in other words, the world is pulverised into ‘a mass of dancing particles of dust’ (FLB 86/115), and this dust is spiritualised into infinitely minute perceptions (FLB 87/116). These tiny and obscure perceptions are not yet representation, that is to say these perceptions are neither related to a whole (an object), nor endowed with consciousness. Before we have clear and conscious experience of objects, there is an ‘unconscious lived experience’ such as we experience in the case of fainting, dizziness, or sleep.159 In these cases 119

conditions of thought: deleuze and transcendental ideas our consciousness loses the power of self-consciousness and plunges into a flow of minute unconscious perceptions. The extreme limit of this line would be death, where death is not defined as the state of a person who ceases to live, but on the contrary a state of catalepsy, in which one is entirely reduced to minute perceptions. In order to describe these distinct levels of experience – ­unconscious lived experience and conscious experience of representations – Leibniz dissociates Descartes’ criteria of the ‘clear-and-distinct’ and the ‘obscure-and-confused’. For Descartes, knowledge that is derived from the senses can only be obscure and confused, while knowledge that is grasped by the understanding or by the natural light of reason is clear and distinct. Leibniz, by contrast, couples the obscure with the distinct and the clear with the confused. That is to say, the minute and unconscious perceptions, though they make up the obscure part of our mind, are perfectly distinct. The sound of each tiny wave or drop of water that together compose the roaring of the sea is distinct. Similarly, the infinitely small appetites that precede the conscious feeling of hunger are distinguishable in elementary forms of hunger for salts, for proteins, for fat, etc. On the other hand, our global conscious perceptions are clear but confused. We perceive the global noise of the sea very clearly, but it remains confused insofar as we cannot grasp its composition. Likewise, the feeling of hunger that starts to rumble in our stomach is perceived clearly, but again it is confused, since we do not consciously distinguish its composites. The unconscious, as Leibniz supposedly conceives it, consists of minute perceptions and minute inclinations or appetites, which are nothing but the obscure and distinct differentials of conscious perception. There is a genesis of our clear and conscious perceptions, which starts from the differentials of consciousness.160 It is important to grasp here that the conception of a differential unconscious is very different from a Freudian unconscious, which is characterised by drives or desires that are in conflict with consciousness.161 For Freud, the unconscious expresses a force that attracts all representations or inclinations opposed to or rejected by ­consciousness. The unconscious and consciousness are two antagonistic forces. By contrast, the differential unconscious is continuous with ­consciousness. There is a passage from the unconscious to consciousness, a psychic continuity. However, this psychic continuity nevertheless involves a jump of planes: from the unconscious, subrepresentational plane to the plane of our conscious representations and appetites. Suddenly we realise that we are hungry. Suddenly we 120

The Demand for Transcendental Genetic Conditions sense the noise of the sea, it is drawn into clarity, although – living near the shoreline – we have become accustomed to the noise and usually do not perceive it any more (cf. Leibniz’s example of the grinding noise of the water mill which I do not perceive consciously because I am already accustomed to it). This last example in particular shows that what is brought to light is in some sense ‘selected’ from the habitual, the regular or the ordinary. Only that which is remarkable and notable for some reason becomes a clear and conscious perception. Leibniz uses the term ‘singular’ as an equivalent for ‘remarkable’ and ‘notable’. According to Deleuze, Leibniz is inspired by the mathematical concept of ‘singularity’ which leads Leibniz to create a philosophical theory: ‘It is a very curious theory that Leibniz was no doubt the first to introduce into philosophy, that we could call the theory of singularities.’162 The theory of singularities is supposed to provide a solution to the question as to how clarity emerges from obscurity, in other words how clear and conscious perceptions are produced from tiny, obscure perceptions. The process involved is not one of simple addition of parts to a whole (FLB 87/116). It is not the case that very small quantities are added up until they compose a determinate measurable quantity. On the contrary, our conscious perceptions must be a product of genetic, differential relations established among minute perceptions. The relationship between conscious perceptions and minute perceptions is one of derivation or integration: ‘The integral is what derives from and is also what operates an integration, a kind of totalisation, but it’s a very special totalisation, not a totalisation through addition.’163 Deleuze uses the theory of singularities as well as additional considerations on derivation and integration (from the eighteenth and nineteenth centuries) for elaborating the conception of a differential unconscious. It is clear that Deleuze’s notion of a differential unconscious exceeds Maimon’s theory of differentials of consciousness by far. Deleuze takes advantage of later developments of the calculus, for instance the notion of a function and the derivative, but ironically uses this additional material to contribute to the differential point of view of the infinitesimal calculus. In the end, Deleuze’s rereading of the differential calculus serves to better explain the transcendental (differential and genetic) psychology of perception: the genetic force of differential relations, and the ‘jump’ from the unconscious and qualitative differentials (presentations) to the conscious perceptions of extensive quantities (representations). There is a ‘genuine cut’ or 121

conditions of thought: deleuze and transcendental ideas ‘caesura’ involved, which, however, does not interrupt the continuity between the unconscious and consciousness, so that the immanence of the differentials is maintained. It is this paradoxical problem which the mathematical model is supposed to solve. We will first have to ask what a singularity signifies on the mathematical level. Deleuze’s Rereading of the Differential Calculus In the discussion of curvilinear figures, singularities designate distinctive points where the nature of the curve changes, that is where it shows a behaviour that falls outside the ordinary or regular. This is the case, for instance, when the curve reaches a maximum or minimum, or else a point of inflection, which marks a change in concavity. Singularities are indicated by the differential relation. For instance, if the differential relation dy/dx, which in terms of intuition gives the gradient of the tangent at a single point, is equal to zero, then the gradient of the tangent is at that point horizontal and the curve of the original function (the so-called ‘primitive’ function) reaches a local maximum or local minimum. Singularities divide the curve of the function into parts or neighbourhoods, whose points are of ordinary or regular character. ‘Each singularity is the source of a series [of regular points] extending in a determined direction right up to the vicinity of another singularity’ (LS 52–3/67; cf. also DR 278/356–7). Through a process of repeated differentiation at a singular point (that is in taking the second derivative, the third derivative, etc.), it is possible to characterise not only one point of the curve, but a whole range of points in the neighbourhood of the singularity.164 That is to say, the qualitative nature of all the regular points in the neighbourhood of a singularity can be characterised or, in geometrical terms, the rate of change of the branches of the curve, whether they are rising or falling quickly, can be determined more and more accurately. Given that all the regular points are continuous across all the different branches between distinct singularities, the whole curve can finally be determined in going from the neighbourhood of one singularity to the neighbourhood of a subsequent singularity and so on. In the nineteenth century, the mathematician Karl Weierstrass provided a method to represent the curve of a primitive function within a specific domain through a power series. Given a primitive (and differentiable) function, we can produce an infinite power series of the form a0 1 a1x 1 a2x2 1 a3x3 1 . . . 1 anxn by summing the 122

The Demand for Transcendental Genetic Conditions successive derivatives taken at a particular point of the function, such that the values of a are calculated using the values of the respective derivatives. Such a power series expansion, or Taylor series, can be said to represent the primitive function in the domain.165 Deleuze recognises an important fact on this point: although we are usually confronted with a function in calculus class that we then have to differentiate by taking derivatives, this usual priority can be reversed. ‘In Deleuze’s rereading of the calculus, the primitive function does not precede the differential relation, but is only the ultimate result or by-product of the progressive determination of that relation.’166 In fact, the differential relation dy/dx precedes the primitive function and can even be said to generate it. Weierstrass’s method proves to be an effective means to determine the characteristics or the behaviour of a function within the neighbourhood of a given point. Thus if we take the power series obtained at each singular point of the primitive function, Deleuze assumes that we can construct the entire curve of the primitive function on the basis of multiple power series. This is a quite different procedure from the determination of the primitive function by exercising the inverse operation of integration (developed by Cauchy). Deleuze presents Weierstrass’s method of approximation using successive derivatives as an alternative approach that is still tied to geometric conceptions and intuitions (insofar as it determines the qualitative ‘behaviour’ of the curve) and therefore faithful to the infinitesimal calculus in its early geometrical phase.167 This exposition by Deleuze is all the more surprising, since it was actually Weierstrass who provided the calculus with a ‘rigorous’ foundation through a programme of redefining geometric ideas in purely arithmetic terms. Weierstrass is best known for separating the calculus from geometrical conceptions or intuitions, which were considered to be vague and problematic. He thereby paved the way for a modern interpretation of the calculus on the basis of set theory. Deleuze, however, criticises the arithmetisation of the differential calculus because of its failure to think the infinite and the expulsion of dynamic concepts (‘fluxions’ and ‘fluents’, passage to limits, ‘vanishing differences’, etc.).168 It eliminates the infinitesimal as a vague and problematic metaphysical concept. Thus Deleuze calls for a return to the so-called ‘barbaric’, ‘pre-scientific’ and ‘esoteric’ interpretations of the differential calculus (DR 170/221). Ironically, Deleuze draws on Weierstrass to defend a view which he sees already adumbrated in Leibniz’s early geometrical calculus: the logical priority of ­differential relations and their generative power. 123

conditions of thought: deleuze and transcendental ideas Apart from the generative power of differential relations, Deleuze adds another important observation: there is a difference of kind between the derivative or differential relation and the primitive function (DR 172/224). While the primitive function deals with relations between finite quantities and is therefore bound to representation, the differential relation prevails between dy and dx, which are not quantities, but qualities that fall outside representation. In other words, the differential relation is not a formula that relates x to y over some range of values for x [. . .]. Rather, the differential relation relates x to y not in breadth, over a range of values, but in depth; it operates in each point on the function, condensing the quality, the character of the entire function into every point.169

We are now in a position to draw some conclusions from the mathematical example of infinitesimal calculus, which Deleuze covers in a unique way from Leibniz to Weierstrass. It has been shown, firstly, that singularities and the differential relations at these distinct points play a decisive role in the generation of the curve of the primitive function, and secondly, that the differential relation differs in kind from the primitive function. Their difference in kind from extensive, measurable quantities renders them suitable candidates for a transcendental philosophy of perception. Released from their mathematical context, differentials can be interpreted as minute perceptions, which are not just smaller but different in kind from conscious perceptions. The reciprocal relations between the differentials produce the conscious experience of the world, which can be interpreted as the curve of the primitive function. This is then how Deleuze envisages the process of generation of conscious perceptions from tiny obscure perceptions: We have to understand literally – that is, mathematically – that a conscious perception is produced when at least two heterogeneous parts enter into a differential relation that determines a singularity [. . .] For example, the sound of the sea: at least two waves must be minutely perceived as nascent and heterogeneous enough to become part of a relation that can allow the perception of a third, one that ‘excels’ over the others and comes to consciousness. (FLB 88/117)

In this sense, the roar of the ocean is the result from productive processes whose differential rule remains unconscious. The mathematical model serves as a transcendental (genetic and differential) explanation of the psychology of perception, which replaces the 124

The Demand for Transcendental Genetic Conditions Kantian account of a simple extrinsic conditioning where concepts are applied to something given in intuition. Thus differential calculus is the psychic mechanism of perception, the automatism that at once and inseparably plunges into obscurity and determines clarity: a selection of minute, obscure perceptions and a ­perception that moves into clarity. (FLB 90/119)

Through Leibniz and Maimon, Deleuze enriches the notion of the transcendental: the transcendental is immanent, genetic, differential and unconscious. It provides a transcendental model of genesis in the sense that unconscious differential mechanisms generate real conscious phenomena. The Notion of ‘Virtuality’ It is important to note that Deleuze’s conception of a differential unconscious is not identical with that of Leibniz or Maimon.170 There is a fundamental difference: Leibniz’s differential unconscious, i.e. the multitude of infinitely minute perceptions or the ‘mass of dancing particles of dust’ of the world (FLB 86/115), is contained within the monad. The relation of the Leibnizian monad to the world is one of inclusion and closure. As Deleuze remarks in his discussion on Leibniz: The danger is that representation conquers difference, that difference, even the infinitely small, is united in an infinite analytic identity. This would mean nothing more than ‘allowing the identical to rule over infinity itself’ (DR 264/339). Similarly, Maimon’s differential Ideas risk being engulfed in an overall identity, namely the infinite understanding, whose principle task is still to produce unity through its conceptual rules. Although Deleuze provides a new focus on Maimon by insisting on the unconscious and sub-representative status of differential Ideas, Maimon nevertheless remains a rationalist: for Maimon, there is nothing outside the understanding, there is no extrinsic given. Obviously, Deleuze’s own conception of a differential unconscious cannot be equated with Leibniz’s or Maimon’s. For Deleuze, the differential unconscious is not included or enclosed within the subject; rather, the differential unconscious is a fracture or rift that opens the subject to an absolute ‘outside’, a true exterior (cf. DR 169/220). Equally, the differential and problematic Ideas are not contained in the subject, but they are immanent in the empirical world. However, this does not mean that Ideas are ‘actual’ like empirical things. 125

conditions of thought: deleuze and transcendental ideas Deleuze eludes the alternative between actual Ideas and Ideas as fictions by stipulating them as virtual Ideas within a virtual, unconscious realm, which is one facet of the empirical world. The notion of virtuality originates from Deleuze’s studies of Bergson and Proust and is further elaborated in Difference and Repetition. Being a vital component of his theory of Ideas, the notion of virtuality needs to be examined here. To begin with, the virtual ought not to be confused with the possible. The possible designates an abstract conceptual possibility of an object that is fabricated only retroactively ‘in the image of what resembles it’ (DR 212/273). It is nothing but a copy from actual facts, a mere abstraction. As Bergson says in his seminal essay ‘The Possible and the Real’: ‘The possible is only the real with the addition of an act of mind which throws its image back into the past, once it has been enacted.’171 We are prone to the illusion that the possible precedes the existence of real things and only waits to be realised. We believe that ‘the possible would have been there from all time, a phantom awaiting its hour’.172 Bergson explains that we probably confuse two meanings when we speak about the possible in such a manner. When we say that something is possible, we want to say that it is not impossible. This implies that the concept of a possible object is not self-contradictory and that there is no hindrance to its realisation. However, ‘from the negative sense of the term “imposs­ ible” you pass surreptitiously, unconsciously to the positive sense’.173 Absence of contradiction and hindrance now means ‘pre-existence’ under the form of an Idea or individual concept. It seems that the Idea or concept already includes all the characteristics of the object, such that existence adds nothing to it but a simple realisation. In Deleuze’s words: ‘The whole of existence is related to a preformed element, from which everything is supposed to emerge by simple “realization” ’ (B 20/9). It is true that philosophers have conceived the process of realisation not as simply as is suggested here. The process of realisation of a possible object proceeds in accordance with two rules: limitation and opposition. From the totality of possible objects, the rule  of limitation restricts the range of possibilities to certain possibles that pass into the real. The rule of opposition ensures the possibility of the object by excluding any contradiction among the predicates of the object. The rule selects from all pairs of opposite predicates only one predicate respectively that is then ascribed to the object. Both limitation and opposition are rules that function through negation 126

The Demand for Transcendental Genetic Conditions and exclusion. That is to say, the process of realisation of objects is ultimately a determination by means of negation in accordance with the principle omnis determinatio est negatio. However, for Deleuze, this principle of determination as negation cannot explain the process of passing into existence: ‘Every time we pose the question in terms of possible and real, we are forced to conceive of existence as a brute eruption, a pure act or leap which always occurs behind our backs and is subject to a law of all or nothing’ (DR 211/273). The possible lacks an account of the genesis of real objects. It may allow for the possibility of an object but this possibility remains abstract. The merely logical possibility of an object does not suffice to explain its reality, that is to provide a sufficient reason for its existence. For this reason, Deleuze takes recourse to the Bergsonian notion of the virtual. Bergson is not only the author who rejects the concept of possibility, it ‘is also he who develops the notion of the virtual to its highest degree and bases a whole philosophy of memory and life on it’ (B 43/37). Thanks to Bergson, the logic of the possible can be replaced by the reality of the virtual. The virtual is not an empty image abstracted from actual experience and thrown backward by the mind as a conceptual possibility. The virtual is a full reality: it is real without being actual and ideal without being abstract (DR 208/269). 174 One of its most fundamental features is its creative potential whose realisation is wholly unpredictable. The virtual does not pre-form or pre-judge the actual objects coming into existence in the way that conceptual possibility does. The virtual is a creative force, a fullness constantly differentiating itself and creating ­something unforeseeable and new. Bergson introduces the notion of virtuality in the context of the distinction between two types of multiplicity (cf. B 38/30–1): a spatial or numerical multiplicity of discrete quantities assembled within homogeneous space and a temporal or qualitative multiplicity (duration), which is not denumerable. It consists of differences in qualities or intensities. For example, the process of dissolution of a sugar lump in water can be regarded as a temporal multiplicity or duration. The two multiplicities differ from one another insofar as spatial multiplicities include differences in degree, while temporal multiplicities include differences in kind. However, Bergson’s opposition of multiplicities only designates two aspects of the same world.175 On the one hand, we can consider the world under the aspect of space, that is in terms of matter and extensities. On the other hand, we can look at the world under the aspect of duration, 127

conditions of thought: deleuze and transcendental ideas that is in terms of qualities or intensities. Qualities or intensities make up the virtual facet of the world, which subsists or insists in the extended and material world. One could also say that virtual and actual are the dimensions of one movement or becoming: the virtual cannot be separated from a movement of actualisation. The virtual becomes actualised through processes of differentiation. ‘For actualization comes about through differentiation, through divergent lines, and creates so many differences in kind by virtue of its own movement’ (B 43/36). In other words, processes of differentiation in the virtual are the real ground from which divergent lines of evolution emerge. The movement from the virtual to the actual designates genuine creation and replaces the ‘false movement of realisation [of the possible] understood as abstract limitation’ (DR 212/274). We can already see where Deleuze is heading: Leibniz’s infinitely minute perceptions or Maimon’s differentials of consciousness are transformed into pure virtualities (DR 279/357). ‘The reality of the virtual consists of the differential elements and relations along with the singular points which correspond to them’ (DR 209/269–70). In this way, Deleuze eludes the illusion of a subordination of difference to identity. The differentials are no longer contained in an overall identity (the infinite analytic identity of the monad or the infinite understanding), but are set free within a virtual realm, which is one facet of the pluralistic, empirical world. According to Deleuze, ‘any hesitation between the virtual and the possible [. . .] is disastrous, since it abolishes the reality of the virtual’ (DR 212/274). Deleuze accuses Leibniz of failing to grasp the distinction between the virtual and the possible. Although ‘no one has been better able to immerse thought in the element of difference and provide it with a differential unconscious, surround it with little glimmerings [of Ideas] and singularities’ (DR 213/275), Leibniz still conceived the realisation of Ideas as ‘realised possibles’. In summary, Deleuze argues that Ideas are virtual. They subsist within a virtual, sub-representative and unconscious realm. The differential unconscious is a fracture or rift in the subject, which opens the subject precisely to this virtual realm, which ‘possesses the reality of a task to be performed or a problem to be solved’ (DR 212/274). In the next chapter we will see how Deleuze expands the notion of virtual Ideas in order to include the Kantian characteristic of Ideas as problems. As we shall see, Deleuze does not stick to the notion of ‘differentials of sensation’ or to a ‘(genetic and differential) psychology 128

The Demand for Transcendental Genetic Conditions of perception’ that we have discussed in this chapter. Differentials of sensation are only one type of Ideas, but there are various other types of Ideas that concern all the faculties of cognition (DR 193/249). Among these Ideas, Deleuze pays particular attention to those that generate thought: ‘Ideas must be called “differentials” of thought, or the “Unconscious” of pure thought’ (DR 194/251). He continues that ‘thought thinks only on the basis of an unconscious, and thinks that unconscious in the transcendent exercise’ (DR 199/258). The transcendent exercise of thought means the suspension of common sense and good sense. Ideas have the role of a paradoxical or problematic element that is capable of pushing the cognitive faculties to a disjoint transcendent exercise. ‘It is a question, therefore, not of a common sense but, on the contrary, of a “para-sense” (in the sense that paradox is also the contrary of good sense’ (DR 194/250). In fact, Deleuze finds a model of this disjoint paradoxical exercise of the faculties in the Kantian account of the experience of the beautiful and the sublime in Kant’s Critique of the Faculty of Judgment.

Notes 1. LS 253/292; see also Deleuze’s lecture course on Kant (14 March 1978). 2. Dosse, Gilles Deleuze et Félix Guattari, pp. 116 and 159. 3. Cf. Leigh, ‘Deleuze, Nietzsche and the Eternal Return’, p. 208. 4. Kant’s fears of such a radical critique subverting the ground of reason itself are well expressed in his Critique of Practical Reason, p. 126: ‘Nothing worse could happen to all these labors, however, than that someone should make the unexpected discovery that there is and can be no a priori knowledge at all. But there is no danger of this. It would be like proving by reason that there is no such thing as reason.’ 5. Cf. Nietzsche, On the Genealogy of Morals, p. 589: ‘The will to truth requires a critique – let us thus define our own task – the value of truth must for once be experimentally called into question.’ 6. Nietzsche, Beyond Good and Evil, p. 199. 7. Ibid., p. 237. 8. Nietzsche, Gay Science, p. 201. 9. Ibid., p. 201. 10. Nietzsche, Beyond Good and Evil, p. 236. 11. Ibid., p. 200. 12. Nietzsche, On the Genealogy of Morals, p. 544. 13. Ibid., p. 533. 14. Ibid., p. 543 [French in the original]. 15. Nietzsche, Twilight of the Idols, pp. 40–1. Nietzsche does not exempt 129

conditions of thought: deleuze and transcendental ideas Kant from this accusation, since Kant – at least with the Critique of Practical Reason – reintroduces a transcendent, intelligible world. 16. Nietzsche, Beyond Good and Evil, p. 236. 17. Patton, Deleuzian Concepts, p. 11. As Paul Patton explains, Deleuze does not content himself with this systematic Nietzsche. In his later writings (particularly in ‘Nomad Thought’) he presents a ‘fragmentary Nietzsche’ who ‘hardly belongs in philosophy at all. He is rather the inventor of a new kind of discourse, a counterphilosophy that is defined by its essential relation to the outside, to intensity and to laughter’ (Patton, Deleuzian Concepts, p. 12). 18. As we have already mentioned in Chapter 1 in the section on the concept of error, the term ‘conceptual persona’, which first appears in What Is Philosophy?, refers to the subject of enunciation of a philosopher. According to Deleuze and Guattari, a philosopher creates a conceptual persona or sometimes even several personae (for instance, Nietzsche’s Zarathustra, Dionysus, the priest, the higher man, Socrates, etc.) who carry out the movements of thought and play an important part in the creation of concepts. It is no longer the philosopher who speaks, but the conceptual persona who says ‘I’ (cf. WP 64/63). 19. Nietzsche, On the Genealogy of Morals, p. 473. 20. Bogue, Deleuze and Guattari, p. 16. 21. Nietzsche, Beyond Good and Evil, p. 395. 22. Nietzsche, On The Genealogy of Morals, p. 476. 23. Ibid., p. 472. 24. Nietzsche, Human, All Too Human, p. 175. 25. Cf. Deleuze, ‘Nietzsche’, p. 73. 26. See also Nietzsche, The Will to Power, section 564 (1885–6) and section 565 (Fall 1886), pp. 304–5. 27. Nietzsche, Beyond Good and Evil, p. 210. 28. Ibid., p. 238. 29. Ibid., p. 238. 30. Nietzsche, The Will to Power, section 715 (November 1887 – March 1888), p. 381. 31. Ibid., section 619 (1885), pp. 332–3. 32. Note that the Kaufmann/Hollingdale translation still mistakenly renders Nietzsche’s ‘an inner world (eine innere Welt)’ as ‘an inner will’. For more on the textual criticism of The Will to Power, see Wolfgang Müller-Lauter, ‘ “Der Wille zur Macht” als Buch der “Krisis” philosophischer Nietzsche-Interpretation’, in Behler et al. (eds), Nietzsche Studien, vol. 25, especially p. 257. 33. Nietzsche, Beyond Good and Evil, p. 238. See also The Will to Power, section 1067 (1885), p. 550. 34. Cf. Somers-Hall, ‘Hegel and Deleuze on the Metaphysical Interpretation of the Calculus’, p. 569. 130

The Demand for Transcendental Genetic Conditions 35. See also NP xi, 7/7–8, 51/57–8, 52/58–9, and Deleuze, ‘Nietzsche’, p. 73. 36. In the terminology of DR, we can say that the Nietzschean couple Dionysus/Ariadne equals the power of difference and repetition. See DR 41/59. 37. Nietzsche, The Will to Power, section 617 (1883–5), p. 330. 38. Ibid., section 692 (March–June 1888), p. 369. 39. Nietzsche, On the Genealogy of Morals, p. 513. See also Nietzsche, The Will to Power, section 643 (1885–6), p. 342. 40. It is worth noting that Deleuze’s interpretation of the relationship between forces effectuated by the will to power is much less conflictual than Nietzsche’s description of the will to power as ‘the tyrannically inconsiderate and relentless enforcement of claims of power’ would suggest (Nietzsche, Beyond Good and Evil, p. 220). However, Deleuze insists that ‘the notions of struggle, war, rivalry or even comparison are foreign to Nietzsche and to his conception of the will to power’ (NP 82/93, also DR 51/72). Deleuze substitutes a differential play of forces for the Nietzschean tyrannically inconsiderate and relentless power claims. 41. Nietzsche, On the Genealogy of Morals, p. 514. 42. Nietzsche, The Will to Power, section 552 (Spring–Fall 1887), p. 298. 43. Deleuze, Lecture Course on Chapter Three of Bergson’s Creative Evolution, p. 72. 44. After having read the manuscript of Maimon’s Essay on Transcendental  Philosophy, Kant acknowledges the ‘excellence’ of Maimon’s Essay in a letter to Marcus Herz, and admits ‘not only that none of my opponents has understood me and the principle question as well as Mr Maimon, but also that only a few people possess such an acute mind for such profound investigations [as he does]’ (Kant, ‘Letter to Herz, 26 May 1789’, in Briefwechsel, p. 395. An English translation can be found in the Appendix to Maimon, Essay, p. 231). Fichte confessed in a letter to Reinhold his limitless respect for Maimon’s talents and warned that future generations would ridicule them for not having appreciated Maimon’s accomplishments (Fichte, ‘Letter to Reinhold, (March or April) 1795’, in Gesamtausgabe, vol. III, p. 282). 45. Not even Kant, who is commonly regarded as a leading figure of the Enlightenment, can be exempt from the charge of anti-Semitism. In a letter to Reinhold he wrote (in stark contrast to the favourable remark he had made only five years earlier): ‘As regards Maimon with his “improvement” of the critical philosophy (a thing Jews like to do to make themselves self-important at the expense of others) I have never really understood what he intended’ (Kant, ‘Letter to Reinhold, 28 March 1794’, in Briefwechsel, pp. 662–3; my translation, D. V.). 131

conditions of thought: deleuze and transcendental ideas 46. Cf. Freudenthal, ‘Between Two Cultures’, p. 2. 47. Atlas, From Critical to Speculative Idealism, pp. 12–13. 48. See, for example, (1) Lecture Course on Chapter Three of Bergson’s Creative Evolution, pp. 72, 77 and 78; (2) NP 52/58 footnote; (3) ‘The Idea of Genesis in Kant’s Aesthetic’, in DI 61; (4) DR 170/221, 173– 4/224–6, 192–3/249, 310/66 footnote, 324/226 footnote, 326/254 footnote; (5) Lecture Course on Kant, 14 March 1978; (6) FLB 89. 49. Guéroult, La Philosophie transcendantale, p. 64. See also Appendix, remark no. 1 with regard to Leibniz, pp. 157–9. 50. Midgley, introduction to Maimon, Essay, p. xlviii. 51. In his excellent ‘Introduction’ to Maimon’s Essay, Midgley mentions the importance of Maimon’s philosophy for a ‘thoroughgoing philosophy of difference in which relations and differences are prior to their objects’ (Maimon, Essay, p. xliv), but he does not refer to Deleuze explicitly. 52. Jones, ‘Solomon Maimon’, in Jones and Roffe (eds), Deleuze’s Philosophical Lineage, pp. 104–29. Smith, ‘Genesis and Difference: Deleuze, Maimon, and the post-Kantian Reading of Leibniz’, in McDonnell and van Tuinen (eds), Deleuze and the Fold, pp. 132–54. Lord, Kant and Spinozism, chapters 5 and 6. 53. Bryant, Difference and Givenness, pp. 8–9, 46, 194 and 242. Kerslake, Immanence and the Vertigo of Philosophy, pp. 10, 145–7 and 165–6 note. Sauvagnargues, Deleuze: L’Empirisme transcendantal, pp. 225–37. As far as we know, the first mention of the Maimon–Deleuze nexus can in fact be found in Michael Roubach’s article ‘Salomon Maimon’s Philosophy and Its Place in the Enlightenment: Wandering in the Land of Difference’, in Freudenthal, Rational Dogmatist, Empirical Skeptic, pp. 86 and 88. However, his reference remains too brief and obscure to be helpful. 54. See CPR Appendix to the Transcendental Analytic: ‘Remark to the Amphiboly of Concepts of Reflection’, pp. 371–83. 55. Kant, ‘Letter to Herz, 26 May 1789’, in Briefwechsel, p. 396. For the English translation see Maimon, Essay, p. 231. Interestingly, in this same letter Kant attempts to draw a distinction between Maimon’s assumption of an intuitive intellect and that of Leibniz (and Wolff). He says ‘I very much doubt that this was Leibniz’s or Wolff’s meaning, or whether it can really be inferred from their definitions of sensibility as opposed to the understanding’ (Maimon, Essay, p. 231). Kant apparently tries to reinterpret Leibniz in the light of a model of distinct cognitive faculties that harmonise with one another. Thus he says that Leibniz had in mind ‘the harmony of two faculties belonging to one and the same being in which sensibility and understanding harmonize in an experiential cognition’ (Maimon, Essay, p. 234). Is this perhaps because he wants to exempt Leibniz from the accusation of a sort of 132

The Demand for Transcendental Genetic Conditions Spinozist monism, which he sees present in Maimon’s way of thinking (Maimon, Essay, p. 231)? For more details on Kant’s rejection of Spinozism see Lord’s excellent study Kant and Spinozism. 56. We follow Henry Allison in the analysis of the Transcendental Deduction as an argument consisting of two parts. See Allison, Kant’s Transcendental Idealism, p. 134: ‘The essence of my interpretation can be expressed in the formula that the first part of the Deduction is concerned with the objective validity (objective Gültigkeit) of the categories and the second part with their objective reality (objective Realität).’ 57. Allison does not seem to distinguish between real (i.e. given spatiotemporal, yet a priori) objects and actual (i.e. empirical) objects. See his definition of ‘objective reality’: ‘The notion of objective reality has an ontological sense. To claim that a concept has objective reality is to claim that it refers or is applicable to an actual object [my emphasis, D.  V.]’ (Allison, Kant’s Transcendental Idealism, p. 135). For Maimon’s purpose, the distinction between ‘real’ and ‘actual’ is vital, since he will use this distinction in the critique of Kant. (Maimon opposes the actual to the real, just as he opposes ‘empirical’ or ‘arbitrary thought’ to ‘real thought’.) 58. What the ‘accepted fact’ in Kant’s regressive transcendental argument exactly is has been interpreted differently in the secondary literature on Kant. It could be simply some knowledge that we possess, scientific propositions of knowledge, or a sort of Cartesian truth about consciousness. 59. For the distinction between regressive and progressive transcendental arguments, see Franks, All or Nothing, p. 208. 60. See Maimon, Essay, p. 186. (References to passages from the Essay are to the page numbers of the German original edition, marked at the top of each page of the translation.) Cf. also Maimon, Philosophisches Wörterbuch, p. 48 and Maimon, Streifereien, p. 73. 61. See, for instance, Maimon, Streifereien, p. 73: ‘Although critical philosophy is to the highest degree systematic, that is, self-coherent [unter sich zusammenhängend], it does not refer to anything real. Its transcendental concepts and principles, categories, ideas, etc. have no reality. With regard to the origin of these forms of thought of the understanding, and with regard to the completeness and systematicity, it [transcendental philosophy] refers to logic’ (my translation, D. V.). 62. Maimon, Versuch einer neuen Logik, p. 476. 63. Maimon, Essay, p. 142; see also pp. 187–8. 64. For more on this issue, see Maimon, Essay, pp. 187–8 and 370–3; Maimon, Versuch einer neuen Logik, pp. 489–90. It seems, by the way, that Kant would agree with Maimon that pure a priori concepts could never be discovered in intuition (cf. CPR A 137/B 176). Engstler 133

conditions of thought: deleuze and transcendental ideas argues that Maimon misconstrues Kant’s claims, and that ‘it seems clear that for Kant, the schema, as a transcendental determination of time, cannot be as it were “read off” [ablesbar] from empirical objects’, in Engstler, Untersuchungen zum Idealismus, p. 87 (my translation, D. V.). 65. CPR A 94/B 127: ‘The unfolding of the experience in which they [the a priori concepts] are encountered, [. . .] is not their deduction (but their illustration), since they would thereby be only contingent.’ 66. Maimon’s letter to Kant (7 April 1789), in Maimon, Essay, p. 229. 67. Midgley, introduction to Maimon’s Essay, p. xxvii. 68. Cf. CPR A 20/B 34: ‘I call all representations pure (in the transcendental sense) in which nothing is to be encountered that belongs to sensation.’ 69. Maimon, Essay, p. 60: ‘So, assuming that time and space are a priori intuitions, they are still only intuitions and not a priori concepts; they make only the terms of the relation intuitive for us, and by this means the relation itself. But not the truth and legitimacy of its use.’ See also Maimon, Essay, p. 64. 70. The different meanings of pure intuition in Kant’s CPR are distinguished in Allison, Kant’s Transcendental Idealism, pp. 94–8. 71. Maimon argues that consciousness requires synthesis, that is to say, ‘something must be given that is thought by the understanding as a manifold (through unity of difference)’ (Maimon, Essay, pp. 130–1). 72. Cf. Maimon, Essay, p. 180: ‘The possibility of thinking space without objects is purely transcendent.’ 73. Ibid., p. 19. 74. Ibid., pp. 346–7 and 135–6. See also Maimon, Versuch einer neuen Logik, p. 480. 75. This argument is clearly presented in Beiser, The Fate of Reason, p. 302. 76. Ibid., p. 301. 77. Maimon’s argument with reference to space can be transferred to time as well. As Maimon explains: ‘So if we nevertheless still represent in space things like water that are identical in intuition, this takes place only in relation to something different, i.e. the representation is transcendent. It is the same with time: if I have slept for, say, a few hours, then I can only perceive the time by means of the different positions of the hands of a clock for example’ (Maimon, Essay, p. 134). 78. Maimon, Essay, p. 20. 79. Ibid., pp. 60 and 64. 80. Ibid., p. 185: ‘I claim, that the synthetic propositions of mathematics are certainly true and universal propositions, but that they are nevertheless not apodictic; rather they are merely assertoric and 134

The Demand for Transcendental Genetic Conditions neither a priori (in my sense of the word) nor pure.’ See also Maimon, Philosophisches Wörterbuch, p. 199. 81. Maimon, Essay, p. 82. 82. Ibid., pp. 20–1. 83. Ibid., p. 63. 84. Ibid. 85. We will not examine here Maimon’s principle of determinability, by means of which he attempted to ground an objective (i.e. necessary) synthesis of the determinable and the determination (see, for instance, Maimon, Essay, pp. 20, 258 and 260). Maimon believed that with the principle of determinability he had found a truly immanent, genetic principle which served as an a priori criterion and even as a sufficient reason (‘real ground of possibility’) for the synthesis of mathematical concepts. But in fact, Maimon could not do without something extrinsically given, namely space as the highest ‘determinable’. Moreover, the principle of determinability cannot be applied outside the realm of mathematics. Therefore we agree with Guéroult that Maimon eventually felt the need to search for another ‘superior principle’, which will be ‘difference’ or the ‘differentials of consciousness’. Cf. Guéroult, La Philosophie transcendantale, p. 53. 86. Maimon, Essay, pp. 394–5. 87. Boyer, The History of the Calculus, p. 299. 88. Ibid., p. 188. There Boyer provides further references with respect to this matter. 89. Ibid., p. 194. 90. Ibid., p. 193. 91. Ibid., pp. 12–13, 212, 216 and 219. 92. Ibid., pp. 201–2. 93. Isaac Newton, quoted in Boyer, The History of the Calculus, p. 202. 94. Ibid., p. 209. 95. Ibid., p. 213. 96. We base the following account on Bos’ article ‘Differentials, HigherOrder Differentials and the Derivative in the Leibnizian Calculus’. 97. Cf. Duffy, ‘The Mathematics of Deleuze’s Differential Logic and Metaphysics’, in Duffy (ed.), Virtual Mathematics, p. 119. 98. Cf. Leibniz, ‘A New Method for Maxima and Minima, as Well as Tangents, Which Is Not Obstructed by Fractional or Irrational Quantities’, quoted in Bos, ‘Differentials, Higher-Order Differentials’, p. 19. 99. Boyer, The History of the Calculus, p. 210. In fact, the definition of dx and dy, which Leibniz provided in the first published account of the calculus (‘A New Method for Maxima and Minima, as Well as Tangents, Which Is Not Obstructed by Fractional or Irrational Quantities’, in Acta eruditorum, 1684), treats differentials as finite, 135

conditions of thought: deleuze and transcendental ideas assignable quantities. However, from his definition of the tangent given above, it becomes clear that his avoidance of differentials was only superficial. Recent studies show that Leibniz regarded the differential as fundamental throughout his work. Modern mathematics, by contrast, subordinates the notion of differential to the notion of limit (in a sense similar to Newton) by defining the derivative to be the limit of the ratio dy/dx. 100. Ibid., p. 10. 101. Cauchy, Œuvres, Ser. 2, vols 3 and 4. 102. Since Weierstrass frequently did not publish his results when he ­actually achieved them, it is rather difficult to put a precise date on his discoveries. Most of Weierstrass’s work became known to the mathematical world through his lectures at the University of Berlin. A collection of his lecture notes can be found in his Mathematische Werke. 103. Maimon, Essay, p. 32. 104. Ibid., p. 32. 105. Ibid., p. 192. He further calls differentials ‘the limits of objects of experience’ – see pp. 186 and 187. 106. Ibid., pp. 32 and 355. 107. Ibid., p. 82. 108. Ibid., p. 75. 109. Ibid., pp. 75–83. 110. Ibid., pp. 192 and 355–6. 111. Ibid., pp. 168–9, 190 and 193. 112. Ibid., pp. 394–6. 113. Cf. Bergman, The Philosophy of Solomon Maimon, p. 266. 114. Boyer, The History of the Calculus, pp. 218 and 219. 115. Maimon, Essay, p. 395; see also p. 122. 116. Ibid., p. 355. 117. Bergman, The Philosophy of Solomon Maimon, p. 260. 118. Maimon, Essay, p. 396. 119. Ibid., pp. 354–5. 120. Somers-Hall, ‘Hegel and Deleuze on the Metaphysical Interpretation of the Calculus’, p. 563. 121. Deleuze, Lecture Course on Spinoza, 17 February 1981. 122. Maimon, Essay, p. 109. 123. Bergman, The Philosophy of Solomon Maimon, p. 258. 124. Cf. Maimon, Essay, p. 355: ‘The pure concepts of the understanding or categories are never directly related to intuitions, but only to their elements, and these are ideas of reason [sic] concerning the way these intuitions arise.’ 125. Ibid., pp. 355–6. 126. Maimon, Philosophisches Wörterbuch, p. 193 (my translation, D. V.) and p. 187. See also Maimon, Essay, p. 419. 136

The Demand for Transcendental Genetic Conditions 127. Maimon, Essay, p. 350. 128. Ibid., p. 206. 129. Cf. Guéroult, La Philosophie transcendantale, p. 65. See also Guéroult, Fichte, pp. 115–17. 130. Maimon, Streifereien, p. 64. 131. Bergman, The Philosophy of Solomon Maimon, p. 218; see also pp. 221–2. Bergman explains Maimon’s attraction to Spinoza with the fact that both thinkers relied on the same background in Jewish philosophy, in particular the medieval philosopher Maimonides and his (Aristotelian) doctrine of the identity of the ens intelligens, the ens intelligibile and the intellectus (p. 34; see also chapters 9 and 10). 132. Maimon, Essay, p. 65. See also Spinoza, Letter 32: ‘As regards the human mind, I maintain that it, too, is a part of Nature; for I hold that in Nature there also exists an infinite power of thinking which, in so far as it is infinite, contains within itself the whole of Nature ideally, and whose thoughts proceed in the same manner as does Nature, which is in fact the object of its thought. Further, I maintain that the human mind is that same power of thinking, not in so far as that power is infinite and apprehends the whole of Nature, but in so far as it is finite, apprehending the human body only. The human mind, I maintain, is in this way part of an infinite intellect’ (in The Letters, pp. 849–50). 133. Kant, Letter to Herz (26 May 1789), in Maimon, Essay, Appendix II, p. 231. 134. Maimon, Essay, pp. 365–6. 135. Note Maimon’s cautious formulation in the following quote: ‘We assume an infinite understanding (at least as idea), for which the forms are at the same time objects of thought, or that produces out of itself all possible kinds of connections and relations of things (the ideas). Our understanding is just the same, only in a limited way. This idea is sublime and will, I believe (if it is carried through), overcome the greatest difficulties of this kind’ (Maimon, Essay, pp. 64–5). 136. In her book Kant and Spinozism (2011), Beth Lord defends a strong Spinozistic reading of Maimon. ‘Maimon’s purpose is to show that transcendental idealism cannot work unless it posits the reality of a Spinozistic supersensible substrate underlying appearances. Maimon thereby attempts to do just what Kant suggests is impossible for us in the Critique of Judgment: to think a supersensible substrate that is both an intelligent and an immanent cause’ (p. 105). See also p. 126: ‘Certainly, Maimon aligns himself with Spinozism in the sense that he takes the infinite understanding to be the infinite idea of all reality, of which our own minds (and all our objects of intuition) are modes. Furthermore, he suggests that our idea of the infinite understanding cannot be the idea of a merely possible being; we necessarily think it 137

conditions of thought: deleuze and transcendental ideas as actualizing itself as our own minds and the objects of our sensible intuition. That is, we necessarily think of the infinite intellect as actual because our understanding is a mode of the infinite intellect, and our thinking is a limited instance of its thinking. The idea of the infinite intellect is in us because we are in it.’ 137. Deleuze, Lecture Course on Chapter Three of Bergson’s Creative Evolution, p. 72. 138. Guéroult, La Philosophie transcendantale, p. 59 and p. 84. 139. Maimon, Essay, p. 251. 140. Ibid., p. 203. 141. Guéroult, La Philosophie transcendantale, p. 84. See also Guéroult, Fichte, pp. 122 and 131. 142. Guéroult, Fichte, p. 122. Such a critique of Maimon can indeed be found in Samuel Atlas, From Critical to Speculative Idealism, p. 117: ‘For to have something “given” and not to be conscious of it is self-contradictory.’ 143. Guéroult, Fichte, p. 122. 144. Ibid., p. 126. 145. Ibid., pp. 122 and 131. 146. Vuillemin, L’Héritage Kantien et la révolution Copernicienne, pp. 48–9 (my translation, D. V.). 147. See DR 310/66 note 13/1, DR 324/226 note 6/1, DR 325–6/254 note 15/1. Furthermore, Deleuze’s admiration for Guéroult can also be seen with respect to his essay on Guéroult’s original genetic-­ structural method which enables Guéroult to adopt a new approach to Spinoza’s Ethics. This method implies bringing out the structure of a philosophical system, that is its constitutive differential elements, their interrelations and organisation in ‘series’, along which the structure or ‘order of reasons’ evolves synthetically (cf. Deleuze, ‘Guéroult’s General Method for Spinoza’, in DI 146–55/202–16). Olivier Revault d’Allonnes, one of Deleuze’s close friends when they were both students at the University of the Sorbonne, reports that Guéroult has always been a great model for them, in particular because of his method of text-interpretation. ‘I have always found that Gilles was a great student of Guéroult’ (quoted in Dosse, Gilles Deleuze et Félix Guattari, p. 122; my translation, D. V.). 148. Samuel Atlas, for instance, clearly states that the two ­possibilities – ­differentials as fictions or as actual realities in an infinite ­understanding – are mutually exclusive and therefore necessitate a choice. Atlas argues that Maimon must be interpreted according to a strictly idealistic view of the differentials. Differentials should be understood as ‘ideas of reason’, that is ‘immanent ideas invented by the mind for the purpose of deducing reality [. . .] from principles posited by the mind’ (Atlas, From Critical to Speculative Idealism, p. 118). 138

The Demand for Transcendental Genetic Conditions 149. Maybe it should be emphasised here that the term ‘differentials of consciousness’ does not imply that differentials are contained within consciousness. As Martial Guéroult explains: ‘There are therefore differentials of consciousness which are neither objects of intuition, nor of consciousness, but the generic (and genetic) elements of the intuitions of this consciousness’ (Guéroult, La Philosophie transcendantale, p. 60; my translation, D. V.). 150. In the discussion following his presentation ‘The Method of Dramatization’ Deleuze speaks indiscriminately of a Leibnizian or Maimonian conception of the unconscious (DI 115/161). 151. ‘For Maïmon, as for Leibniz, reciprocal determination of differentials does not refer to a divine understanding, but to tiny perceptions as representatives of the world in the finite self’ (FLB 89/119). 152. Maimon’s letter to Kant, 20 September 1791, in Immanuel Kant’s Werke, vol. X, pp. 92–4. 153. ‘Inconspicuous perceptions are thus not parts of conscious perception, but requisites or genetic elements, “differentials of consciousness”. Even more than Fichte, Salomon Maïmon – the first post-Kantian who returns to Leibniz – draws all the consequences from this kind of psychic automatism of perception’ (FLB 89/118). 154. Maimon, Essay, pp. 31–2. 155. Ibid., p. 81. 156. Ibid., p. 82. 157. Ibid., p. 205. According to Cassirer, the seeming ambiguity about the provenance of differentials – are they ‘differentials of sensation’, ‘Ideas of the understanding’ or ‘Ideas of reason’? – is due merely to a lack of clarity in Maimon’s expression. While it is true that Maimon refers the differentials sometimes to sensibility, sometimes to the understanding and sometimes to reason, he does so in different manners and from different points of view. Cassirer argues that the overall idealistic character of his theory remains unaffected: ‘the sensible manifold [can be resolved] into a rational manifold’. See Cassirer, Das Erkenntnisproblem in der Philosophie, pp. 100–1. 158. Deleuze, Lecture Course on Spinoza, 17 February 1981. 159. Deleuze, Lecture Course on Leibniz, 29 April 1980. 160. Ibid. 161. Cf. DR 106/140 and Lecture Course on Leibniz, 29 April 1980. 162. Deleuze, Lecture Course on Leibniz, 29 April 1980. For Deleuze, the mathematical concept of singularity is very fruitful for philosophy. Mathematics makes use of the conceptual couple singular/ordinary (that is it opposes singular points of a function to ordinary or regular points). By contrast, general logic always opposes the singular to the universal (as in the case of singular and universal judgements). By introducing the mathematical distinction of the singular and the 139

conditions of thought: deleuze and transcendental ideas ordinary into the realm of philosophy, Deleuze actually creates new criteria for the relevance or necessity of a proposition. This means that we are no longer concerned with the question whether a proposition is true or false, but rather whether it is relevant, remarkable or interesting (cf. WP 111/106, 82/80). As Deleuze says, ‘the notions of relevance, necessity, the point of something, are a thousand times more significant than the notion of truth. Not as substitutes for truth, but as the measure of the truth of what I’m saying’ (N 130/177). Generally speaking, the art of thinking would be the capacity to distinguish singular points from ordinary points, that is remarkable and interesting ideas from banal and stupid remarks. 163. Deleuze, Lecture Course on Leibniz, 29 April 1980. 164. Leibniz had also considered a repeated application of differentiation, which would yield higher-order differentials. He defined the secondorder differential ddx or d2x as a variable infinitely small with respect to dx. In the same way, one could define further differentials of higher orders that further application of the operator d would yield (Bos, ‘Differentials, Higher-Order Differentials’, p. 19). However, Leibniz’s definition remains vague, since he could not explain in what way the differentials of higher order differ from first-order differentials. He also did not distinguish between differentials of independent and dependent variables (Boyer, The History of the Calculus, p. 211). The point is that Leibniz lacked the concept of a function, which describes a unidirectional relation between an ‘independent’ variable x and a ‘dependent’ variable y. In the absence of the concept of function, the concept of derivative could not be developed either. Thus in order to outline a ‘theory of singularities’, Deleuze takes advantage of later developments of the calculus. 165. Cf. Duffy, ‘The Mathematics of Deleuze’s Differential Logic and Metaphysics’, pp. 128–9. 166. Evens, ‘Math Anxiety’, p. 111. 167. As Duffy says: ‘Deleuze is therefore able to cite the contribution of Weierstrass’s theorem of approximation in the development of the differential point of view of the infinitesimal calculus as an alternative point of view of the differential calculus to that developed by Cauchy, and thereby establish a historical continuity between Leibniz’s differential point of view of the infinitesimal calculus and the differential calculus of contemporary mathematics, thanks to the axioms of nonstandard analysis which allow the inclusion of the infinitesimal in its arithmetization’ (Duffy, ‘The Mathematics of Deleuze’s Differential Logic and Metaphysics’, p. 132). 168. Cf. Deleuze, Lecture Course on Leibniz, 29 April 1980. 169. Evens, ‘Math Anxiety’, p. 111. 170. Cf. Deleuze’s reply to Philonenko in the discussion subsequent to 140

The Demand for Transcendental Genetic Conditions Deleuze’s paper ‘The Method of Dramatization’, DI 115/161: ‘To sum things up, I don’t have the same conception of the unconscious as Leibniz or Maïmon.’ 171. Bergson, ‘The Possible and the Real’, p. 100. 172. Ibid., p. 101. 173. Ibid., p. 102. 174. Deleuze takes this formula from Proust who characterises Ideas in such a way: ‘Réels sans être actuels, idéaux sans être abstraits’. In Proust, A la recherche du temps perdu, vol. III, p. 873. 175. Cf. B 29/20: ‘Dualism is therefore only a moment, which must lead to the re-formation of a monism.’

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3

Ideas as Problems

In the previous chapter we saw how Maimon took Kant’s transcendental philosophy in a radically new direction with his notion of differential Ideas of the understanding which serve to explain the genesis of real experience. We then saw how Deleuze reconstructed Maimon’s Ideas of the understanding as virtual Ideas belonging to an intersubjective differential unconscious. In this chapter we will continue our examination of Deleuze’s theory of Ideas by means of a closer analysis of the Kantian theory; in particular we will see the importance to Deleuze of Kant’s characterisation of Ideas as problems. We will also see how Maimon’s freeing of Ideas from exclusively belonging to the faculty of reason is taken further in Deleuze’s notion of Ideas that ‘occur throughout the faculties and concern them all’ (DR 193/249). It is important to note that Deleuze uses the notion of ‘faculty’ in a different sense than it has traditionally been used in philosophy. First of all, he not only refers to sensibility, imagination, memory, understanding and reason, but also to what he calls a faculty of speech, a faculty of ‘sociability’, a faculty of ‘vitality’, and he leaves open the possibility ‘for faculties yet to be discovered, whose existence is not yet suspected’ (DR 143/186–7). In the second place, Deleuze argues that faculties are not given ready-made, but emerge and develop with the Ideas or problems they encounter. Thirdly, it must be emphasised that the doctrine of the faculties cannot be grounded on a simple empirical psychologism. Rather, it needs to be related to an ontology of Ideas or, in Deleuze’s words, a ‘dialectic of Ideas’. Fourthly, the faculties are not faculties of a sovereign and self-present subject (a Cartesian Cogito or Transcendental Ego). They can only be faculties of a split subject, which is open to the ‘outside’ or to a differential unconscious. In the light of this modified notion of a faculty which is free of all psychologism, Deleuze calls for a return to the doctrine of the faculties: ‘the doctrine of the faculties is an entirely necessary component of the system of philosophy’ (DR 143/186). Now, Deleuze ascribes to each faculty a corresponding Idea 142

Ideas as Problems with its own ‘transcendent object’. In saying that an Idea has a transcendent object, this is not to say that the Idea is a concept of something beyond any possible experience. The object of the Idea is the problem or the ‘problematic’ (DR 169/219). This means that each faculty discovers at its extreme limit something which it cannot grasp (from the point of view of its empirical exercise) but which it is forced to grasp nevertheless. We have already encountered the sentiendum of sensibility,1 i.e. that which can only be sensed but which is imperceptible from the point of view of representation. The sentiendum is the differential manifold of minute and obscure perceptions, or the ‘being of the sensible’ (DR 140/182). Deleuze also introduces an imaginandum of the faculty of imagination (DR 143/186), a memorandum of memory,2 a cogitandum of thought.3 The sentiendum, imaginandum, memorandum and cogitandum are all Ideas or ‘transcendental signs’ for something which can never be given in representation but which must be grasped nonetheless. For Deleuze, reason is no longer the privileged faculty of Ideas as it was for Kant, since there are Ideas corresponding to each of the faculties. However, this does not mean that there are types of Ideas that exclusively concern only one corresponding faculty. As Deleuze says, Ideas are ‘not the exclusive object of any one [faculty] in particular, not even of thought’ (DR 193/250), but they occur throughout the faculties and concern them all. A sort of communication arises between the faculties, which is initiated through the Ideas they encounter. To put it in more concrete terms, Ideas set their corresponding faculty into motion and carry it to its extreme limit, but at the same time this violence is communicated from one faculty to another (DR 194/251). For instance, sensibility is set into motion by the encounter with its sentiendum and it forces memory in its turn to remember the memorandum. Memory then forces thought to grasp the cogitandum, that which can only be thought. ‘The violence of that which forces thought develops from the sentiendum to the cogitandum’ (DR 141/184). Thought can only grasp its cogitandum at the extremity of the ‘fuse of violence’ along which each faculty is pushed to its transcendent exercise. The important thing to notice is that the faculties no longer cooperate harmoniously as in the case of recognition of an object. In fact, an identifiable object of experience cannot elicit the transcendent exercise of the faculties, only the ‘sign’ or problematic Idea that is beyond recognition can do so. The sign or Idea is the object of a ‘fundamental encounter’ (DR 139/182). In Proust and Signs Deleuze gives us a preliminary understanding 143

conditions of thought: deleuze and transcendental ideas of what he means by a fundamental encounter with a sign or Idea. The narrator in Proust’s In Search of Lost Time encounters many different types of signs: the frivolous signs of society life, the deceptive signs of love, the sensuous signs of the material world and the essential signs of art. Some are more obtrusive than others, but they all inflict themselves on the narrator with necessity. For example, being haunted by jealousy the narrator tries to track down the lies of his beloved and to intrude into her secret world. Every love affair is ‘a dispute of evidence’ (PS 117/143) and the jealous lover finds himself in ‘a delirium of signs’ (PS 122/150). His task is to decipher the ‘spiritual element’, the ‘essence’ or ‘truth’ out of the complex of sensation. Proust opens a kind of ‘inner space’ in the empirical, a space of essences or Ideas that are nevertheless in the sensible. It is important to note here that the sign is not to be identified with the object that emits the sign. For example, at one point in the novel the  narrator experiences the rising up of ‘the in-itself of Combray’ (the town of his childhood) or a splinter of the pure past when he takes a bite of the madeleine, but the secret of the sign does not lie in the taste of the cake dipped in tea (DR 122/160 note). Equally, the love affair with Albertine does not reveal the secret of love: the narrator’s love for Albertine is a repetition of his love for Gilbert, which is a repetition of his love for his mother, which is a repetition of Swann’s love for Odette. These different repetitions form two adult series (the love between Swann and Odette and the love between the adolescent narrator and Albertine) that are brought in communication by an infantile series, i.e. the narrator’s childhood events when he was filled with love for his mother, knew Swann as the family’s friend and later adored Gilbert, the beautiful daughter of Swann and Odette. These series coexist within an ‘intersubjective unconscious’ (DR 124/163). In sum, if we seek the truth of a sign (‘the in-itself of Combray’ or the ‘never-lived reality of the Virgin’, DR 85/115), we need to abstain from an objectivist temptation. The truth of the sign is not to be found in the object emitting the sign. We may now be tempted to look for the truth of the sign in subjective associations of ideas. In the first book of In Search of Lost Time, we see Swann as a prisoner of his own subjective states. He is captured by Vinteuil’s musical theme or Botticelli’s ‘Sephora’ which he links with his love for Odette. But this subjective compensation is not a solution either. The truth of the sign, or its essence, ‘transcends the states of subjectivity no less than the properties of the object’ (PS 36/48). According to Proust, the truth of the sign is somewhere behind the appearances: 144

Ideas as Problems it is ‘real without being actual, ideal without being abstract’. In its purest form it is best manifested in the signs of art that aim to make the invisible visible. While the main focus in Deleuze’s early book Proust and Signs is on the different types of signs, it will be seen that in subsequent books Deleuze mostly substitutes the notion of Ideas-problems for the concept of sign. We believe that the reason for this is that the concept of sign usually presupposes a consciousness that interprets and deciphers the signs given to it. By contrast, Ideas-problems, according to Deleuze’s final definition of Ideas as structural multiplicities of reciprocally determined differential elements, are objective and unconscious structures that evolve through self-organising processes. This definition of Ideas allows Deleuze to replace the subjective procedures of interpretation with unconscious or impersonal processes elicited by the genetic force of Ideas. For the development of his own ‘calculus or dialectic of Ideas’, we will show that Deleuze adopts important aspects of Kantian Ideas and further invokes some mathematical theories and concepts which he borrows from the French philosopher and mathematician Albert Lautman (1908–44).4

Kant on Ideas of Pure Reason The opening sentence of the first Introduction to Kant’s Critique of Pure Reason reads as follows: Human reason has the peculiar fate in one species of its cognitions that it is burdened with questions which it cannot dismiss, since they are given to it as problems by the nature of reason itself, but which it also cannot answer, since they transcend every capacity of human reason. (CPR A vii)

Kant’s investigation starts off with the startling observation that reason poses questions and problems to us which cannot be solved by our capacity of thought. Reason finds within itself pure concepts which apply neither to any object of experience nor to anything outside experience. It is nonetheless tempted to use these concepts in the determination of transcendent objects, of things-inthemselves, and thus experiments with a transcendent application of these ­concepts to objects outside experience. Thereupon such self-proclaimed sciences as rational psychology (psychologia rationalis), rational cosmology (cosmologia rationalis) and transcendental theology (theologia transcendentalis) emerge, promising to provide 145

conditions of thought: deleuze and transcendental ideas knowledge of transcendent objects. But, as Kant will show, they inevitably stumble into ‘transcendental illusions’, that is transcendental paralogisms and antinomies that give rise to antithetical worldconcepts (for instance, ‘The world must have a beginning in time’ and ‘The world-series is infinite’). The controversies about issues transcending any possible experience demarcate the traditional battlefield of metaphysics. Kant calls the concepts of pure reason, which trespass our empirical limitations and lure us into metaphysical speculations of thought, ‘transcendental Ideas’. The transcendence of our finite perspective is, however, only the consequence of a misuse of transcendental Ideas and cannot be imputed to reason or the Ideas themselves. The ideas of pure reason can never be dialectical in themselves; rather it is merely their misuse which brings it about that a deceptive illusion arises out of them; for they are given as problems for us by the nature of our reason, and this highest court of appeals for all rights and claims of our speculation cannot possibly contain original deceptions and semblances. Presumably, therefore, they have their good and purposive vocation in regard to the natural predisposition of our reason. (CPR A 669/B 697)

Kant draws the concept of Ideas from Plato. However, according to the Platonic account, Ideas can actually only be intuited through a form of reminiscence which involves the task of transcending our finite point of view, that is of transgressing the limits that nature has set to the empirical exercise of our faculties. In the Transcendental Dialectic, Kant explains: Plato made use of the expression idea in such a way that we can readily see that he understood by it something that not only could never be borrowed from the senses, but that even goes far beyond the concepts of the understanding (with which Aristotle occupied himself), since nothing encountered in experience would ever be congruent to it. Ideas for him are archetypes of things themselves, and not, like the categories, merely the key to possible experiences. In his opinion they flowed from the highest reason, through which human reason partakes in them; our reason, however, now no longer finds itself in its original state, but must call back with toil the old, now very obscure ideas through a recollection (which is called philosophy). (CPR A 313/B 370)

It should be noted that Kant misconstrues Plato by attributing to him the notion of a ‘highest reason’ or divine understanding, within which the ideas exist.5 As the editors of the recent English edition of Kant’s Critique of Pure Reason point out, ‘it was not Plato’s doctrine 146

Ideas as Problems that ideas are the thoughts of God, but this doctrine did originate in syncretistic Platonism from the period of the Middle Academy.’6 Paul Guyer and Allen W. Wood explain that Platonists like Philo of Alexandria, Plotinus and St Augustine, as well as all those who merged Platonism with Christian religion, developed a theory of Ideas as existing within the divine mind. However, despite this misinterpretation, Kant is right in describing Platonic Ideas as something transcendent, as archetypes of actions and things in the world, for which we have to reach out in a process of reminiscence. Plato considered Ideas as efficient causes, not only in morality but also in regard to nature itself.7 That is to say, Plato thought that Ideas are a constitutive ground and can actually cause their object. Kant, on the contrary, will reject both claims: Ideas of pure reason are neither transcendent nor do they have a constitutive function. Instead, he defines them as a priori concepts given within the mind that serve a ‘good and consequently immanent use’ (CPR A 642/B 670). This immanent use aims at the understanding and is always regulative, never constitutive. Kant only allows moral Ideas to have a constitutive function as original causes. Thus practical reason, through its Ideas, brings about the reality of the objects of these Ideas. As Kant says: ‘practical reason even has the causality actually to bring forth what its concept contains’ (CPR A  328/B  385). Yet, Ideas of pure reason have a regulative use only, namely ‘to give unity a priori through concepts to the understanding’s manifold cognitions, which may be called “the unity of reason”, and is of an altogether different kind than any unity that can be achieved by the understanding’ (CPR A  302/B  359). Transcendental Ideas demand a unified use of the understanding and an extension of this unity of the understanding, if possible, to the unconditioned, that is the totality of conditions. The unconditioned, Kant says, contains ‘a ground of synthesis for what is conditioned’ (CPR A 322/B 379). In a certain respect, Kant endorses Plato’s theory of Ideas: If we abstract from its exaggerated expression, then the philosopher’s spiritual flight, which considers the physical copies in the world order, and then ascends to their architectonic connection according to ends, i.e., ideas, is an endeavour that deserves respect and imitation. (CPR A 318/B 375)

In fact, Kant attempts something quite similar to Plato. Just as Plato sought to capture the cosmos in a unified and ordered whole, so Kant seeks to comprehend all the cognitions of the understanding 147

conditions of thought: deleuze and transcendental ideas in a unified system. The transcendental Ideas of pure reason point all the concepts of the understanding in one and the same direction, that is they let the concepts of the understanding ‘converge at one point, which, although it is only an idea (focus imaginarius) [. . .] nonetheless still serves to obtain for these concepts the greatest unity alongside the greatest extension’ (CPR A  644/B  672). However, while Plato considered Ideas to provide an objective, constitutive ground, i.e. an ideal architectonic for the cosmos as a unified whole, Kant concedes that the systematic unity (as mere idea) is only a projected unity, which one must regard not as given in itself, but only as a problem; this unity, however, helps to find a principle for the manifold and particular uses of the understanding, thereby guiding it even in those cases that are not given and making it coherently connected. (CPR A 647/B 675)

Thus, Kant says, the systematic unity is ‘merely something subjectively and logically necessary, as method’ (CPR A 648/B 676), not objectively necessary. However, this seems to be a provisional conclusion only. We agree with Henry Allison, Christian Kerslake and others that the systematic unity of empirical knowledge is more than a ‘logical principle’ (CPR A 648/B 676), the function of which is to help the understanding by means of Ideas to secure unity and coherence. Systematic unity is more than a heuristic method, a recommendation or desideratum pursued by reason, but rather a genuinely transcendental principle that requires some kind of deduction (albeit different from the one of categories).8 As Allison points out, this ‘raises the puzzle about how a principle could have both transcendental status and a merely regulative function’.9 We will come back to this point in the section on the problem of a transcendental deduction of Ideas of reason below which deals with the problem of the transcendental deduction of Ideas of reason. Now let us bring Deleuze into the discussion. What Deleuze takes over from Kant is the definition of Ideas as ‘problems’ constituting ‘a unitary and systematic field which orientates and subsumes the researches or investigations in such a manner that the answers, in turn, form precisely cases of solution’ (DR 168/219). Without the presupposition of a problem – i.e. a unitary systematic field, or horizon – no cases of solution could be found. Indeed, although Deleuze usually rejects ‘methods’ in the wake of his critique of the dogmatic Image of thought, this can be said to be a method that he 148

Ideas as Problems adopts himself. For instance, in trying to understand a philosophy, we have to find out what drives this particular philosophical thinking. We must raise ourselves to the level of the underlying ‘problem’. The way in which a philosopher actualises this problem within a unitary, symbolic field under certain conditions and phrased in a specific terminology determines the solution. Solutions always occur as a function of the explication of a problem or problematic field (as in a vector field the local trajectories of solution curves are determined by a singularity in the immediate vicinity). In an interview with Claire Parnet, Deleuze comments on the reason for engaging in the history of philosophy.10 He sees the engagement in the history of philosophy as a long ‘apprenticeship’ in which one learns how to restore the problems that have affected a philosopher and are often concealed from view, and to discover what is innovative in the concepts created in response. According to Deleuze, if one has not found the problem to which a concept corresponds, philosophy remains abstract. He goes on to say that philosophical problems do not always stay the same: they are not simply discovered as something ‘given’, but need to be constituted. This means that in articulating a traditional philosophical problem, in relating it to one’s own conditions and stating it in one’s own terms, one no longer poses it in the same way as it has been posed before. In this sense, the constitution of problems and the creation of concepts as their solutions are an inexhaustible task. There is an evolution that can best be described as a ‘becoming of thought’. Problems evolve and do not simply disappear in their solutions: ‘they are the indispensable condition without which no solution would ever exist’ (DR 168/219), but the condition itself is plastic and changing. The problem is determined at the same time that it determines what it conditions, in other words the condition itself does not remain indifferent or unaffected by the way a solution is determined. Philosophers are compelled to commence and recommence perpetually, to cope with problems that undergo transformations as soon as they are actualised. We must therefore discern the following characteristic features of problems: (1) Solutions do not pre-exist their problems, rather problems are essentially without solution, that is without a final, conclusive solution which answers them once and for all. In this sense, problems are transcendent. In comparison, Kant stated that transcendental Ideas are concepts that ‘exceed the bounds of all experience, in which no object adequate to the transcendental idea can ever occur’ (CPR A  327/B  384). They are given as problems insofar as no corresponding object can ever be 149

conditions of thought: deleuze and transcendental ideas found in experience. For instance, the concept of an absolute whole of experience is a transcendental Idea, ‘since, because we can never project it in an image, it remains a problem without any solution’ (CPR A  328/B  384). (2) Problems are not only transcendent but immanent at the same time (DR 163/212). This means that they are not isolated from the field of solutions but instead entertain an immanent, intrinsic relation with their solutions. They ‘insist’ or ‘persist’ in the solutions. It is important to point also to the differences between Kant’s and Deleuze’s conception of Ideas. For Deleuze, Ideas are problematic, objective structures providing a sufficient reason for the genesis of thought. Kant, on the contrary, still refers to them as subjective, a priori principles providing unity and systematicity as transcendental conditions of knowledge. For Kant, the faculty of transcendental Ideas or problems is reason. Ideas or problems occur within the mind; they are bound up with the transcendental ‘I’. With regard to the question of objective reality, transcendental Ideas are even more remote from objective reality than categories, because no corresponding object of experience can be given to them in concreto. The systematic unity and completeness that transcendental Ideas demand can never be achieved in empirical experience (CPR A 567/B 595). For this reason, ‘no objective deduction of these transcendental ideas is really possible, such as we could provide for the categories’ (CPR A 336/B 393). Deleuze, on the contrary, releases transcendental Ideas from their attachment to the subject and defines them as objective structures. In a sense, Deleuze says, Kant has already pointed out a dimension of objectivity, and in fact Kant claims that as a transcendental principle the systematic unity of nature must be presupposed as ‘objectively valid and necessary’ (CPR A 651/B 679) or at least must have ‘objective but indeterminate validity’ (CPR A  663/B  691). In Deleuze’s words: Kant likes to say that problematic Ideas are both objective and undetermined. The undetermined is not a simple imperfection in our knowledge or a lack in the object: it is a perfectly positive, objective structure which acts as a focus or horizon within perception. (DR 169/219–20)

Deleuze analyses three components of Kantian transcendental Ideas: (1) Ideas are undetermined since no adequate object corresponds to them in experience. (2) Yet, Ideas are determinable by analogy with objects of experience, and (3) they carry the ideal of a complete and 150

Ideas as Problems infinite determination, insofar as they grant affinity to all the concepts of the understanding, such that a continuous transition from every specific concept to every other through a graduated increase of varieties is made possible. The manifold of empirical concepts can thus be brought under a few concepts of the understanding. Ideas, therefore, present three moments: undetermined with regard to their object, determinable with regard to objects of experience, and bearing the ideal of an infinite determination with regard to concepts of the understanding. (DR 169/220)

Deleuze, however, criticises Kant for leaving two of the three moments extrinsic: Ideas are determinable only in relation to objects of experience, and bear the ideal of determination only in relation to concepts of the understanding (DR 170/220–1). Contrary to Kant, Deleuze demands that transcendental Ideas need to be defined as self-organising, intrinsic problematic structures. Let us now turn to Kant’s attempt to provide some kind of deduction, that is to somehow answer the question of the objectivity of transcendental Ideas. The Problem of a Transcendental Deduction of Ideas of Reason It is not sufficiently clear how this deduction is to be understood, whether or not Kant actually undertakes it and what its formal structure is. In any case, it can be argued that Kant needs to give some kind of deduction for transcendental Ideas ‘in order to justify the precise validity and demonstrations that ideas can have’.11 Kant appears to promise a deduction in Section Three of Book One of the Transcendental Dialectic, but this interpretation is not certain since the decisive passage in the Critique of Pure Reason remains ambiguous due to a blurred spelling and a subsequent difference in reading. Is Kant saying ‘we can undertake a subjective introduction [Anleitung] to them [the transcendental Ideas] from the nature of our reason’ or ‘we can undertake a subjective deduction/derivation [Ableitung] of them from the nature of our reason’ (CPR A 336/B 393)? Moreover, no systematic argument in the sense of a deduction can be made out in the section indicated by Kant. Therefore opinions as to what the purport of Kant’s subjective ‘introduction/deduction’ is diverge considerably. Perhaps Kant has in mind to provide a kind of ‘birth certificate’ for them by tracing the transcendental Ideas from the categories of relation 151

conditions of thought: deleuze and transcendental ideas that correspond to the three formal species of syllogism (categorical, hypothetical and disjunctive synthesis). According to this line of argument the strategy of Kant’s deduction consists in extending the categories of relation to the unconditioned, i.e. the totality of conditions (cf. CPR A 322/B 379). Thus the categorical synthesis, which corresponds to the category of inherence and subsistence (substantia et accidens) and which attributes a predicate to a subject, necessarily leads to the concept of the absolute unity of the thinking subject. That is to say, by indefinitely running through a series of terms which all function as predicates (i.e. determinations which can only occur in connection with a determinable), one will finally reach a term which is no longer a predicate but a subject which is thought in itself and cannot be attributed to any other term. The hypothetical synthesis, which corresponds to the category of causality and dependence and claims the existence of a cause for each effect, will lead to the whole sum of conditions by ascending in the series of conditions to the absolutely unconditioned, that is a presupposition which presupposes nothing further. The disjunctive synthesis, which corresponds to the category of community and represents an aggregate of reciprocally determining elements, can be extended to the highest rational concept of an All of reality (omnitudo realitatis), that is the complete manifold of all real or possibly real predicates as members of the division of this highest original concept. In this way pure reason provides the ­transcendental Ideas of the soul, the world and God. However, the objection can be made that this tracing of transcendental Ideas from categories of relation is not the purport of a deduction, no more than the tracing of the table of transcendental categories from Aristotle’s logical functions of all judgements is a deduction. Kant describes it as merely providing the clue (Leitfaden) to the discovery of the categories, their deduction being a quite separate matter (CPR A 70/B 95). In a similar way the categories just provide a schema, which allows for a classification of transcendental Ideas, but does nothing with respect to a grounding or warrant for their alleged necessity with respect to empirical inquiry. Hence what a deduction really requires is to demonstrate the objective validity and objective reality of a priori concepts that (allegedly) borrow nothing from empirical experience but are nonetheless necessary conditions for knowledge or experience. That is to say, a deduction has to provide first an account of how the a priori concepts can count as necessary conditions for the production of knowledge (the problem 152

Ideas as Problems of objective validity), and second a demonstration of the empirical instantiation of the a priori concepts (the problem of objective reality). As Kant admits, the transcendental Ideas cannot be given a corresponding object in experience, so they are even more remote from objective reality than the categories. However, we can still demand a deduction in the first sense: a justification of the objective validity of transcendental Ideas. Although Ideas are not ‘constitutive’ for nature, they are constitutive for knowledge. This means that transcendental Ideas are conditions of knowledge (though not of objects of experience as the categories), and as such their validity must be justified by means of a deduction. As Kerslake notes, this deduction indeed occurs in the Appendix to the Transcendental Dialectic under the heading ‘On the final aim of the natural dialectic of human reason’.12 There, Kant says: One cannot avail oneself of a concept a priori with any security unless one has brought about a transcendental deduction of it. The ideas of reason, of course, do not permit any deduction of the same kind as the categories; but if they are to have the least objective validity, even if it is only an indeterminate one, and are not to represent merely empty thought-entities (entia rationis ratiocinantis), then a deduction of them must definitely be possible, granted that it must also diverge quite far from the deduction one can carry out in the case of the categories. That deduction is the completion of the critical business of pure reason, and it is what we will now undertake. (CPR A 669–70/B 697–8)

In the following passage Kant declares that transcendental Ideas are schemas. Although they do not determine any object of experience, they represent an imagined object or thought-entity which serves to represent other objects to us, ordered in accordance with the conditions of a maximum unity, that is in relation to the imagined object in the Idea. As Kerslake puts it: ‘The Idea thus is a schema of the concept of unconditioned concepts for the orientation of “other” concepts.’13 According to Kant, we are justified in assuming the transcendental Ideas as objective (CPR A  673/B  701), since they provide us with the systematic unity necessary for the acquisition of knowledge.14 However, the imagined objects in the Ideas should not be thought in themselves, but only relative to the world of sense. Kant distinguishes between assuming something absolutely from assuming something relatively (CPR A  676/B  704). In the case of transcendental Ideas, we assume their ideal objects only relatively, that is as regulative principles. Kant concludes: 153

conditions of thought: deleuze and transcendental ideas And this is the transcendental deduction of all the ideas of speculative reason, not as constitutive principles for the extension of our cognition to more objects than experience can give, but as regulative principles for the systematic unity of the manifold of empirical cognition in general, through which this cognition, within its proper boundaries, is cultivated and corrected more than could happen without such ideas, through the mere use of the principles of understanding. (CPR A 671/B 699)

Thus the claim to validity is finally warranted in that transcendental Ideas are schemas for ideal objects in relation to which our experience finds its maximum of systematic unity. Without this ideal focus or horizon that reason posits through its Ideas ‘we would have no reason, and without that, no coherent use of the understanding, and, lacking that, no sufficient mark of empirical truth’ (CPR A 651/B 679).15 According to Kant, this would mean that the classification of natural things in terms of a hierarchical taxonomy of genera and species (such as the classificatory system of Linnaeus; cf. CJ 20: 216), or the construction of systematic explanatory scientific theories, would be impossible for natural sciences. With regard to theory construction, for example, we would be confronted only with a contingent, distributive unity of empirical laws, without being capable of realising relations of derivation, i.e. the derivability from higher-level laws, and the final comprehension of the indefinitely many empirical laws in a collective unity under a few principles. Therefore transcendental Ideas are necessary conditions for the possibility of systematic empirical knowledge. If we ruled out this possibility in advance, our empirical scientific inquiries into the inner nature of things and the laws of nature would be absurd. This is why the understanding, which is legislative with regard to possible objects of experience, is ultimately dependent on reason and its Ideas of purposiveness, unity or totality in nature. Reason has an indispensable task in unifying, totalising and conditioning through its Ideas (cf. CPR A 326/B 382–3). Deleuze’s Rejoinder To be sure, Deleuze is very critical of Kant’s account of transcendental Ideas as unifying or totalising conditions that are supposed to ground a system of nature. As Deleuze says, ‘Kant held fast to the point of view of conditioning without attaining that of genesis’ (DR 170/221). The Kantian account of conditioning is flawed, not only in the case of categories as we have already discussed, but also 154

Ideas as Problems in the case of transcendental Ideas. Kant conceives of Ideas and their imagined objects in analogy to real things. Thus he states that the imagined objects in the Ideas ‘should be grounded only as analogues of real things, but not as things in themselves’ (CPR A 674/B 702). What Kant means by this analogical relation becomes clearer in his discussion of the Idea of a supreme being as the schema of the ideal object ‘God’. Kant allows himself to posit an intelligent being or being of reason (ens rationis ratiocinatae), though not absolutely, but only ‘relative to the world of sense’ (CPR A 677/B 705). He says that we must consider all the things in the world as if they had a supreme and all-sufficient ground [. . .], namely an independent, original, and creative reason, as it were, in relation to which we direct every empirical use of our reason in its greatest extension as if the objects themselves had arisen from that original image of all reason. (CPR A 672–3/B 700–1)

In fact, what Kant has beforehand condemned as an illusion of pure reason – namely the ‘ideal of reason’ of a supreme individual being standing ‘at the summit of the possibility of all things, providing the real conditions for their thoroughgoing determination’ (CPR A 582–3/B 610–11) – proves to be not only a natural and unavoidable illusion but also a useful and compelling fiction for the systematic unity of the empirical world. Kant will pursue this thought further in the Critique of the Power of Judgment where he calls upon us to assume an understanding more powerful than our own for purposes of reflection (not for determining judgements).16 However, the Kantian account of the fiction of a supreme being becomes problematic and dangerously close to a ‘transcendental subreption’ when he starts to determine this mere Idea of a supreme being in anthropomorphic terms as the highest intelligence, that is in analogy with the empirical concept of an intelligence: Still more, in this idea we can allow certain anthropomorphisms, which are expedient for the regulative principle we are thinking of, without fear of blame. For it is only an idea, which is by no means related directly to a being different from the world, but rather referred to the regulative principle of the world’s systematic unity, but only by means of a schema of that unity, namely of a supreme intelligence that is its author through wise intentions. (CPR A 697/B 725)

Kant continues that ‘we must presuppose such a being’, i.e. ‘a unique wise and all-powerful world author’ (CPR A 698/B 726), and ascribe to it an ‘infinite perfection’ (CPR A 700/B 728). Kant conceives the 155

conditions of thought: deleuze and transcendental ideas supreme being in analogy with real things, only extending what we are acquainted with in the empirical world to infinity.17 For Deleuze, however, the transcendental must be purged of all resemblance to the empirical if it really is to serve as a ground (cf. LS 123/149). The transcendental, conceived as a mere abstract doubling of the conditioned, only uncovers the conditions of possibility (of experience or systematic knowledge in general), and not, as Deleuze demands, the conditions of genesis. Kant’s procedure of thinking the objects in the transcendental Ideas as analogues of empirical things is complicit with the logic of resemblance. In this way, transcendental Ideas cannot, as Kant wants, ‘be explained through the concept of the unconditioned, insofar as it contains a ground of synthesis for what is conditioned’ (CPR A 322/B 379). The ground that Kant offers is no more than a copy (décalque) of the empirical that is elevated to a transcendental level. The Kantian transcendental Idea is the sum total of conditions that are thought in the image of the empirical and remain abstract forms without any genetic potential. By contrast, Deleuze demands something unconditioned which is capable of assuring a real genesis (cf. LS 19/30). For Deleuze, Ideas will be conceived as genetic and differential multiplicities. This means that their determination is purely intrinsic and need not rely on a determination by analogy with empirical concepts. Hence Deleuze states that the transcendental Idea is an internal problematic objective unity of the undetermined, the determinable and determination. Perhaps this does not appear sufficiently clearly in Kant: according to him, two of the three moments remain as extrinsic characteristics (if Ideas are in themselves undetermined, they are determinable only in relation to objects of experience, and bear the ideal of determination only in relation to concepts of the understanding. (DR 170/220–1, my emphasis, D. V.)

Before we turn to Deleuze’s theory of Ideas that is heavily inspired by differential calculus, we will look at the role of Ideas in Kant’s third Critique. In The Critique of the Power of Judgment Kant considers different ways in which rational Ideas can be presented in sensible nature, for instance the presentation of Ideas in the beautiful of nature, in the sublime, and finally the aesthetic Ideas of the genius. Daniel Smith argues that in this way rational Ideas enter into an ‘operative relationship’ with reflecting judgement, which in contrast to determining judgement is made without concept and allows for a free and indeterminate play of the faculties.18 We will have to spell out 156

Ideas as Problems what this operative relationship between Ideas and reflecting judgement consists in. This will result in a very different picture to the one that was presented in the Critique of Pure Reason, where the Idea or ‘what is only in the idea [works] as a ground for the harmonious use of reason’ (CPR A 693/B 721). Now, in the Critique of the Power of Judgment Kant uncovers a type of judgement which suspends with the harmonious exercise of the faculties upon a supposed same object and instead induces their ‘discordant accord’ (DR 146/190). We will have to show how Ideas are related to this paradoxical exercise of the faculties that Deleuze characterises as a ‘para-sense’ (DR 146/190).

The Genetic Power of Ideas Kantian Ideas of reason, as we have seen, represent the totality of conditions or the ideal of a complete determination in relation to concepts of the understanding. Their object is a something in general, i.e. a complete systematic unity with which we are not acquainted in the empirical world. In other words, Ideas of reason are absolute concepts without intuition. Nonetheless, Ideas of reason have a good and immanent use for our faculty of cognition. They constitute horizons or ideal foci beyond possible experience towards which the concepts of the understanding converge. In this way, Ideas of reason endow our cognitions with a maximum of systematic unity. However, as has been pointed out, their misuse brings about deceptive illusions. Ideas of reason ought not to be taken as determinations of objects, i.e. things in themselves. Their object is always ‘indeterminate’ and ‘problematic’ for our faculty of cognition. Yet reason experiences an interest in finding some kind of presentation of Ideas in sensible nature. This is so because between the theoretical realm of knowledge, i.e. sensible nature, and the practical or moral realm of freedom, i.e. the supersensible, ‘there is an incalculable gulf fixed [. . .], so that from the former to the latter (thus by means of the theoretical use of reason) no transition is possible’ (CJ 5: 175–6). But if it is possible to show that sensible nature is suitable to express or symbolise something supersensible or receive the effects of moral concepts (e.g. the concept of freedom), then theoretical and practical philosophy can be connected. In the Critique of the Power of Judgment Kant finally seeks to provide a passage from theoretical cognition of sensible nature to practical cognition of the supersensible in the subject. The key notion is that of reflecting judgement which comprises both aesthetic and teleological judgements, the two 157

conditions of thought: deleuze and transcendental ideas parts of the Critique of the Power of Judgment. We need to maintain some caution, since aesthetic judgements and teleological judgements are two quite different types of reflecting judgement.19 However, what is common to both is that, in contrast to determining judgements, reflecting judgements are made without a concept. They do not seek the determination of an object, but instead bear witness to a free and indeterminate play of the subjective faculties. This free and indeterminate play, manifested in reflecting judgement in general, animates and strengthens the faculties and thus promotes the receptivity of the mind for the moral feeling (CJ 5: 197). According to Deleuze, Kant develops in the third Critique a genetic viewpoint that is capable of accounting for the genesis of the relations between the faculties, an account which was still lacking in the Critique of Pure Reason and the Critique of Practical Reason. This means that for the first time Kant attempts to give a sufficient reason for the presumed a priori fact that the faculties can agree in a harmonious accord in spite of their distinct natures. In the first two Critiques, ‘Kant appeals to faculties that are ready-made, whose relation or proportion he seeks to determine, already supposing such faculties are capable of some harmony’ (DI 61/86). But in the Critique of the Power of Judgment Kant pursues the question as to how the free mutual harmony of all the faculties arises. Hence, for Deleuze, the third Critique plays a fundamental role within Kant’s opus of critical philosophy: ‘Beneath the determinate and conditioned relations of the faculties, it discovers free agreement, indeterminate and unconditional’ (DI 69/98). Focusing on the aesthetic part of the Critique of the Power of Judgment, Deleuze works out three parallel geneses: [. . .] the sublime, or a genesis of the reason-imagination agreement; purpose connected with the beautiful, or a genesis of the imagination-understanding agreement according to the beautiful in nature; and genius, or a genesis of the imagination-understanding ­agreement according to the beautiful in art. (DI 68/97)

According to Deleuze’s reading, there is an accord of faculties only on the ground that each faculty is capable of operating according to its own nature and entering into a free, indeterminate and also discordant play. This is why, in Deleuze’s view, ‘Kant’s Critique in general ceases to be a simple conditioning to become a transcendental Education, a transcendental Culture, a transcendental Genesis’ (DI 61/86). 158

Ideas as Problems The Notion of Reflecting Judgement The novelty in the Critique of the Power of Judgment that will allow for a genetic viewpoint of the free play of the faculties is Kant’s notion of reflecting judgement. John Zammito has argued that this idea of reflecting judgement occurred to Kant quite late when he was already in the process of writing the third Critique. Initially, the third Critique was conceived by Kant as a ‘Critique of Taste’, in which he wanted to present a kind of a priori principle for the faculty of feeling pleasure and displeasure and elaborate this in a critique of the beautiful.20 Then in early 1789, Kant came up with the notion of reflecting judgement, presumably when he was busy with writing the First Introduction to the Critique of the Power of Judgment. The fundamental distinction of reflecting from determining judgements led to the transformation of the ‘Critique of Taste’ into the Critique of the Power of Judgment, i.e. a work which comprises not only aesthetic but also teleological judgements. It is assumed that a considerable body of material (such as the ‘Analytic of the Sublime’, §§23–30) was inserted into the already composed ‘Critique of Taste’ only after Kant has worked out the implications of the new idea of a critique of the power of judgement.21 Kant defines the distinction between determining and reflecting judgement in the following way: The power of judgment in general is the faculty for thinking of the particular as contained under the universal. If the universal (the rule, the principle, the law) is given, then the power of judgment, which subsumes the particular under it [. . .], is determining. If, however, only the particular is given, for which the universal is to be found, then the power of judgment is merely reflecting. (CJ 5: 179)

Reflecting judgement thus ascends from the particular to the universal, that is from the manifold of particular empirical laws in nature to equally empirical but higher principles, in order to ground the possibility of a systematic unity in nature. Zammito points out that already in the Critique of Pure Reason Kant had considered such cases in which the particular is given and the universal concept is assumed only problematically. There Kant ascribed to reason in its ‘hypothetical use’ the task of finding the universal concept, and distinguished it from the ‘apodictic use’ of reason which applies to cases in which the universal is given and only judgement is required for subsuming the particular under it (cf. CPR A 646/B 674). 159

conditions of thought: deleuze and transcendental ideas In making the distinction between the ‘apodictic’ and the ‘hypothetical’ use of reason in judgments, Kant came closest to anticipating the key distinction of reflective from determinant judgment which he enunciated in the First Introduction [to the Critique of the Power of Judgment].22

Thus Zammito’s understanding of the third Critique is that in it Kant is transferring the hypothetical function of reason to the reflecting power of judgement.23 It should be noted that in the first Critique, judgement was not considered a faculty in its own right but a function belonging to the understanding (CPR A 69/B 94, A 81/B 107). In the third Critique the faculty of judgement is presented as an intermediate faculty between reason and the understanding.24 It fulfils the role of a mediator, or in other words of an overarching faculty, since it brings together all the other cognitive faculties to the end of producing a single cognitive product, i.e. the judgement. At this point, Deleuze offers a quite different reading of the power of judgement, which to our knowledge has no predecessors. According to Deleuze, the power of judgement is not a further single faculty in the family of higher faculties of cognition. Instead, he argues that since judgements always imply several faculties, the power of judgement simply consists in their accord, ‘whether an accord already determined by one of them playing a legislative role or, more profoundly, in a free indeterminate accord’ (KCP 51/87). Deleuze concludes that Kant did not discover a ‘new’ intermediate faculty of judgement but only elaborated the account of judgement he had already given. The novelty of Deleuze’s reading is that the power of judgement can no longer be interpreted as a spontaneous and innate faculty. On the contrary, if the power of judgement consists in an accord of faculties, the question arises how the accord is effectively engendered? Deleuze distinguishes three general types of accord of the cognitive faculties: the logical common sense, the moral common sense and the aesthetic common sense. His interpretation is arguably still in line with what Kant himself says. For Kant certainly makes use of the notion of ‘common sense’ (sensus communis), by which ‘must be understood the idea of a communal sense, i.e., a faculty for judging’ (CJ 5: 293). Furthermore, he discriminates between a logical common sense (sensus communis logicus) and an aesthetic common sense (sensus communis aestheticus) (CJ 5: 295). While the aesthetic common sense represents ‘the effect of the free play of our cognitive powers’ (CJ 5: 238), the relationship of the faculties in the logical common sense is ‘lawful, under the constraint 160

Ideas as Problems of determinate concepts’ (CJ 5: 295). In other words, the logical common sense designates an a priori accord of imagination, understanding and reason in which understanding is the legislative faculty assigning to each faculty its specific task. Although the acquisition of knowledge is actually in reason’s speculative interest, ‘pure reason leaves everything to the understanding’ (CPR A 326/B 383–4), since it cannot apply its principles immediately to objects of experience. With respect to Kant’s Critique of Practical Reason, Deleuze further distinguishes a ‘moral common sense’, i.e. an a priori accord of understanding and reason with reason being the legislative faculty. In sum, ‘saying that judgement determines an object is equivalent to saying that the accord of the faculties is determined, or that one of the faculties exercises a determining or legislative function’ (KCP 50/85). In the following we will look at Kant’s account of the free and indeterminate account of the faculties with regard to the experience of the beautiful, the sublime and the principle of genius, and consider the intervention of Ideas in the respective reflecting judgements. Exposition of Aesthetic Judgements of Taste In the first two Critiques, Kant presupposes an a priori determinate accord between the cognitive faculties, that is a harmonious relationship with fixed proportions depending on the predominant interest of reason and the particular legislative faculty in this given interest: ‘this agreement is always proportioned, constrained, and determinate’ (DI 57/81). But by what right can we assume such an accord as an a priori fact, since the faculties are essentially distinct in nature? The faculties must first of all, by themselves and spontaneously, be capable of an indeterminate accord without legislation. Now, in the Critique of the Power of Judgment, Kant envisions such a free and indeterminate accord in the aesthetic common sense. The aesthetic judgement, for instance ‘this lily is beautiful’, judges the representation of a single object independent of concepts with regard to the pleasure it arouses. This feeling of pleasure should not be confused with the empirical satisfaction we experience when the representation of an object is ‘agreeable’ to our senses and suitable for our interests. Any interest spoils the judgment of taste and deprives it of its impartiality [. . .]. Taste is always still barbaric when it needs the addition of charms 161

conditions of thought: deleuze and transcendental ideas and emotions for satisfaction, let alone if it makes these into the standard for its approval. (CJ 5: 223)

Kant is concerned with a higher form of pleasure, which is a completely disinterested pleasure (CJ 5: 205), not in the least biased by the existence of the object and the sensible attraction and charm elicited by it. For in the latter case, the aesthetic judgement of taste would remain private; it would only bear on the personal liking of the one who is immediately affected. But the beautiful is that which pleases universally and the pleasure that it induces is expected of everyone else as necessary (CJ 5: 218–19). Judgements of taste lay claim to universal consent and necessity. The difficulty for Kant will be to demonstrate this universality and necessity of judgements of taste, since from the logical point of view aesthetic judgements are singular propositions and are not grounded in any conceptualisation. The universality and necessity they express must therefore be of a special kind. In fact, the aesthetic universality can only be ‘subjective’ because ‘the predicate of beauty is not connected with the concept of the object considered in its entire logical sphere, and yet it extends it over the whole sphere of those who judge’ (CJ 5: 215). Aesthetic judgements require an intersubjective validity, i.e. a universal assent of the whole sphere of judging subjects, which, however, must at the same time be reconcilable with ‘an autonomy of the subject judging about the feeling of pleasure in the given representation’ (CJ 5: 218). The compulsion toward an agreement can therefore only be based on an indeterminate concept. This means that determinate concepts of the understanding, which can be applied to objects of sensible intuition through schemas, are excluded from aesthetic judgements. Furthermore, the necessity of an aesthetic judgement can only be called ‘exemplary’ insofar as it only demands the assent of everyone at the example of a singular instance (CJ 5: 237). Hence, with regard to the judgement ‘this lily is beautiful’, we assume that our aesthetic experience of pleasure is communicable to and valid for everyone, and consequently that everyone feels compelled to agree with it. But what exactly is the determining ground for the communicability of my pleasure and the universal consent? The basis for the judgement of taste cannot be sought in the subjective private conditions of one’s perception. By issuing a judgement of taste one has to take everyone else’s way of reflecting upon the object into account. Now this happens by one holding his judgment up not so much to the actual as to the merely possible judgments of others, and putting 162

Ideas as Problems himself into the position of everyone else, merely by abstracting from the limitations that contingently attach to our own judging; which is in turn accomplished by leaving out as far as is possible everything in one’s representational state that is matter, i.e., sensation, and attending solely to the formal peculiarities of his representation or his representational state. (CJ 5: 294)

Thus the material existence of the object plays no role in grounding the judgement of taste. The higher form of pleasure, which accompanies the judgement of taste, is no immediate result from the object in its sensual richness but rather from the reflection upon the form of the object, i.e. its formal elements – the design or the composition (CJ 5: 225). More precisely, the ‘aesthetic form’ is not simply conceived as a property of the object, but is merged with the reflection of the object in the imagination. The determining ground for the pure judgement of taste is thus the formal purposiveness of the object in relation to the subjective faculties. As Kant says, the determining ground can be nothing other that the state of mind that is encountered in the relation of the powers of representation to each other insofar as they relate a given representation to cognition in general. The powers of cognition that are set into play by this representation are hereby in a free play, since no determinate concept restricts them to a particular rule of cognition. (CJ 5: 217)

Hence the reflection upon the aesthetic form of a given object, its design or composition, occasions a purposive relationship of the subjective faculties, that is a certain state of mind, which is distinguished through its universal communicability. What happens is that the imagination is left free to synthesise according to its own lawfulness without being constrained to schematise according to concepts of the understanding (a ‘lawfulness without law’). Imagination freely corresponds to the understanding as the faculty of concepts in general, such that there is a ‘subjective correspondence of the imagination to the understanding without an objective one’ (CJ 5: 241). According to Deleuze, imagination in its free spontaneity does not schematise: ‘schematism is always the act of an imagination which is no longer free, which finds its actions determined in conformity with a concept of the understanding’ (KCP 41/71). At one place, Kant defines the freedom of imagination as ‘the fact that it schematizes without a concept’ (CJ 5: 287). Deleuze, however, insists that ‘schematism without a concept’ is a bad choice of expression. The free and spontaneous exercise of imagination consists in its reflection upon 163

conditions of thought: deleuze and transcendental ideas the object and its productive inventiveness. It appears that Kant agrees that imagination considered in its freedom cannot be taken ‘as reproductive, as subjected to the laws of association, but as productive and self-active (as the authoress of voluntary forms of possible intuitions)’ (CJ 5: 240). Kant provides as examples English landscape gardens or baroque furniture whose extravagant variety of forms ‘pushes the freedom of the imagination almost to the point of the grotesque’ (CJ  5: 242). In these cases, imagination is freed from stiff (mathematical) regularity that comes across as constraint and induces boredom. Likewise, in natural instances such as ‘the changing shapes of a fire in a hearth or of a rippling brook’ imagination sustains its free play (CJ 5: 244). Kant concludes that taste seems to fasten not so much on what the imagination apprehends in this field as on what gives it occasion to invent, i.e., on what are strictly speaking the fantasies with which the mind entertains itself while it is being continuously aroused by the manifold which strikes the eye. (CJ 5: 243)

In the aesthetic common sense imagination is thus discovered in its original exercise: free reflection and spontaneous, inventive production. It relates to the understanding in a non-specified correspondence, that is it finds itself in agreement only with indeterminate concepts of the understanding (KCP 41/71). In sum, in the First Book of the Analytic of the Beautiful, Kant presupposes the indeterminate aesthetic common sense as the ground for us to produce a determinate common sense. But he has not yet attended to the question whether the aesthetic common sense or taste is an original and natural faculty, or only the idea of one that is yet to be acquired and is artificial [. . .] – this we would not and cannot yet investigate here; for now we have only to resolve the faculty of taste into its elements and to unite them ultimately in the idea of a common sense. (CJ 5: 240)

In Deleuze’s reading, Kant occupies himself in the Analytic of the Beautiful with the task of exposition and he postpones the crucial question, whether the aesthetic common sense is naturally given or whether there is a principle or Idea that can provide us with a rule for producing the aesthetic common sense in us. According to Deleuze, Kant already implicitly suggests that it is not sufficient to assume the aesthetic common sense as a natural fact, but that there needs to be an explanation of how it is engendered in the soul according to 164

Ideas as Problems a principle or Idea. Indeed, it appears that Kant presupposes a kind of ‘indeterminate norm’ (CJ 5: 239) for the genesis of the aesthetic common sense.25 However, a definite answer to the problem of the genesis of the aesthetic common sense can only be given in a deduction, that is a deduction of aesthetic judgement. Contrary to the deduction of synthetic a priori judgements in the Critique of Pure Reason, the deduction of aesthetic judgements is not concerned with the right of conditioning or necessary subjection of given intuition under a priori concepts (quid juris?). Instead, the problem is now one of deducing the genesis of the agreement among faculties: this problem could not make its appearance as long as one of the faculties was considered legislative with respect to the others, binding them in a determinate relation. (DI 61/86)

According to Deleuze, Kant must, however, first turn to the aesthetic judgements of the sublime in order to find the key for the required deduction of judgements of taste. Deleuze will offer a novel reading which explains the confusing order of sections in the Critique of the Power of Judgment – for instance, the insertion of the Analytic of the Sublime (§§23–30) between the Analytic of the Beautiful and the Deduction of the Judgments of Taste, which in its turn is followed by §49 which contains the analysis of genius. Deleuze explains the order of sections from the systematic point of view of a problem, namely the problem of a transcendental genesis of the relationship between the faculties. The Sublime and the Model of Genesis With regard to the experience of the sublime Kant will explore the relation of aesthetic judgements to Ideas of reason, and envision the possibility of finding a ‘presentation’ of rational Ideas in sensible intuition. In fact, he will show that aesthetic judgements, in particular the judgement of the sublime, make us feel the reality of the Idea of a supersensible substrate of humanity, and in this sense reveal the animating principle which engenders the free original exercise of each faculty and their reciprocal accord. What will emerge from an exposition of the experience of the sublime is that the accord of the faculties is the product of a veritable transcendental genesis. In the experience of the sublime, the imagination is confronted with something ‘which is great beyond all comparison’ (CJ 5: 248, emphasis in original), for instance with the immensity of a certain 165

conditions of thought: deleuze and transcendental ideas representation, its formlessness or violent power. Although this overwhelming experience is occasioned by the presence of certain representations of natural objects, the sublime is strictly speaking not the property of an object. It is only by means of a ‘subreption’ that we ascribe to an object in nature what in fact has its source in the self (CJ 5: 257). However, Kant’s account of the sublime in some way resorts to this subreption, since it testifies to our capacity of representing sublimity in objects.26 Kant distinguishes two types of the sublime – the mathematically and the dynamically sublime – and refers each of them to an aspect of reason with its corresponding Ideas. Thus the mathematically sublime brings theoretical reason and the principle of ‘totality’ into play, the dynamically sublime practical reason and the principle of ‘autonomy’. Let us begin with the mathematically sublime. What happens is that in the face of an immense representation (e.g. the starry heaven above us27), reason poses a claim for absolute totality and demands of the imagination that it represents the immense magnitude in one intuition. The underlying problem is that of infinity. While reason is capable of completely comprehending the infinite under one concept, i.e. an Idea of reason (CJ 5: 255), the imagination fails to offer an intuitive whole of something infinite or absolutely great (such as infinite space or past time). The aesthetic estimation of a magnitude (which as ‘aesthetic’ proceeds independently of ­numerical concepts) involves two actions of the faculty of imagination: apprehension and comprehension (CJ 5: 251). The task of apprehension poses no ­specific problem; it can go on indefinitely. In other words, imagination is able to take in spatio-temporal units ad infinitum. But a difficulty arises when the imagination attempts to achieve comprehension, that is to encompass the partial ­representations in one individual intuition. For when apprehension has gone so far that the partial representations of the intuition of the senses that were apprehended first already begin to fade in the imagination as the latter proceeds on to the apprehension of further ones, then it loses on one side as much as it gains on the other, and there is in the comprehension a greatest point beyond which it cannot go. (CJ 5: 252)

Thus the faculty of imagination ‘soon reaches its maximum’ (CJ 5: 252) and finds itself unable to fulfil the demand of reason to present the Idea of a whole. Pushed to the limits of its power, imagination is confronted with its inadequacy for estimating an immense 166

Ideas as Problems magnitude. We experience the impotence of the imagination as an intense feeling of displeasure or pain. But imagination’s ‘striving to advance to the infinite’ and its subsequent failure ‘awakens the feeling of a supersensible faculty in us’ (CJ 5: 250), namely reason, which by means of its rational Ideas has the power to overstep the limits of sensibility. In making ‘intuitable the superiority of the rational vocation of our cognitive faculty over the greatest faculty of sensibility’, the imagination discovers its own true vocation (CJ 5: 257). Thus even the imagination has a supersensible destination for the imagination, although it certainly finds nothing beyond the sensible to which it can attach itself, nevertheless feels itself to be unbounded precisely because of this elimination of the limits of sensibility; and that separation is thus a presentation of the infinite, which for that very reason can never be anything other than a merely negative presentation, which nevertheless expands the soul. (CJ 5: 274)

Hence the conflict between reason and imagination in which imagination seems to succumb by admitting its impotence actually makes the unattainability of rational Ideas in sensible nature palpable for us and thus induces a feeling of the superiority of reason. Thereby imagination achieves an (albeit merely negative) presentation of rational Ideas and the conflict of imagination and reason gives rise to subjective purposiveness: For just as imagination and understanding produce subjective purposiveness of the powers of the mind in the judging of the beautiful through their unison, so do imagination and reason produce subjective purposiveness through their conflict: namely, a feeling that we have pure self-­sufficient reason, or a faculty for estimating magnitude, whose pre-eminence cannot be made intuitable through anything except the inadequacy of that faculty which is itself unbounded in the presentation of magnitudes (of sensible objects). (CJ 5: 258)

The violent relation between reason and imagination is resolved into a ‘discordant concord, a harmony in pain’ (DI 62/87); in Kant’s words, imagination and reason are ‘harmonious even in their contrast’ (CJ 5: 258). This harmony gives rise to a pleasure ‘that is possible only by means of a displeasure’ (CJ 5: 260) and therefore amounts to what can be called a ‘negative pleasure’ (CJ 5: 245). The explanation of the dynamically sublime goes along similar lines. The experience of the dynamically sublime is occasioned by the spectacle of the power of nature, that is material forces such as thunderstorms, volcanic eruptions, destructive hurricanes, the 167

conditions of thought: deleuze and transcendental ideas boundless and turbulent ocean or massive waterfalls (CJ 5: 261). These natural forces make us aware of our physical powerlessness, endanger our possessions and threaten our health and life. Through these violent impressions imagination is pushed to the point where ‘the mind can make palpable to itself the sublimity of its own vocation over nature’ (CJ 5: 262). We might be abased as natural beings, but we experience a ‘self-preservation of quite another kind’ (CJ 5: 261), namely as moral beings. We feel ‘superior to nature within us, and thus also that outside us’ (CJ 5: 269). Equally, just as in the case with the mathematically sublime, the imagination first suffers a deprivation of its freedom. It is used as an ‘instrument of reason and its ideas’ (CJ 5: 269) and forced ‘to treat nature as a schema for them’ (CJ 5: 265). However, by being subjected to this violence of reason, imagination is finally endowed with a much greater power than it sacrifices: it is freed from confinement within the borders of sensibility and undergoes a necessary enlargement to the point where it is capable of giving a negative presentation of the moral Ideas of reason. Thus reason exercises a dominion over imagination ‘in order to enlarge it in a way suitable for its own proper domain (the practical) and to allow it to look out upon the infinite, which for sensibility is an abyss’ (CJ 5: 265). The judgement of the sublime, although it seems to be instilled by something absolutely great in nature, is in fact initiated by reason and its Ideas. It expresses a ‘predisposition to the feeling for (practical) ideas, i.e., to that which is moral’ (CJ 5: 265). The judgement on the sublime thus has its ‘foundation in human nature’, or more concretely in the supersensible substrate of the subject (the soul). It is important to note, however, that, although the predisposition to the feeling for Ideas of reason is already anchored in the soul, Kant claims that for judgements of the sublime a certain culture or refinement is required to make our mind susceptible to Ideas of reason.28 In Deleuze’s reading, this ‘culture’ is not to be understood as an education delivered by school, the church or other institutions. The sublime is not an affair of ‘some empirical and conventional culture; but the faculties which the sublime puts in play point to a genesis of their agreement within immediate discord. This is a transcendental genesis, not an empirical culture’ (DI 63/89). What Deleuze has in mind is a culture or formation which takes place involuntarily, without method and control by the subject, and which communicates a violence to the cognitive faculties causing their discord. Deleuze stresses Kant’s point that ‘the agreement of the imagination and 168

Ideas as Problems reason is engendered in discord. Pleasure is engendered in pain’ (DI 62/88). Thus the transcendental genetic condition of the harmonious relationship of the faculties imposes itself from the outside: it is the exterior of thought, or the unthought in thought which is unthinkable but must be thought nevertheless. By contrast, Kant grounds the transcendental genetic condition again within the subject in saying that the ‘unifying point of all our faculties a priori’ is in the supersensible, the soul. For Kant, ‘no other way remains to make reason selfconsistent’, that is to maintain the unity of reason (of theoretical and practical reason) (CJ 5: 341). Kant conceives the ‘soul’, i.e. the focal point to which all faculties converge, as a genetic subjective principle (unconditioned and self-grounding) from which each faculty extracts its original force and unfolds a free, spontaneous exercise independent of any constraints of common sense, that is unbound by empirical representation. For the case of the sublime Deleuze discerns a genetic model of the relations of imagination and reason. Now he poses the question of whether similar geneses of the relations of the faculties are possible for the subject elsewhere. If this were so, the model of genesis could be extended to the other faculties and each faculty would have its free, original exercise. In Kant’s deduction of judgements of taste, Deleuze sees precisely this: a genetic account of the free, spontaneous exercise of imagination, understanding and reason. Symbolism in Nature Once Kant has worked out the theory of the sublime and along with it revealed our capacity to represent sublimity in objects, he is able to offer a transcendental deduction of judgements of taste. The crucial insight is that beautiful objects, or rather objects that are reflected formally in imagination and deemed beautiful, can be taken to symbolise Ideas of reason. This means that in the symbol a relation is secured between the supersensible and the beautiful object in our intuition. The possibility of symbolisation in nature provided Kant with the opportunity to bring reason into his account of the beautiful that he had previously grounded on a free play between imagination and understanding alone. But he did not sufficiently explain how it comes about that imagination is left free to synthesise and associate, while the understanding is only involved as ‘is requisite for a cognition in general’, ‘without presupposing a determinate concept’ (CJ 5: 217–18). Now Kant suggests that judgements of taste have to do 169

conditions of thought: deleuze and transcendental ideas with indeterminate concepts of the understanding and that it is only through the intervention of reason that the understanding becomes indeterminate and imagination free. In other words, reason will provide (through its Ideas) a transcendental grounding for the free harmony of the faculties in the sense of beauty. We can easily see why judgements of the sublime are in no need of a transcendental deduction: ‘The sublime in nature is only improperly so called, and should properly be ascribed only to the manner of thinking, or rather to its foundation in human nature’ (CJ 5: 280). That is to say, the sublime has its ground only in the relations of the subjective faculties of our mind; it does not rely on any object outside of us. To be sure, the feeling of the sublime is occasioned by the presence of an immense or powerful representation of an object, but this object is itself completely unpurposive and the sublime is only ‘projected’ upon it. In reality, judgements of the sublime are an expression of the purposive relation of the cognitive faculties. The analysis of the feeling of the sublime demonstrates how these relations are effectively engendered, and this account is simultaneously a deduction of judgements of the sublime. The case of judgements of beauty is more complex. The purposiveness of the relations of the faculties in the experience of natural beauty is inseparable from the reflection on the form of the object. Although it is true that this relation to the object is merely one of reflection and not of determination (as in judgements of cognition), nevertheless this relation to the object is enough for judgements of taste to require a special warrant, that is a deduction for their claim to (subjective) universality and necessity. For this reason, Kant has to provide grounds for the free play of the faculties within the reflecting judgement on beauty and the high feeling of pleasure connected with it. In the transitional paragraph (§30) that bridges the account of the sublime and the deduction of pure aesthetic judgements, Kant turns his attention to a striking feature of nature: the abundance of beautiful objects which are scattered even in the depths of the ocean, where the human gaze hardly ever reaches (CJ 5: 279). The subjective purposiveness of the beautiful formations suggests the existence of inner ends in nature. Kant, however, categorically rules out the possibility of a realism of purposiveness. In other words, it is impossible for us to ever objectively determine real ends or purposes in nature. Moreover, every beautiful formation can be explained by blind natural mechanisms. Kant refers to fluid substances that are apparently older than the solid and produce beautiful shapes 170

Ideas as Problems when they condense or solidify (as for instance the formation of a crystal) (CJ  §58). Nevertheless, he acknowledges that the aptitude of nature to produce beautiful objects deserves our attention. Nature apparently has the positive property of instilling an awareness of the internal purposiveness of our faculties through its beautiful objects. In Kant’s words, ‘nature has the property of containing an occasion for us to perceive the inner purposiveness in the relationship of our mental powers in the judging of certain of its products’ (CJ 5: 350). Thus the internal accord of our faculties actually implies an external accord between nature and our intellectual faculty, albeit this external accord can only be contingent: ‘The agreement thus has no goal’ (DI 64/90). There cannot be a necessary subjection of nature, because in this case the aesthetic judgement would proceed by determinate a priori concepts and no longer be merely heautonomous (legislating only for itself). In any case, reason has a profound interest in this contingent accord between nature and the subjective faculties. It is of great importance that nature should at least show some trace or give a sign that it contains in itself some sort of ground for assuming a lawful correspondence of its products with our satisfaction that is independent of all interest [. . .], reason must take an interest in every manifestation in nature of a correspondence similar to this. (CJ 5: 300)

Through the abundance of beautiful and free formations, nature proves to be inherently qualified for the presentation of the concept of ends or moral Ideas of reason. In Deleuze’s reading, this intellectual interest of reason is a ‘meta-aesthetic interest’ synthetically connected with our judgement of taste, which is nonetheless entirely disinterested in the material existence of the object. The intellectual interest is not an interest in beauty as such; it remains external to the judgement of taste. ‘In other words, esthetic pleasure is disinterested, but we feel a rational purpose when the productions of nature agree with our disinterested pleasure’ (DI 65/92). The meta-aesthetic interest of reason is primarily attached to the ‘free materials’ of nature, that is the fluid substances, or colours and sounds. As Kant admits, ‘the charms in beautiful nature, which are so frequently encountered as it were melted together with the beautiful form, belong either to the modifications of the light (in the colouring) or of the sound (in tones)’ (CJ 5: 302). It is remarkable that Kant at this point no longer abstracts from the ‘charms’ of an object, its colour and sound. Hitherto it appeared that he favoured a 171

conditions of thought: deleuze and transcendental ideas kind of ‘formalism’ in art, since he insisted with respect to pictorial or plastic arts that it is always the design that counts, or with respect to music the formal structure of composition. Now he enlarges his formal aesthetic of taste by adding what Deleuze calls ‘a material meta-aesthetic’ (KCP 48/83), insofar as he explicitly refers to colours and sounds as the decisive features associable with moral Ideas. Kant takes as examples the song of a bird symbolising joy and contentment with its existence, and the variety of colours symbolising different virtues. What exactly is the role of the moral Idea here? Let us consider one of Kant’s examples in greater detail. When a white lily is taken as a symbol of pure innocence, the concepts of ‘whiteness’ and ‘lily’ are thereby artificially enlarged into indeterminacy (or as Freud would put it, the concepts of the understanding become ‘overdetermined’). In any case, through the intervention of reason and its moral Idea the understanding exhausts its capacity of determination, and imagination is set free to associate new representations which are not given in the concepts of ‘whiteness’ and ‘lily’. At one point, Kant describes this procedure of imagination as ‘the transportation of the reflection on one object of intuition to another, quite different concept, to which perhaps no intuition can ever directly correspond’ (CJ 5: 353). In other words, imagination manages to render moral Ideas sensible by finding an indirect presentation of the morally good. Kant also calls this indirect presentation of rational Ideas in sensible intuition ‘symbolisation’ or ‘hypotyposis’. However, the definition he gives of the procedure of ‘hypotyposis’ again puts much emphasis on the formal aspect and explains it in an analogy with schematisation: To a concept which only reason can think, and to which no sensible intuition can be adequate, an intuition is attributed with which the power of judgment proceeds in a way merely analogous to that which it observes in schematization, i.e., it is merely the rule of this procedure, not of the intuition itself, and thus merely the form of the reflection, not the content, which corresponds to the concept. (CJ 5: 351)

According to this definition, we abstract in symbolisation from the perceptible content of a given object, only reflect upon its form and use the formal rule or concept as a schema for an Idea of reason. Kant sees here an analogy of symbol to schema. In schematisation a rule, which specifies the concept, is applied directly to sensible intuition (in disregard of the particular content). In symbolisation, the power of judgement has to perform ‘a double task, first applying the 172

Ideas as Problems concept to the object of a sensible intuition, and then, second, applying the mere rule of reflection on that intuition to an entirely different object, of which the first is only the symbol’ (CJ 5: 352). For instance, the way in which a handmill functions, that is through the application of an external force, represents a merely externally constrained mechanism and as such it is taken to symbolise the despotic rule of an absolute monarch ruling only by his single will. On the other hand, the internal mechanism through which the soul governs the body is taken as the formal rule for a purposive governance according to internal laws and therefore is used as a symbol for a good and just monarch.29 In light of this definition of symbolisation and the given examples, it seems that a symbol is a kind of structural metaphor, in which only the form or the structural organisation of an object is considered, then extracted as a rule and transported to another object that otherwise could perhaps not be given any intuition at all. A frequently used contemporary example of such a structural metaphor is the symbolisation of politics or warfare by means of a sports game (such as football). Two things need to be said here as an objection to Kant’s definition of symbols in analogy to schemas. First, Kant is not quite right to parallel the imagination’s act of symbolisation, which proceeds in a loose accord with indeterminate concepts of the understanding and is animated by indeterminate Ideas of reason, with the imagination’s act of schematisation, which is conceived as a mere construction of determinate concepts in sensible intuition (as in geometry, for instance). This is to say that the act of symbolisation is an autonomous and creative act of the imagination30 which is not comparable to the forced exercise of imagination in schematisation.31 Second, Kant’s previous examples of symbolisation, such as the symbolic presentation of pure innocence in the object of the white lily, certainly associate rational Ideas with the free materials of sensible nature, that is colours, sounds, etc. Kant’s move to make the reflection on mere form or structure and the principle of analogy the basis for the imagination’s free, spontaneous and productive act of symbolisation is suspect. Symbolisation is rather comparable to the creation of ‘aesthetic Ideas’ that Kant describes as the faculty of genius. As we will see in the following section, genius consists in the capacity of finding imaginative representations for the expression and cultural communication of rational Ideas. Let us go back, however, to the problem of the deduction of judgements of taste, in other words to the genesis of the relations of the 173

conditions of thought: deleuze and transcendental ideas faculties in the aesthetic common sense. In the exposition of aesthetic judgements Kant had assumed a free, mutual harmony between imagination and understanding. Now, however, we can see that reason must have already been involved from the start, that reason indeed lies at the origin of the whole enterprise. This is because the experience of the beautiful implies a moral disposition, or in Kant’s words the beautiful is the symbol of the morally good, and [. . .] only in this respect (that of a relation that is natural to everyone, and that is also expected of everyone else as a duty) does it please with a claim to the assent of everyone else, in which the mind is at the same time aware of a certain ennoblement and elevation above the mere receptivity for a pleasure from sensible impressions, and also esteems the value of others in accordance with a similar maxim of their power of judgment. (CJ 5: 353)

In summary, the universal assent and feeling of pleasure connected with the aesthetic judgement on a singular object have their transcendental ground in a subjective, yet universally valid, principle: the free, indeterminate accord of the cognitive faculties that are animated and enlivened by moral Ideas of reason and reason’s interest in their objective reality. Genius as the Faculty for Aesthetic Ideas Kant’s deduction of aesthetic judgements of taste, the principle of which, as we have seen, is reason’s meta-aesthetic interest in nature’s production of beautiful objects and its suitability for symbolising moral Ideas, left a problematic division between natural beauty and the beautiful in art. Indeed, Kant denies that the beautiful in art provides any ‘proof of a way of thinking that is devoted to the morally good or even merely inclined to it’ (CJ 5: 298). He claims that there is no inner affinity between the fine arts and a morally good way of thinking. Art is either mere imitation of natural beauty, or is intentionally directed toward our satisfaction. Thus Kant remarks that the man in a museum, who ‘gladly leaves the room in which are to be found those beauties that sustain vanity and at best social joys and turns to the beautiful in nature’ bears witness to a beautiful soul favourable to the moral feeling and deserves our esteem (CJ 5: 300). However, this separation of the beautiful in nature and in art is not justified by the discussion in the Analytic of the Beautiful, where Kant refers indiscriminately to aesthetic judgement on beauty as such 174

Ideas as Problems and bases the feeling of pleasure it arouses on a free play of imagination and understanding. For this reason, Kant may have felt the need to restore the unity of the two types of the beautiful in sections 58 and 59. He achieves this reunification by considering beautiful art as the product of genius, the faculty for aesthetic Ideas, through which art acquires its rule. Kant distinguishes aesthetic Ideas from rational Ideas of reason. While the Idea of reason is a concept (of the supersensible) to which no adequate intuition can ever be given, the aesthetic Idea is an intuition for which no concept can be found adequate. The rational Idea is an indemonstrable concept of reason, and the aesthetic Idea an inexponible representation of the imagination (CJ 5: 342). Kant describes the relation between both as oppositional, yet complementary: ‘One readily sees that it [the aesthetic Idea] is the counterpart (pendant) of an idea of reason, which is, conversely, a concept to which no intuition (representation of the imagination) can be adequate’ (CJ 5: 314). Contrary to Kant, Deleuze stresses that ‘this is a false opposition; there are not two sorts of Ideas’ (DI 67/94–5). ‘The aesthetic Idea is really the same thing as the rational Idea: it expresses what is inexpressible in the latter’ (KCP 48/82). He argues that for Kant, the objects of both aesthetic and rational Ideas are ‘spiritual events’ (KCP 47/81) beyond the boundaries of experience. An Idea of reason either denotes invisible beings, beings of heaven or hell, or it refers to empirical events such as death or love and elevates them to events of the spirit. An aesthetic Idea, on the other hand, also expresses something inexpressible that cannot be found in nature, because it invents a second nature whose phenomena are spiritual events (KCP 48/81–2).32 The imagination (as a productive cognitive faculty) is, namely, very powerful in creating, as it were, another nature, out of the material which the real one gives it. We [. . .] transform the latter, no doubt always in accordance with analogous laws, but also in accordance with principles that lie higher in reason (and which are every bit as natural to us as those in accordance with which the understanding apprehends empirical nature); in this we feel our freedom from the law of association (which applies to the empirical use of that faculty), in accordance with which material can certainly be lent to us by nature, but the latter can be transformed by us into something entirely different, namely into that which steps beyond nature. (CJ 5: 314)

Imagination is here described as a productive faculty that proceeds freely in a spontaneous and ‘transcendent’ exercise. It creates from 175

conditions of thought: deleuze and transcendental ideas the material that it finds in nature a new and richer material (supplemented with further representations) and thereby ‘aesthetically enlarges the concept itself in an unbounded way’ (CJ 5: 315). Yet the creation of a ‘second nature’ or an ‘aesthetic Idea’ requires more than ‘the rapidly passing play of the imagination’ (CJ 5: 317). What is presupposed is ‘the happy relation [. . .] of finding ideas for a given concept on the one hand and on the other hitting upon the expression for these’ (CJ 5: 317) in order to make what is unnameable in a certain representation universally communicable. This talent is called ‘genius’: it is a rather exceptional ‘inborn predisposition of the mind (ingenium) through which nature gives the rule to art’ (CJ 5: 307). This does not mean that nature functions as the normative standard that art has to imitate and that it can approximate to perfection if we are skilled and diligent apprentices. Quite to the contrary, it means that nature has equipped a few selected individuals with a certain disposition of mental powers which cannot be attained by the following of rules but which is a ‘natural gift’ (CJ 5: 307). The artist-creator endowed with genius is able to create aesthetic Ideas that render rational Ideas sensible and occasion much thinking, that is they give more to think than can be grasped and made distinct in any determinate thought (CJ 5: 314 and 5: 315). Aesthetic Ideas strengthen our cognitive faculties and animate the mind by opening up for it an immeasurable field of representations related to a concept. The creation of aesthetic Ideas itself is a procedure that for the main part occurs unconsciously and hence the author of a product that he owes to his genius does not know himself how the ideas for it come to him, and also does not have it in his power to think up such things at will or according to plan, and to communicate to others precepts that would put them in a position to produce similar products. (CJ 5: 308)

According to Kant, the products of genius are characterised by a ‘certain boldness in expression’ and a ‘deviation from the common rule’ in the sense of a ‘deformity’. However, it is not possible, as it were, to read off from these products a rule or precept as to how to produce art. Every attempt to imitate the art of the genius will become a sort of ‘aping’, and the spirit and boldness of the original artwork will be lost in the imitation, which will ‘suffer from anxious caution’ (CJ 5: 318). The products of genius are not examples apt for imitation ‘but for emulation by another genius, who is thereby awakened to the feeling of his own originality, to exercise freedom 176

Ideas as Problems from coercion in his art in such a way that the latter thereby itself acquires a new rule’ (CJ 5: 318). Thus the work of a genius casts an appeal toward another genius across intermediate spaces and times. An intersubjective community of geniuses is thus constituted. The question to ask here is, what function this Kantian ‘romanticism’ concerning the genius has with regard to the overall aesthetic project of finding an a priori and genetic principle for the free use of the cognitive faculties. We can say that the genius also functions as an a priori genetic principle for the ‘unintentional subjective purposiveness in the free correspondence of the imagination to the lawfulness of the understanding’ (CJ 5: 317–18). However, the genius stands on the side of the production of beautiful art. What is more, the genius is a very ‘rare phenomenon’, being a ‘favourite of nature’ (CJ 5: 318). Thus, as Deleuze points out, ‘we are faced with this difficulty: how can such a genesis have a universal implication, if it is governed by the singularity of genius?’ (DI 68/96). An answer can be found in the distinction of two capacities that the artist or genius ought to possess: one is ‘spirit’, i.e. the animating principle in the mind that provides rich material for products of art. Spirit is the capacity that constitutes the originality of the artist-genius; it is given by nature as a gift and cannot be attained by the most hard-working imitator and apprentice. However, spirit is only one essential element of the character of the genius, because taste is also required. The abundance of material has to be worked on and given a form, and thus presupposes academic training and the knowledge of determinate rules (CJ 5: 310). Taste, like the power of judgment in general, is the discipline (or corrective) of genius, clipping its wings and making it well behaved or polished; but at the same time it gives genius guidance as to where and how far it should extend itself if it is to remain purposive; and by introducing clarity and order into the abundance of thoughts it makes the ideas tenable, capable of an enduring and universal approval, of enjoying a posterity among others and in an ever progressing culture. (CJ 5: 319)

If the products of genius are to stand up to the power of judgement, then it is necessary that the artist-genius finds the form that not only contents himself, but that is favourable to the judgement of taste and therefore not detrimental to the freedom in the play of the cognitive faculties on the part of the spectator. If the artist-genius is able to do both, create the materials and give form to his art, then the artwork assumes a central place in culture. Indeed, art can then serve as a 177

conditions of thought: deleuze and transcendental ideas model, that is have an exemplary function as a standard or a rule for judging (CJ 5: 308). Thus it will instil in the spectator the feeling that he is capable of freely and self-actively judging the beautiful object, it will animate his faculties to a free accord, strengthen the mind and enhance its susceptibility for moral Ideas. In this way, the genetic principle of genius, which pertains to an elect of nature, acquires the value of a universal principle when considered in its effects on the community of those who judge. We have seen throughout the preceding sections on Kantian Ideas in the Critique of the Power of Judgment that Deleuze’s interest focuses on the different types of genesis of the proportion of mental powers and the various ways in which rational Ideas can be presented in sensible nature. In the sublime the presentation is direct but negative, and done by projection; in natural symbolism or in the interest of the beautiful the presentation is positive but indirect, and is achieved by reflection; in genius or in artistic symbolism the presentation is positive but secondary, and is achieved through the creation of another nature. (KCP 48–9/83)

The crucial part of Deleuze’s argument is that it is through the encounter with rational Ideas rendered sensible by their incarnation in nature that our faculties are animated to transgress the imposed restriction of logical common sense and to act spontaneously and freely within a discordant accord. Deleuze makes the aesthetic common sense the object of a transcendental genesis (KCP 42/73). In all three cases of aesthetic judgement, reason brings its rational and moral Ideas into play. In other words, Ideas have a certain genetic power that bears on the relations of the cognitive faculties and gives rise to their paradoxical disjoint exercise in the aesthetic common sense. In Deleuze words, ‘Ideas, far from having as their milieu a good sense or a common sense, refer to a para-sense which determines only the communication between disjointed faculties’ (DR 146/190). Daniel Smith argues that aesthetic judgements provide the model for this operative relationship between Ideas and the ­paradoxical exercise of the faculties: It is precisely because of the intervention of the Ideas of reason (which enlarge the concepts of the understanding) that the imagination becomes free and the concepts of the understanding become indeterminate in ­aesthetic judgments.33 178

Ideas as Problems Although Ideas of reason are never fully and positively incarnated in nature, they nonetheless provoke the mind’s effort to make the representation of the senses adequate to the Ideas (CJ 5: 268). This means that the ultimate ‘unattainability’ of cognising nature as the presentation of something supersensible elicits the inventiveness and creativity of imagination. Deleuze will retain this Kantian aspect of the impossibility of cognition and transform it into the ‘powerlessness’ (DR 147/192) of thought to fully grasp the transcendental element, i.e. the Idea or the problematic, which remains empirically unthinkable. In fact, Kant discovered the Idea or the problematic as the transcendental horizon, which essentially belongs to nature, things and events, and he also discovered the transcendent exercise of the faculties and their discordant accord, which is elicited by the contingent encounter with the transcendental element. Deleuze will put to use all these Kantian aspects for his own conception of Ideas: the objective and problematic character of Ideas, their capacity of being presented in the sensible world (the ‘sign’), their unattainability or transcendence from the point of view of cognition, and their genetic power to release a transcendent exercise of the faculties.

Deleuze’s Dialectic of Ideas Known for his ‘anti-dialectical’ and ‘anti-Hegelian’ tendencies, Deleuze surprises the reader by presenting a ‘dialectic’ of Ideas in Chapter Four of Difference and Repetition, entitled ‘Ideas and the Synthesis of Difference’ (‘Synthèse idéelle de la différence’). The use of the term ‘dialectic’ is certainly meant provocatively but it also implies the sincere resumption of a long tradition of ‘dialectical thought’ albeit in a renewed manner. Deleuze is never simply ‘against’ his ostensible enemies (Plato, Kant, Hegel, etc.): he rather mobilises some of their ideas and concepts and develops them further from the point of view of a philosophy of difference or the ‘­differential’. As Daniel Smith says: In this manner, Deleuze places himself squarely within the heritage of his so-called ‘enemies’ – the great philosophers of dialectics: Plato and Aristotle, Kant, and Hegel – and develops his concept of dialectics through them. In this sense, Deleuze’s reworking of dialectics extends beyond both Hegel and Kant.34

179

conditions of thought: deleuze and transcendental ideas According to Deleuze, ‘dialectic is the art of problems and questions, the combinatory or calculus of problems as such’ (DR 157/204). In his view, dialectical thought is seriously perverted when the ‘problematic’ is misunderstood: Whenever the dialectic ‘forgets’ its intimate relation with Ideas in the form of problems, whenever it is content to trace problems from propositions, it loses its true power and falls under the sway of the power of the negative, necessarily substituting for the ideal objecticity [objectité] of the problematic a simple confrontation between opposing, contrary or contradictory, propositions. This long perversion [dénaturation] begins with the dialectic itself [that is, with Plato], and attains its extreme form in Hegelianism. (DR 164/213)

Let us consider Aristotle’s Dialectic, for example. Aristotle’s Dialectic deals with the manner of posing problems, whereas the Analytics is concerned with the formal procedures by which syllogisms reach a conclusion. However, for Aristotle, the art of posing problems consists for the most part in making out the points of views that are shared by the majority of people. These generally shared opinions form the places (the topoi) that serve as the premises or the solution of a problem. As we have already seen, Deleuze criticises Aristotle for falling prey to the ‘natural illusion’, that is, for tracing problems from propositions of common sense (mere doxa). Deleuze also blames Aristotle, as well as Kant and others for succumbing to the ‘philosophical illusion’ on which we will have more to say in the next section on Deleuze’s mathematical sources. But first let us now turn briefly to Deleuze’s criticism of Plato’s, Kant’s and Hegel’s dialectic. That Plato recognised a profound relation between problems and Ideas can readily be seen in the Socratic dialogue Meno. In the focus of this dialogue is a geometrical problem that finally leads the disciple to ‘remember’ the original Idea. However, the Platonic theory of problems is completely dependent on ‘the classic master–pupil situation where the pupil understands and follows a problem only to the extent that the master already knows the solution and provides the necessary adjunctions’ (DR 180/233). According to this model, one remains in an infantile state, in dependency on a master who sets the problem, knows the solution and has the powerful authority to determine the result as true or false (DR 158/205). The situation seems different in Plato’s aporetic dialogues, where the search for truth that pursues the question ‘What is X?’ leads into contradictions. The aporetic dialogues do indeed present problems without solution, 180

Ideas as Problems yet the aporia is in fact only a propaedeutic means for delineating a domain of problems that will then be determined by other procedures (cf. DR 188/243). It does not lead to a new conception or a new manner of posing questions and problems. Nevertheless, Deleuze remarks in favour of Plato that Plato’s dialectic does not yet attribute to the negative moment (the moment of contradiction) the decisive role which it will play later in the Hegelian dialectic (DR 63/88). Deleuze says that it is Kant who must be credited with first stipulating the problem as the true object of the Idea and consequently with discovering ‘the real source of the dialectic’ (DR 161/209). Ideas for Kant are purely problematic. That is, they are no longer conceived as transcendent essences as in Plato. However, as we have seen, Deleuze insists that transcendental Ideas have to be released from the (transcendental) subject and their analogical relation to the empirical, in order to acquire a status of ‘ideal “objecticities [objectités]” possessing their own sufficiency and implying acts of constitution and investment in their respective symbolic fields’ (DR 159/206). One of the important features of Ideas as objective structures is that they are both transcendent and immanent. Ideas are fully immanent which is to say that there is no gap between their ideal objectivity and their immanence in the empirical, historical world. There is an objectivity, Deleuze says, ‘which implies that Ideas no more than Problems do not exist only in our heads but occur here and there in the production of an actual history’ (DR 190/246). It follows that the question that corresponds to Ideas cannot be that of essence ‘What is X?’ but has to be diversified according to the incarnation of Ideas in empirical circumstances. The leading questions are therefore ‘who?’, ‘when?’, ‘in which cases?’, ‘how?’, ‘from what viewpoint?’ ‘These questions are those of the accident, the event, the multiplicity – of difference – as opposed to that of the essence, or that of the One, or those of the contrary and the contradictory’ (DR 188/244). This is why Deleuze finds the nature of the dialectic distorted when it is based on the Platonic question ‘What is X?’ The answer to the question ‘What is X?’ ‘is always God as the locus of the combinatory of abstract ­predicates’ (DR 188/243). Deleuze’s criticism of Hegel is well-known and can be found throughout his work (in particular that of the early period). According to Deleuze, Hegel’s dialectic starts off with abstract concepts or ‘generalities’ and constructs a dialectical movement by means of the intermediary of an opposite (equally general) concept. But ‘of what use is a dialectic that believes itself to be reunited with 181

conditions of thought: deleuze and transcendental ideas the real, when it compensates for the inadequacy of a concept that is too broad by invoking the opposite concept, which is no less broad and general?’ (B 44/38). In fact, nothing moves in the dialectical movement as conceived by Hegel. It is a ‘false movement – in other words, the abstract logical movement of “mediation” ’ (DR 8/16). Opposition and contradiction cannot be the moving force of the dialectical process; rather they ‘seemed to us to be surface effects and conscious epiphenomena, while the unconscious lived on problems and differences’ (DR 268/344). Deleuze especially criticises the Hegelian dialectic for substituting the negative for the problematic and differential. However, the history of dialectical thought does not stop with Hegel. Deleuze points to the largely unknown mathematician and philosopher Albert Lautman (1908–44) who – inspired by reflections on Plato and Heidegger – proposed the concept of ‘dialectical Ideas’ which display an ideal reality distinct from the factual existence of mathematical facts, objects and theories. Lautman’s principal thesis is that mathematics participates in a dialectic that dominates it.35 In his essay ‘Nouvelles recherches sur la structure dialectique des mathématiques’ (1939), he sets out to analyse the nature of this domination in terms of abstract Ideas and their concrete realisations in mathematical theories. As we will see, Lautman had a great impact on Deleuze. Indeed, we must say that the characterisation of Ideas as differing in kind from mathematical theories or solutions and as being both transcendent and immanent comes originally from Lautman (cf. DR 178–9/231–2). Nowhere better than in the admirable work of Albert Lautman has it been shown how problems are first Platonic Ideas or ideal liaisons between dialectical notions, relative to ‘eventual situations of the existent’; but also how they are realised within the real relations constitutive of the desired solution within a mathematical, physical or other field. It is in this sense, according to Lautman, that science always participates in a dialectic which points beyond it – in other words, in a meta-mathematical and extra-propositional power – even though the liaisons of this dialectic are incarnated only in effective scientific propositions and theories. Problems are always dialectical. (DR 163–4/212–13)

It is important to note that Lautman’s version of Platonism is, in fact, very different from what is generally defined as Platonism in mathematics. For Lautman, the realm of Ideas is not separated from its field of realisation through an irreducible rift such as that between 182

Ideas as Problems the eidos and its representation, or the ideal model and its copy.36 Lautman says: We do not understand by Ideas the models whose mathematical entities would merely be copies, but in the true Platonic sense of the term, the structural schemas [schémas de structure] according to which the effective theories are organized.37

Thus Lautmanian Ideas are not exactly Platonic Ideas but structural schemas that establish possible relations between pairs of concepts. Examples of such conceptual couples would be ‘local/global’, ‘intrinsic/extrinsic’, ‘continuous/discontinuous’, ‘finite/infinite’, etc. According to Lautman, we can have access to the realm of Ideas by examining different mathematical theories that affirm the existence of a common structural schema or dialectical Idea. This means that through a descriptive analysis, relying upon concrete mathematical examples, one can attain the realm of dialectical Ideas.38 However this is not to imply that dialectical Ideas are mere logical abstractions taken from the concrete. Instead they have to be understood in a Heideggerian way as ontological questions or problems: ‘Insofar as “posed questions”, they [the dialectical Ideas] only constitute a problematic relative to the possible situations of entities.’39 The type of anteriority they involve is that of the question in relation to the answer: ‘It is of the nature of the response to be an answer to a question already posed, and this, even if the idea of the question comes to mind only after having seen the response.’40 In his ‘principal thesis’, a text published in 1938, Lautman describes the type of anteriority of dialectical Ideas as follows: ‘The only a priori element that we conceive is given in the experience of the exigency of the problems, anterior to the discovery of their solutions [. . .]. We understand this a priori in a purely relative sense, and with respect to mathematics.’41 However, Lautman emphasises that the logical schemas [schémas logiques] of dialectical Ideas are ‘not anterior to their realization within a theory’.42 In other words, they are not anterior in the sense of a chronological anteriority. Nor is the type of anteriority involved that the logicists (members and proponents of the Vienna Circle) advocate, namely the foundational anteriority of logic to mathematics.43 According to this logicist view, the whole of mathematics was supposed to be reconstructed from a small number of primitive logical concepts and propositions. As Simon Duffy explains in his essay on Lautman, Lautman was strictly opposed to such logical positivism: 183

conditions of thought: deleuze and transcendental ideas Against the logicist claim that the development of mathematics is dominated a priori by logic, Lautman proposes a ‘metaphysics of logic’, and calls for the development of a ‘philosophy of mathematical genesis’.44

Indeed, Lautman favours a very special type of anteriority of dialectical Ideas in relation to mathematics. He describes it in terms of a relation of intrinsic genesis. An intimate link [lien intime] thus exists between the transcendence of Ideas and the immanence of the logical structure of the solution to a dialectical problem within mathematics. This link is the notion of genesis which we give it [. . .] by describing the genesis of mathematics from the Dialectic.45

Lautman’s concept of genesis by no means indicates a genesis that takes place in one way only as in the case of Platonic Ideas. Rather the matter is one of a reciprocal genesis. On the one hand, dialectical Ideas have a productive power. One might say that the conceptual couples produce a dialectical movement that gives rise to new theories. In Lautman’s words: ‘The genesis is then no longer conceived as the material creation of the concrete from the Idea, but as the advent [venue] of notions relative to the concrete within an analysis of the Idea.’46 There are thus certain mechanisms ‘in which the analysis of Ideas is extended in effective creation, in which the virtual is transformed into the real’.47 For instance, according to Simon Duffy, ‘in the case of the example of the local–global conceptual couple, the new mathematical theory that was effectively created was Poincaré’s qualitative theory of differential equations, or the theory of automorphic functions.’48 On the other hand, mathematical theories can give rise to a dialectical Idea, insofar as they extract a logical schema or pair of notions. As Lautman puts it: But mathematical theories can conversely give rise to the idea of new problems that have not previously been formulated abstractly. Mathematical philosophy, as we conceive it, therefore consists not so much in retrieving a logical problem of classical metaphysics within a mathematical theory, than in grasping the structure of this theory globally in order to identify the logical problem that happens to be both defined and resolved by the very existence of this theory.49

Lautman thus develops a new conception of metaphysics, a metaphysics relative to mathematics, or as Simon Duffy calls it, a ‘metamathematics in metaphysical terms’.50 It is necessary to turn from the 184

Ideas as Problems mathematical theories to the metaphysical, i.e. the dialectic, which is, however, intimately connected with mathematics through a process of intrinsic genesis. The importance of Lautman’s theory of dialectical Ideas for Deleuze has probably already become apparent. For Deleuze, Lautman’s work stands out as an original landmark in the history of modern epistemology, for it recognises the ‘double irreducibility of “problems” ’ (DR 323/211, note 22/1), that is to say, both the global formation of a transcendental problematic structure and its immanence in local solutions. As Lautman puts it: Insofar as posed problems, relating to connections that are likely to support certain dialectical notions, the Ideas of this Dialectic are certainly transcendent (in the usual sense) with respect to mathematics. On the other hand, as any effort to provide a response to the problem of these connections is, by the very nature of things, constitution of effective mathematical theories, it is justified to interpret the overall structure of these theories in terms of immanence for the logical schema of the ­solution sought after.51

The very status of dialectial Ideas as being both transcendent and immanent with respect to mathematical theories resonates with Deleuze’s claim of the transcendence and immanence of problems with respect to their solutions. Furthermore, Lautman as well as Deleuze both insist on the ‘ontological distinction’ between dialectical Ideas-problems and their solutions and determine the nature of the relation between them as an intrinsic genesis. Interestingly, Lautman had already used the term ‘virtual’ to characterise the ideal reality of dialectial Ideas and described the movement of effective creation as a transformation from the virtual into the real. However, despite the obvious parallels between Lautman and Deleuze, there are considerable differences as well. First of all, as Duffy has pointed out, Ideas for Deleuze are more Kantian than Platonic in character. They have to be understood as ‘purely’ problematic.52 Furthermore, we would argue that Lautman and Deleuze differ in the way in which the structure of Ideas is conceived: while Lautman defines Ideas as structures constituted by contrary concepts, i.e. ‘couples of opposites’, which act as poles of tension within the structure, Deleuze conceives the structure of Ideas rather as an open and differential multiplicity. In this respect, we maintain that Deleuze is more influenced by Maimon and Bergson than by Lautman.53 A final 185

conditions of thought: deleuze and transcendental ideas point needs to be mentioned which is perhaps even more important than the similarities and differences between Lautman and Deleuze that we have discussed so far. Duffy points to the fact that Deleuze draws from Lautman ‘his strategy of engagement with a range of discourses throughout his work’.54 According to Lautman, mathematics plays the role of a model for a theory of problems: ‘Mathematics thus plays with respect to the other domains of incarnation, physical reality, social reality, human reality, the role of model in which the way that things come into existence is observed.’55 In an earlier text, Lautman further explains: ‘Mathematical logic does not enjoy in this respect any special privilege. It is only one theory among others and the problems that it raises or that it solves are found almost identically elsewhere.’56 Deleuze completely aligns himself with Lautman in claiming that mathematics is not in any way privileged (in the sense that mathematics would provide the ‘Platonic evidence’ for a superior dialectic). Mathematics is just one domain among others, in which Ideas express themselves technically. Ideas-problems belong to a realm of their own, that is a dialectical realm. Problems are always dialectical and each dialectical problem is duplicated by a symbolic field in which it is expressed. That is why it must be said that there are mathematical, physical, biological, psychical and sociological problems, even though every problem is dialectical by nature and there are no non-dialectical ­problems. (DR 179/232)

Deleuze takes up Lautman’s suggestion and develops a theory of Ideas-problems, the application of which is not only shown relative to mathematics but also in relation to other sciences (physics, biology) and cultural studies. However, it cannot be denied that mathematics does play a particular role for Deleuze’s theory of problems. This becomes most apparent in the way that Deleuze uses mathematical concepts to expound the ‘calculus of problems’ (concepts such as singularity, differential relation, multiplicity, adjunction of fields, solution curves, etc.). We will therefore have to examine the relation between philosophy and mathematics for Deleuze more closely. Does Deleuze conceive philosophy as a reflection on mathematics, as a philosophy of science? Or does mathematics simply provide examples that serve as illustrations for contentious philosophical issues? Is the use of mathematical terms ‘merely’ metaphorical? Or, on the contrary, does mathematics play a foundational role for philosophy? Keeping these questions 186

Ideas as Problems in mind, we will continue with a brief sketch of the mathematical sources that Deleuze draws upon to develop his theory of Ideasproblems. These mathematical models will primarily be differential calculus and the theory of dynamical systems, the Riemannian notion of multiplicity and Galois’ theory of polynomial equations. For our purposes it suffices to deal with the first two, and to pursue some of the reflections undertaken in the previous chapter.57 Deleuze’s Mathematical Sources: Weierstrass, Poincaré, Riemann For Deleuze, Ideas are essentially problems. Traditionally, problems have been evaluated by the logical possibility of their being solved: ‘the truth of a problem consists only in the possibility that it receive a solution’ (DR 159/207). Under the heading of the seventh postulate of the dogmatic image of thought, Deleuze describes this tendency of basing the ‘truth’ of a problem upon its solvability (that is upon a merely extrinsic criterion) as a ‘philosophical illusion’ (DR 159/207), which he diagnoses in Aristotle and Kant among others. From there, a fatal circle arises: A problem is solvable only to the extent that it is ‘true’, but we always tend to define the truth of a problem in terms of its solvability. Instead of basing the extrinsic criterion of solvability upon the internal character of the problem (Idea), we make the internal character depend upon the simple external criterion. (DR 179/233)

Deleuze demands that the ‘solvability’ of a problem must depend on its internal characteristic or structure: ‘It must be determined by the conditions of the problem, engendered in and by the problem along with the real solutions’ (DR 162/210). To use another Deleuzian phrase: the solutions to a problem are intrinsically determined by the distribution of ‘singularities’. In the previous chapter, in the discussion of Maimon, we have already introduced some basic mathematical concepts and properties of the differential calculus. We came across the intrinsic genetic force of the differential, that is the possibility of generating a function from a given differential relation. It was Karl Weierstrass who developed a method of local integration known as Weierstrass’s theorem on the approximation of analytic functions. According to this method, the successive derivations taken at a singular point can be written in an infinite sum, a so-called Taylor series or power series expansion. 187

conditions of thought: deleuze and transcendental ideas The sum of such a power series approximates the expanded function in the neighbourhood of the singular point (provided that any remainder approaches zero as the polynomial becomes an infinite series). Furthermore, Weierstrass developed a method using ‘circles of convergence’, a circle of convergence being defined as the domain around a singular point, in which an analytic function (representing the expanded power series) is differentiable at each of its points. Through the successive adjunction of more and more circles of convergence we can gradually construct the whole domain over which the analytic function is continuous.58 Weierstrass thereby showed that the function generated by a first power series could be analytically extended over every path that does not encounter a ‘pole’, that is a particular kind of singularity at which the continuity breaks down and the power series obtained diverge. Lautman emphasises the specific role of singular points (cf. DR 324/230, note 9/1) in this method: singularities do not only divide up the domains in which the generated analytic function can be defined, they also allow the passage from the locally defined analytic function to its global characterisation. Thanks to Weierstrass it was ultimately possible to represent an entire analytic function that is continuous over its whole domain. However, Weierstrass could not solve the problem of the representation of functions whose graph consists of curves with infinite branches, that is to say where the power series obtained do not converge to the function but diverge. Only in the late 1800s with Poincaré’s ‘qualitative theory of non-linear differential equations’,59 was it possible to represent such complex functions in a plane. Poincaré extended the geometry of curves to a study of surfaces and their functions in an effort to understand the behaviour of dynamic systems (such as the planetary system). Duffy explains that Poincaré discovered a new kind of singularity, so-called ‘essential singularities’, where the values of the function close to the singularity ‘fluctuate through a range of different possibilities without stabilizing’.60 According to Poincaré, we need to distinguish four types of singularities situated in a vector field: saddle points, nodes, foci and centres. The first type of singularity is the saddle point or dip (col), through which only two solution curves pass, acting as asymptotes for neighbouring curves. A saddle point is neither a maximum nor minimum, since the value of the function either increases or decreases depending on the direction of movement away from it. The second kind of singularity is the node (nœud), which is a point through which an infinite number of 188

Ideas as Problems curves pass. The third type of singularity is the point of focus (foyer), around which the solution curves turn and towards which they approach in the same way as logarithmic spirals. And the fourth, called a centre, is a point around which the curves are closed, concentric with one another and the centre.61

These singularities determine the topological behaviour of the solution curves, that is their local trajectories in the immediate neighbourhood. In the language of physics, the singularities function as ‘attractors’ determining the trajectories of the curves that fall within their ‘sphere of influence’.62 Smith describes the application of Poincaré’s mathematical theory to a dynamic system in weather forecasting. Non-linear equations can thus be used to model objectively problematic (or indeterminate) physical systems, such as the weather (Lorenz): the equations can define the virtual ‘attractors’ of the system (the intrinsic singularities toward which the trajectories will tend in the long term), but they cannot say in advance which trajectory will be actualised (the equation cannot be solved), making accurate prediction impossible. A problem, in other words, has an objectively determined structure ­(virtuality), apart from its solutions (actuality).63

On the basis of these (mathematical and physical) examples we can clearly discern a qualitative difference between the (virtual) problemelement and the (actual) solution-element. Singularities have to be understood as the problematising function that determines a fundamental system of solutions, whereby not all of the solutions will become actualised. We have come to the point where we can cast a first glance at Deleuze’s formal characterisation of problems and the way they generate cases of solutions. Deleuze defines Ideas as virtual systems of differential relations between reciprocally determined genetic elements, internally structured by the distribution of singularities and ordinary points that determine the conditions of the problem.64 However, before we proceed further with Deleuze, we need to introduce another very important notion which Deleuze uses in order to characterise Ideas: the notion of ‘multiplicity’. As Deleuze says, ‘an Idea is a ‘complex theme’, an internal multiplicity – in other words, a system of multiple, non-localisable connections between differential elements which is incarnated in real relations and actual terms’ (DR 183/237). The notion of multiplicity is deeply influenced by 189

conditions of thought: deleuze and transcendental ideas Riemann’s notion of ‘multiplicity’ or ‘manifold’ (Mannigfaltigkeit) (though Deleuze equally draws upon Bergson’s theories of multiplicities65). Let us therefore turn to a very brief sketch of Riemann’s mathematical achievement. Bernhard Riemann (1826–66) revolutionised modern mathematics in almost every main field: algebra, analysis, geometry and topology, and his work provided the foundations for the new disciplines of the differential geometry of surfaces and topology.66 Central to the discussion here are Riemann’s radical ideas concerning ‘spatiality’ and ‘multiplicity’ and in particular the distinction between discrete and continuous multiplicities that he introduced in his inaugural lecture of 1854 ‘Über die Hypothesen, welche der Geometrie zu Grunde liegen’.67 While Riemann considers discrete multiplicities as formed by isolated rather than continuously connected elements where the relations subsisting between them are imposed from outside, continuous multiplicities can be intrinsically defined by the relations that exist between the ‘open sets’ of points or ‘open spaces’. The concept of continuous multiplicity allows Riemann to imagine the nature of spatiality as a conglomerate of local spaces and networks of relationships among them in a way that is not biased by any extrinsic determination. Thus, for instance, a surface can be conceived of as a space in itself without imposing on it the unity of a three-dimensional Euclidean space, in which it would be submerged. In the absence of any external reference to a universal ambient space with fixed dimensions, the multiplicities can form ‘n-dimensional spaces’, ‘n’ being the variable number of coordinates assigning values to each point in such a multiplicity. In defining multiplicities by way of their internal properties, Riemann is able to work with spaces of any dimension, even with infinite-dimensional spaces. This does not mean that the Euclidean space is completely annihilated in the Riemannian type of differential geometry. In fact, a given local space (that is the accumulation of points in a neighbourhood) can be covered by a Euclidean or Cartesian coordinate-map. In Lautman’s words: Each neighborhood is therefore like a small bit of Euclidean space, but the connection from one neighborhood to the next neighborhood is not defined and can be done in an infinity of ways. The most general Riemann space is thus presented as an amorphous collection of juxtaposed pieces that aren’t attached to one another.68

To which Deleuze and Guattari respond in A Thousand Plateaus by saying: ‘if we follow Lautman’s fine description, Riemannian 190

Ideas as Problems space is pure patchwork’ (ATP 485/606). Riemannian space is the precursor for Deleuze’s and Guattari’s concept of ‘smooth space’ (in contrast to ‘striated space’) which appears in A Thousand Plateaus. However, Riemann already plays an important role in Difference and Repetition to the extent that he provides one of the main sources for the formal characterisation of Ideas as multiplicities of differential relations and corresponding singularities. Ideas are structural multiplicities defined by their internal properties and the relations that subsist among them. They defy the use of any external categories, such as the imposition of the concepts of the understanding of the one and the many: Multiplicity must not designate a combination of the many and the one, but rather an organisation belonging to the many as such, which has no need whatsoever of unity in order to form a system. The one and the many are concepts of the understanding which make up the overly loose mesh of a distorted dialectic which proceeds by opposition. The biggest fish pass through. [. . .] Instead of the enormous opposition between the one and the many, there is only the variety of multiplicity – in other words, difference. (DR 182/236)

Deleuze defines the Idea as an ‘n-dimensional, continuous, defined multiplicity’ (DR 182/236). As an example he mentions the Idea of colour, which for him manifests itself in white light (insofar as all the wavelengths of colours are seen together).69 The Idea of colour is a three-dimensional multiplicity. In fact, we can discern three dimensions or variables with respect to colour: namely hue, lightness and saturation. These dimensions are like singular points, which in the processes of actualisation generate as ‘solutions’ the diversity of particular colours with a defined degree of hue, lightness and saturation embodied in sensuous objects. By continuity Deleuze may refer to the continuous variation of the dimensions, that is their increase or decrease in power (the intensity of a spectral colour), or the continuity in the colour spectrum itself (wavelength or frequency). Having now outlined Deleuze’s main mathematical sources from which he draws his definition of problematic Ideas as ‘multiplicities or complexes of relations and corresponding singularities’ (DR 163/212) that generate cases of solutions (as in the case of solution curves that fluctuate around a singular point without stabilising), we can proceed with describing further formal characteristics and the functioning of Deleuze’s calculus of problematic Ideas. 191

conditions of thought: deleuze and transcendental ideas The Formal Characteristics of Ideas-Problems In Chapter Four of Difference and Repetition, Deleuze summarises the chief formal characteristics of Ideas-problems as follows: Ideas always have an element of quantitability, qualitability and potentiality; there are always processes of determinability, of reciprocal determination and complete determination; always distributions of distinctive and ordinary points; always adjunct fields which form the synthetic progression of a sufficient reason. There is no metaphor here, except the metaphor consubstantial with the notion of Ideas, that of the dialectical transport or ‘diaphora’. (DR 181/235)

As can be seen from this quotation, Deleuze primarily employs mathematical terms to characterise Ideas-problems and he insists that he is not using these terms metaphorically. What occurs, according to Deleuze, is a ‘diaphora’, that is a dialectical transport of notions from their original mathematical domain to a new meta-mathematical, philosophical context, in which they serve a new function. This new function, however, is not completely unrelated to their original use in the mathematical field. For this reason, we will try to clarify Deleuze’s usage of terms by linking it to their mathematical sources. In the previous section we have learned that, for Deleuze, Ideas are multiplicities composed of differential genetic elements (singularities and ordinary points). He now describes the internal topological processes that take place within the Idea: processes of determinability, reciprocal determination and complete determination. The elements of quantitability, qualitability and potentiality designate pure potentials of the Idea to engage in these processes according to the principles of determinability, reciprocal determination and complete determination. Let us look at each of these three elements (or pure potentials) and corresponding principles that govern the internal topology of problematic Ideas: 1. The first thing to point out is that the differential genetic elements (dx, dy) of the Idea are wholly undetermined. They have no prior identity, no defining property, no sensible form, that is no fixed quantity or particular value. Mathematically, a differential dx is an infinitesimal variation of some variable x. Now, Deleuze says, the differential can be called ‘the pure element of quantitability’ (DR 171/222) insofar as it is the ideal cause for the genesis of (extended) quantities. This process of genesis relies on the reciprocal determination of differentials. However, the 192

Ideas as Problems salient trait that makes the reciprocal determination possible in the first place is the determinability of differentials. Although the differential elements dx and dy are undetermined, they are perfectly determinable in relation to one another. Thus the principle that corresponds to them is the principle of determinability (DR 172/223). 2. It is important to emphasise that the differential genetic elements do not exist independently from one another, but always in a reciprocally determined relation (dy/dx). This means that the ­differential relation does not externally relate determined quantities. Rather its relata are ‘qualities’ which are defined as intensive differences (where a difference intrinsically relates to a difference). Consequently, there is a difference of kind (an ontological difference, in fact) between the differential relation constituting a ­differential equation and the so-called primitive function. While the differential equation deals with ‘qualities’ or ‘intensive differences’ (differentials), the primitive function is concerned with determined quantities given in intuition. This is why Deleuze calls the determinable form of the differential relation the ‘pure element of qualitability’ (DR 173/224). But it also has another reason: every differential equation can itself be differentiated; thus a firstorder differential gives rise to a second-order differential, and this again to a third-order differential, etc. The differentiation is taken to a higher degree, insofar as it expresses no longer the differentiation of a ‘supposedly constant relation (“variability”) but, on the contrary, [. . .] a degree of variation of the relation itself (“variety”)’ (DR 173/224). For Deleuze this testifies to the power of Ideas to give rise to Ideas of Ideas – what Deleuze also refers to as different ‘orders of Ideas’ (different degrees of differential relations) – such that an internal variety or multiplicity of Ideas is created. Thus the pure element of qualitability pertains to the differential genetic elements insofar as they are related to one another and even give rise to higher orders of differential relations. 3. As we have seen in our previous discussion of the importance of singularities, the existence and distribution of singular points provide the conditions of the problem and account for its complete determination (DR 177/230). That is, the effectively determined values of the differential relations completely define the problem and the topological behaviour of the solution curves. Mathematically speaking, the process of complete determination is (approximately) achieved by the repeated differentiation of a 193

conditions of thought: deleuze and transcendental ideas differential relation at a singular point, resulting in a series of functions with increased power. More precisely, while the operation of taking the first derivative amounts to a ‘depotentialisation’ (DR 174/226) (for instance, if y 5 x2 1 y3, we differentiate by writing dy 5 2xdx 1 3y2dy), the derived function is increasingly potentialised by the operation of repeated differentiation. By summing these higher-order derivatives in the order of their increasing power, that is in the order of their increasing degree (the degree being the highest exponent, or power, of the function), we create a power series expansion of the form a0 1 a1x 1 a2x2 1 a3x3 1 . . . 1 anxn. It shows that as the power series successively expands, it undergoes a corresponding increase in degree, or power. Since an expanding function also increasingly converges with an analytic function, the mathematical power becomes an expression of the increasing potential, or capacity for convergence.70 Thus the gradual determination of the differential relations (the terms of the power series) increasingly brings us closer to the ‘solution’, the expanded function. ‘In this sense, the differential is indeed pure power, just as the differential relation is a pure element of potentiality’ (DR 175/227). By means of this formal characterisation of the processes and principles that govern the problematic Idea, Deleuze shows that the Idea is only subject to internal constraints and no longer dependent on extrinsic factors (as Kantian Ideas are). Due to their internal topological structure, Ideas-problems themselves provide the sufficient reason that allows for the genesis of cases of solutions. This whole process of production or genesis Deleuze designates with the complex notion of different/ciation (DR 209/270).71 ‘Differentiation’ (written with a ‘t’) characterises the internal topological processes generating the proper space of the problem. In the words of Salanskis: Deleuze sees differentiation mathematically as the process of the selfdetermination of the problem at its specific level, a determination which places some constraints on the actual values, places shapes and properties on what counts as a solution to the problem.72

‘Differenciation’ (written with a ‘c’) characterises processes of the concrete formation of individual solutions within a symbolic field relative to the Idea-problem. Mathematically speaking, differenciation refers to the integral curves constituted in the neighbourhood of singularities. 194

Ideas as Problems In this regard, four terms are synonymous: actualise, differenciate, integrate and solve. For the nature of the virtual is such that, for it, to be actualised is to be differenciated. Each differenciation is a local integration or a local solution which then connects with others in the overall solution or the global integration. (DR 210–11/272)

What Deleuze describes here is a process of genesis which goes from the virtual Idea-problem with its multiple, non-localisable connections of differential elements to its actualisation in real relations and actual terms. Deleuze calls the type of genesis from the virtual to the actual a ‘static genesis’ (DR 183/238), which he understands as a correlate of the notion of ‘passive synthesis’.73 In other words, the static genesis is not actively performed by some kind of agency at a particular time. Instead, we have to conceive of it as the instantiation of a structure that takes place in rhythms and with different speeds (accelerations and interruptions) determined by the respective symbolic field of actualisation. One example can be found in genetics that has as its object the genetic structure of organisms, that is the existence and distribution of chromosomes and their function (cf. DR 185/240). Chromosomes, the carriers of genes, appear as a differential structure or multiplicity, the elements of which are reciprocally determined and non-localisable in terms of absolute space-time coordinates. Genetics investigates the potentiality of the genetic structure to control cell construction and function, and to account for repetition and difference in phylogeny, both on a reproductive and evolutionary scale. New research (arising in the second half of the twentieth century) suggests that the genetic structure is not to be understood as an immutable ‘dictatorial’ system. Rather it can be actualised in multiple ways, at different speeds and different times in response to environmental stimuli. (In the language of biology, the thesis is that the so-called developmental plasticity and phenotypic adaptivity of an organism to its environment bring out previously unexpressed potentials of hereditary DNA.)74 The example of genetics shows the complex interactions between the virtual and the actual, the realm of Ideas-problems and the field of solutions. There is a specific time (differential speeds and rhythms) involved in the actualisation of the Idea-problem. Every structure has a purely logical, ideal or dialectical time. However, this virtual time itself determines a time of differenciation, or rather rhythms or different times of actualisation which correspond to the relations and singularities of the structure and, for their part, measure the passage from virtual to actual. (DR 210–11/272) 195

conditions of thought: deleuze and transcendental ideas While it might seem at first view that the virtual determines the actual in a one-sided process, this view would amount to a reductionist ‘Platonic’ version of the relationship between the virtual and the actual. But we need to introduce time and recognise its true meaning of ‘creative actualisation’ (DR 216/278). Deleuze says that rhythms or different times of actualisation measure the passage from virtual to actual. There are thus temporal processes along the lines of differenciation which determine differential relations to become actualised (DR 246/317). The different times of differenciation play an ­important role in the actualisation of the Idea (DR 217/280). Deleuze’s meta-theory or dialectic of problematic Ideas as we have characterised it so far still remains quite abstract due to its mathematical expression. It is therefore appropriate to cite some of Deleuze’s own examples at this place. In Difference and Repetition, Deleuze elaborates three examples in considerable detail: (1) the example of atomism as a physical Idea (DR 184/238–9); (2) the organism as a biological Idea (DR 184–5/239–40); and (3) social Ideas in the Marxist sense (DR 186/240–1). In the first example, Deleuze refers to Epicurus’ ancient theory of atomism. Deleuze argues that Epicurus considered atoms, i.e. the imperceptible particles of nature, as forming a differential multiplicity, calling the differential relation between the atoms clinamen. According to this reading, clinamen does not simply designate an indeterminate change of movement of atoms testifying to the existence of a free will (as Lucretius would have it). By contrast, in his letter to Herodotus, Epicurus defines clinamen as the product of a reciprocal determination between atoms that occurs ‘in a time smaller than the minimum continuous time thinkable’ (quoted in DR 184/238). Deleuze emphasises the use of the terminology of Eudoxos’ method of exhaustion. However, he admits that this example taken from the ancient theory of atomism is not completely satisfactory, since Epicurus’ atoms still retain too much independence and only engage in external spatio-temporal relations. The second example bears on the famous controversy between the French naturalists Étienne Geoffroy Saint-Hilaire and George Cuvier in the first half of the nineteenth century. In a series of public debates they discussed the question of whether form or function determine the phenomena of life. Cuvier defended a ‘functionalist’ approach to biology, claiming that similarities in the anatomy of different animal species, for instance between particular organs, are the product 196

Ideas as Problems of a similar function. Cuvier further held that different organisms evolved independently from one another, following only their genetic line of the species. Geoffroy Saint-Hilaire, on the contrary, belonged to the ‘formalist’ school of thought (or, as one might say, a ‘transcendental biology’). He believed that the diversity of animal species could be derived from a single underlying form or structure which consists of abstract anatomical elements and their ideal relations. His comparative studies on vertebrates seemed to prove that a common structure of bones in the same relative positions could be found in different vertebrates. Thus the hyoid of the cat consists of nine small bones, while that of man consists of five, the other four being bent towards the skull. Geoffroy Saint-Hilaire explained the modifications between the species by means of processes of bending and deformation determined by environmental factors. In Deleuze’s terms, the actualisation of the structural multiplicity or Idea proceeds ‘in accordance with reasons and at speeds determined by the environment, with accelerations and interruptions, but independently of any transformist passage from one actual term to another’ (DR 185/239– 40). Geoffroy Saint-Hilaire’s theory of a single archetypal structure is not as obscure and speculative as it might seem at first glance, and such a structuralist approach has enjoyed a revival in modern genetic biology. As we have already discussed in our example given above, genes are defined as a differential multiplicity of chromosomes which appear as loci, that is within a complex structure of non-localisable relations of proximity. This genetic structure can be regarded as a transcendental or archetypal form, provided that by this we do not mean a dictatorially determining and active form, but rather a problematic Idea which actualises itself in response to environmental conditions. Apart from these two physical and biological examples, Deleuze provides a further example from the socio-economic, political sphere. He treats ‘the economic’ as a problem or Idea that ‘is never given properly speaking, but rather designates a differential virtuality to be interpreted, always covered over by its forms of actualisation’ (DR 186/241). The Idea of the economic is defined as a multiplicity of relations of production and relations of property, its abstract elements being representatives of property, means of production and abstract labour-power. Since the relations between the elements are social relations, Deleuze also says that the economic instance is constituted by a ‘social multiplicity’ (DR 186/240). The actualisation of the socio-economic Idea can take different forms dependent 197

conditions of thought: deleuze and transcendental ideas on the contingent, empirical and historical conditions which are given.75 The important thing about the socio-economic Idea as a multiplicity is that it involves no pre-existing identities. These are only the product of a common sense that tends to objectify the virtual multiplicity: ‘It makes society a thing that can be seen, remembered and thought. [. . .] common sense reifies sociability; it displaces the practice, the process of the constitution of social relations, with the product.’76 The capitalist and wage-labourer of capitalist society are actualisations of virtual, reciprocally determined relations of production and the determination of contingent circumstances. In other words, actual class relations, political and juridical relations are cases of solutions which answer the socio-economic problematic. Although we can see that Deleuze here makes extensive use of Marxist theory and terminology, he also modifies Marx or at least Marxism to a certain extent. First of all, Deleuze does not consider actual economic relationships as the essence of society as a whole, rather those actual relationships, and all social relationships, are the incarnation of economic relations as differential virtualities that may be actualised in different ways. So we have something like the priority of the economic as found in Marx, without the economic essentialism as found in certain forms of Marxism.77

Furthermore, Deleuze does not regard capitalist society as the c­ ulmination of a dialectical development of social formations. The actualisation of the socio-economic Idea does not follow any universal law or dialectic of contradictions. Instead of being an abstract transcendent principle, the Idea is not larger than what it determines, that is it is itself determined by the contingent empirical circumstances. Therefore the series of social formations as solutions to the Idea of the economic resembles rather a discontinuous line with cuts and limiting poles. In Anti-Oedipus, Deleuze and Guattari will reconceptualise Marx’s universal history so that ‘universal history is the history of contingencies, and not the history of necessity. Ruptures and limits, and not continuity’ (AO 140/163). The Relation between Mathematics and Philosophy Now let us return to some of the questions we raised before, concerning the status of mathematical theories and notions for philosophical thinking. How does Deleuze conceive of the relation between mathematics and philosophy? First we can rule out the thesis that 198

Ideas as Problems philosophy be understood as a reflection on mathematics. As Deleuze and Guattari say in What Is Philosophy?, one does not gain anything for philosophy if one tries to define it in terms of reflection. On the contrary, the object of philosophy is lost.78 Besides, mathematicians or scientists have no need for philosophers to reflect on their theories and never have had such a need. We may describe Deleuze’s engagement with mathematics (and the history of mathematics) as the creation of an encounter between two disciplines which can generate new movements of thought in philosophy, that is give rise to new philosophical concepts displacing traditional ones. We already came across some of the new philosophical concepts that are created through the encounter with mathematics, such as the ‘differential’ or the ‘singular’ (as opposed to the ordinary or regular, and no longer to the universal or general). Now Deleuze mobilises mathematics for the conception of Ideas-problems fascinated by the way how problems are expressed relative to the field of solution that they determine (for example, how singularities of vector fields determine the topological behaviour of solution curves). Deleuze recognises that the distinction between the problem as a genetic differential structure and its fundamental system of solutions has the potential to lead to new conceptualisations of the traditional philosophical concepts of problem and solution. Is Deleuze then applying mathematics to philosophy? Deleuze would clearly deny this. Following Lautman, Deleuze says that mathematics, for instance the differential calculus, is just one symbolic field in which dialectical Ideas are incarnated, and it might not even necessarily represent the most complete form of the expression of problems and the constitution of their corresponding solutions (DR 181/235). We have to remember that the dialectic is ontologically anterior. It is the question posed beforehand, although the Idea of the question does not come to mind until after the study of the exemplary domain. This means that by virtue of the study of differential calculus and the problems it poses in mathematics we can reach the ‘universality of the dialectic’, a mathesis universalis of what it means to think (DR 181/235). In fact, one could say that the dialectic establishes for its Ideas-problems a differential calculus not only in mathematics but in each symbolic field: Each engendered domain, in which dialectical Ideas of this or that order are incarnated, possesses its own calculus. [. . .] It is not mathematics which is applied to other domains but the dialectic which establishes for its problems, by virtue of their order and their conditions, the direct 199

conditions of thought: deleuze and transcendental ideas differential calculus corresponding or appropriate to the domain under consideration. (DR 181/235)

Differential calculus, in the particular sense in which it is deployed in mathematics, is a specific mathematical tool that entirely belongs to mathematics, ‘even at the very moment when it finds its sense in the revelation of a dialectic which points beyond mathematics’ (DR 179/232). Without doubt Deleuze is here manoeuvring on dangerous ground, which will not be approved by mathematicians or scientists thinking in terms of rigorous exact definitions. Deleuze is, however, aware of the danger: Of course, we realize the dangers of citing scientific propositions outside their own sphere. It is the danger of arbitrary metaphor or of forced application. But perhaps these dangers are averted if we restrict ourselves to taking from scientific operators a particular conceptualizable character which itself refers to non-scientific areas, and converges with science without applying it or making it a metaphor. (CIT 125/169)

Deleuze denies at several places that his deployment of mathematical or scientific notions involves the use of metaphor (DR 181/235 and 190/246). If we take this claim at face value, how then can mathematical or scientific concepts be put to use in philosophy? Deleuze first restricts this usage to a sub-set of mathematical or scientific concepts, those that are essentially ‘inexact’. They can be given a philosophical (or even artistic) conceptual dimension and made rigorous in a way that is not directly scientific. As Deleuze explains in an interview: There are two sorts of scientific concepts. Even though they get mixed up in particular cases. There are concepts that are exact in nature, quantitative, defined by equations, and whose very meaning lies in their exactness: a philosopher or writer can use these only metaphorically, and that’s quite wrong, because they belong to exact science. But there are also essentially inexact yet completely rigorous concepts that scientists can’t do without, which belong equally to scientists, philosophers, and artists. They have to be made rigorous in a way that’s not directly scientific, so that when a scientist manages to do this he becomes a philosopher, an artist, too. This sort of concept’s not unspecific because something’s missing but because of its nature and content.79

It is not altogether clear whether one should indeed say that scientists become philosophers (or artists) when they reflect on their proper creations, as is suggested in this quotation. In fact, Deleuze renounces 200

Ideas as Problems this claim in What Is Philosophy? as a bad joke (WP 6/11, quoted in note 78). What is more interesting with respect to this quotation is that Deleuze appeals to the potential of essentially ‘inexact’ mathematical or scientific concepts.80 These inexact concepts seem to possess an excess of sense, which can be mobilised in contexts that are distinct from the one in which they are usually (and justifiably) used. They are essentially ‘mobile’ concepts due to their ‘vagueness’ or ‘inexactitude’.81 As such they are capable of generating a movement of thought that transcends their usual sphere of application and arouses a synthesis with new conceptual components in another sphere. Why should we voluntarily block the movement of thought by clinging to concepts with exact and rigorous definitions within their traditional context? In his article ‘Bernhard Riemann’s Conceptual Mathematics and the Idea of Space’, Plotnitsky argues in favour of interactions taking place between philosophical and mathematical thinking, and between both and artistic thinking. The Riemannian concept of multiplicity is just one example that has proved to be very inspiring not only for Deleuze but also for Bergson and Husserl.82 We do not believe that Deleuze has recourse to mathematical language because of its being the best tool to express a ‘dogmatic metaphysics’ (in the Kantian use of the term) as Salanskis suggests.83 Besides, Deleuzian ‘metaphysics’, if we want to use this expression, should not be equated with the dogmatic metaphysics that Kant seeks to abandon, but on the contrary with a type of post-Kantian ‘transcendentalism’. As Deleuze says, the discovery of the ‘problematic’ has to be seen in a transcendental horizon, ‘as the transcendental element which belongs “essentially” to beings, things and events’ (DR 195/252). Deleuze explicitly refers to the problematic as a transcendental field, and it is this concept of ‘transcendental’ that we aim to track down in this book. Furthermore, we would argue that Deleuze’s understanding of the relation of philosophy and mathematics essentially differs from the style of philosophy which Badiou champions.84 While for Badiou the ‘little style’ of philosophy would be a philosophy of mathematics belonging to the genre of epistemology or philosophy of science, the ‘grand style’, which he considers the predominant task of philosophy, is characterised by its relation to mathematics as its necessary condition and foundation. Badiou’s criticism of Deleuze for not choosing the right mathematical models and rejecting axiomatic set theory is based on a misunderstanding. Deleuze does not use mathematical theories in order to ground philosophy, or to provide an ontological model. Instead, Deleuze 201

conditions of thought: deleuze and transcendental ideas attempts to draw from mathematics those concepts that give us food for thought or force us to think. How do we understand the nature of problems, their truth and relation to cases of solution? Can we conceive of a multiplicity that is intrinsically defined and not subject to external conditioning or totalisation? It is Deleuze’s interest in the irreducibility of problems and their status as problematic Ideas endowed with a genetic power that motivates his engagement with mathematics, in particular with the differential calculus and the Riemannian notion of a structural multiplicity.

Notes   1.   2.   3.   4.

  5.

  6.   7.   8.

DR 140/182, 141/184, 194/251. DR 140/183, 141/183. DR 141/183–4, 194/251. With regard to Deleuze’s discussion of Kant, we will mainly refer to his book Kant’s Critical Philosophy: The Doctrine of the Faculties (1963) and his seminal essay ‘The Idea of Genesis in Kant’s Esthetics’ (first published in 1963). Deleuze’s involvement with Lautman’s philosophy is rather hidden, but significant traces can be found in Chapter Four of Difference and Repetition. Cf. CPR A 568/B 596: ‘What is an ideal to us, was to Plato an idea in the divine understanding, an individual object in that understanding’s pure intuition, the most perfect thing of each species of possible beings and the original ground of all its copies in appearance.’ See the explanatory note by the editors and translators Paul Guyer and Allen W. Wood in CPR p. 746, note 86. Plato’s claim that Ideas are causes (aitiai) of natural things can be found in Phaedo 100c–102a, Republic 508e, Timaeus 29a–30b. Cf. Allison, ‘Is the Critique of Judgment “Post-Critical”?’, pp. 78–92. In this article, Allison argues that Kant’s third Critique, which appeals to the purposiveness of nature understood as a transcendental principle of a specific form of systematic unity, does not entail the abandonment of the basic commitments and principles of the first Critique. For Allison, the third Critique has to be understood as building upon Kant’s initial critical position. His main argument is that in the Appendix to the Transcendental Dialectic Kant ascribes not only a regulative function to reason’s Ideas of systematicity and purposiveness, but also already a transcendental role, that is the role of a condition of the possibility of coherent experience. In his book on Kant and Deleuze, Christian Kerslake argues as well that the Appendix to the Transcendental Dialectic contains a transcendental deduction of Ideas of reason, cf. Kerslake, Immanence and the Vertigo of Philosophy, p. 191. 202

Ideas as Problems   9. Allison, ‘Is the Critique of Judgment “Post-Critical”?’, p. 81. For Allison, there is no contradiction involved in both the claim that the Idea of systematicity has a regulative function as a logical principle and the claim that this logical principle presupposes a transcendental principle. 10. Deleuze, ‘H as in “History of Philosophy” ’, in L’Abécédaire. 11. Kerslake, Immanence and the Vertigo of Philosophy, p. 191. 12. Ibid. 13. Ibid., p. 192. 14. In this paragraph, CPR A 673/B 701, Kant explicitly exempts cosmological Ideas from this use, for they produce antithetical world-concepts (for instance, they equally give rise to both the concept of a world which is infinite in past time and consists of infinitely many parts and the concept of a world which has a definite beginning in time and a finite spatial extension). In comparison, psychological and theological Ideas do not induce reason to run up against these antinomies and are therefore suitable as action-guiding rules. However, on another occasion Kant indiscriminately refers to all psychological, theological and cosmological Ideas as ‘regulative principles for the systematic unity of the manifold of empirical cognition in general’ (CPR A 671/B 699). 15. Allison explains that ‘Kant is not claiming that systematicity is, of itself, a sufficient criterion of empirical truth, as if the systematic embeddedness of an empirical generalization or “law” in an overarching theory or set of laws were sufficient to account for its truth. The claim is rather that systematicity is necessary in order to have a sufficient criterion of empirical truth, and therefore, a coherent employment of the understanding, or as the second passage [CPR A 654/B 682] suggests, virtually any valid employment of the understanding at all’ (in Allison, ‘Is the Critique of Judgment “Post-Critical”?’, p. 82). 16. Cf. CJ 5: 180 and 5: 181. It can be argued, by the way, that these passages testify to Maimon’s influence on Kant, namely the impact of Maimon’s idea of an infinite understanding. Although, as we have seen, Kant already assumed in the Critique of Pure Reason a ‘being of reason’ as a ground of systematicity, he did not yet conceive of it in terms of an understanding. 17. ‘Just for this reason we are also justified in thinking of the world-cause in the idea not only according to a subtle anthropomorphism (without which nothing at all could be thought about it), namely as a being that has understanding, liking and disliking, and desire and will in conformity with them, etc., but also in ascribing to that being infinite perfection far transcending what we could justify on the basis of our empirical acquaintance with the world-order’ (CPR A 700/B 728). 18. Smith, ‘Deleuze, Kant, and the Theory of Immanent Ideas’, p. 49. 19. Their difference lies in the way they refer to the underlying a priori 203

conditions of thought: deleuze and transcendental ideas principle of purposiveness. In the case of teleological judgements, purposiveness is taken as objective, material, implying ends, while in the case of aesthetic judgements purposiveness is clearly subjective, formal, excluding any end (cf. KCP 54/92–3). 20. See Kant’s letter to Reinhold, 28–31 December 1787, in Kant’s Briefwechsel, pp. 513–15. Selections are translated in Zweig (ed.), Kant’s Philosophical Correspondence, pp. 127–8. 21. For more details of the evolution of Kant’s third Critique, see Zammito, The Genesis of Kant’s Critique of Judgment, pp. 5, 7 and 275–6. 22. Zammito, The Genesis of Kant’s Critique of Judgment, p. 166. 23. Zammito assumes that the reformulation of the whole issue in terms of the faculty of judgement and not of reason is due to Kant’s high estimation of reason: ‘Judgment as a faculty has none of the prestige and dignity which Kant cannot help but invest in reason. Indeed, he finds the occasion to lay the blame for all error squarely at the door of the faculty of judgment’ (Zammito, The Genesis of Kant’s Critique of Judgment, p. 167). 24. See CJ 5: 168. See also First Introduction (1790) 20: 201, 20: 208 and 20: 245, and Second Introduction (1793) 5: 177 and 5: 197. 25. In CJ, §57 Kant will explicitly claim a necessary relation of aesthetic judgements of taste to an indeterminate concept, which is an Idea of reason. 26. In the First Introduction to the Critique of the Power of Judgment, Kant calls precisely this capacity of representing sublimity in objects a ‘feeling of spirit [Geistesgefühl]’. 27. CJ 5: 270. Kant notes that the most suitable examples for pure aesthetic judgements of the sublime can be found in ‘raw nature’. Products of art (such as buildings, columns, etc.) cannot adequately illustrate the sublime, since there is always a human end attached to them that determines the form as well as the magnitude. Natural things (such as animal organisms) whose concepts evoke a determinate end are equally improper examples; see CJ 5: 252–3. 28. CJ 5: 265: ‘He [the unrefined person] will see in the proofs of the dominion of nature given by its destructiveness and in the enormous measure of its power, against which his own vanishes away to nothing, only the distress, danger, and need that would surround the person who was banished thereto.’ 29. Kant’s second example that uses the analogy of the relation between soul and body is not particularly helpful: since we do not have a clear and communicable intuition of the relation between soul and body, it cannot well serve as a symbol for the good governance of a monarchical state. 30. Cf. Schaub: ‘What Kant describes as “the transportation of the reflection on one object of intuition to another, quite different concept, to 204

Ideas as Problems which perhaps no intuition can ever directly correspond” [CJ 5: 353] is in effect a most complex and obscure procedure, a truly creative, inventive and autonomous act of the imagination’ (Schaub, Gilles Deleuze im Wunderland, p. 74; my translation, D. V.). 31. We do not wish to say that geometrical construction is not a very inventive activity, but it surely involves a different kind of creativity than the one in symbolisation. Furthermore, to Kant’s eyes, the construction rule of a geometrical figure, say a triangle, already attaches to the concept, albeit obscurely and in a hidden way, and therefore ‘simply’ requires an a priori presentation in (pure or empirical) intuition. See CPR A 713/B 741 and B 17. 32. On behalf of his own philosophical concept of Idea, Deleuze will retain the relation of Ideas and events, but he will define events in terms of the virtual (not spiritual or mental). 33. Smith, ‘Deleuze, Kant, and the Theory of Immanent Ideas’, p. 50. 34. Smith, ‘Deleuze, Hegel, and the Post-Kantian Tradition’, pp. 126–38. 35. Lautman, ‘New Research’, p. 199. Lautman’s collected work was first published in 1977 under the title Essai sur l’unité des mathématiques et divers écrits by Union Générale d’Éditions. This first collection of his work was reissued in 2006 by Vrin under the title Les Mathématiques, les idées, et le réel physique. In quoting texts from Lautman, we will use Simon Duffy’s recently published English translation which relies on the Vrin edition. 36. Alunni notes that Lautman will rather ‘situate himself on the side of a radical questioning of this “traditional metaphysics” which was initiated by Heidegger through what he called “the going beyond” and Destruktion. Such an alignment [. . .] should radically disqualify his all-too famous Platonism – or at least in the sense that it is traditionally, and offhandedly, attributed to him’ (Alunni, ‘Continental Genealogies’, p. 73). 37. Lautman, ‘New Research’, p. 199. 38. Thus Lautman writes in the Introduction to his thesis ‘Essay on the Notions of Structure and Existence in Mathematics’ (1938): ‘The method that we follow is essentially a method of descriptive analysis, mathematical theories constitute for us a given within which we try to identify the ideal reality with which this matter is involved’ (p. 92). 39. Lautman, ‘New Research’, p. 204. 40. Ibid., p. 204. 41. Lautman, ‘Essay on the Notions of Structure and Existence in Mathematics’, p. 189. Lautman refers to this text as his ‘principal thesis’, in order to distinguish it from his ‘secondary thesis’, that is his ‘Essay on the Unity of the Mathematical Sciences in their Present Development’. Both essays appeared in 1938 and made up his thesis in fulfilment of the requirements of the Doctorat D’Etat. 205

conditions of thought: deleuze and transcendental ideas 42. Lautman, ‘Essay on the Notions of Structure and Existence’, p. 188. 43. Cf. Lautman, ‘New Research’, pp. 203–4. 44. Duffy, ‘Albert Lautman’, p. 373, see also pp. 358–9. 45. Lautman, ‘New Research’, p. 206. 46. Ibid., p. 200. 47. Ibid., p. 203. 48. Duffy, ‘Albert Lautman’, p. 367. 49. Lautman, ‘Essay on the Notions of Structure and Existence’, p. 189. 50. Duffy, ‘Albert Lautman’, p. 364. 51. Lautman, ‘New Research’, pp. 205–6. 52. Duffy, ‘Albert Lautman’, p. 370: ‘There is no ideal reality associated with ideas in Deleuze but rather ideas are constituted by the purely problematic relation between conceptual couples.’ 53. Simon Duffy does not point to this difference. Instead he contends that ‘For Deleuze, it is the problematic nature of the relations between conceptual couples that incarnate problematic ideas and which govern the kinds of solutions that can be offered to them’ (Duffy, ‘Albert Lautman’, p. 370, my emphasis, D. V.). Contrary to Duffy, we hold that Deleuze does not conceive the structure of Ideas in terms of binary conceptual oppositions, but rather in terms of a differential multiplicity. 54. Duffy, ‘Albert Lautman’, p. 367. 55. Lautman, ‘New Research’, p. 203. 56. Lautman, ‘On the Reality Inherent to Mathematical Theories’, p. 28. 57. For a brief account of Deleuze’s engagement with Abel and Galois, see Salanskis, ‘Mathematics, Metaphysics, Philosophy’, pp. 52–3; Smith, ‘Axiomatics and Problematics’, pp. 159–61; and Bowden, The Priority of Events, pp. 113–14. 58. Lautman describes Weierstrass’s local method of constructing the analytic continuity of a function within a whole domain as follows: ‘Take as a new center a point inside the first circle, both a new series and a new circle of convergence is thus obtained that can extend beyond the first. The new series extends the first if their values coincide in the common part of the two circles. The series can thus be extended in all directions up to the points in the immediate neighborhood in which the series obtained diverge. Thus we see that in this method the domain is not circumscribed in advance, but rather results from the infinite succession of local operations’, in Lautman, ‘Essay on the Notions of Structure and Existence, pp. 96–7. 59. Kline, Mathematical Thought, p. 732. 60. Duffy, The Logic of Expression, p. 82. 61. Ibid., p. 82. Cf. also Kline, Mathematical Thought, p. 733. 62. Cf. Durie: ‘In this context, a singularity can function as an “attractor” or “basin of attraction”, in such a way that, if, at a given point, the trajectory of the system falls within the sphere of influence of the basin 206

Ideas as Problems of attraction, then it will inevitably tend towards the attractor’ (Durie, ‘Problems in the Relation between Maths and Philosophy’, p. 175). 63. Smith, ‘Axiomatics and Problematics’, pp. 161–2. 64. See, for instance, DR 163/212, 173–4/225, 181/234, 244/315. 65. Cf. B 39/31–2, ATP 483–4/604. In fact, Bergson’s philosophical ideas concerning space and time are based on Riemann’s geometry and concept of manifold. Plotnitsky says: ‘Bergson’s duration may be seen [. . .] as an extraction or distillation of an inexact, qualitative, nonnumerical concept of multiplicity or manifoldness from Riemann’s concept of manifold, a concept that is juxtaposed to “metric manifoldness or the manifoldness of magnitude”, a (mathematical) exact, numerical counterpart of it in Riemann’s overall conceptual architecture of manifold’ (Plotnitsky, ‘Manifolds: On the Concept of Space in Riemann and Deleuze’, p. 191). 66. For more details, see Plotnitsky, ‘Bernhard Riemann’s Conceptual Mathematics and the Idea of Space’, pp. 105–30. 67. For an English translation, see: Riemann, ‘On the Hypotheses which lie at the Foundation of Geometry’, in Ewald (ed.), From Kant to Hilbert, pp. 652–61. 68. Lautman, ‘Essay on the Notions of Structure and Existence’, p. 98. 69. Cf. DR 206/266–7 and 182/236. 70. Cf. Duffy’s very helpful discussion of this and related issues in The Logic of Expression, ch. 3, in particular pp. 77–8. 71. The full formula is actually ‘indi-drama-differenti/ciation’ (DR 246/317) which also takes account of spatio-temporal dynamisms involved in the ‘dramatisation’ of Ideas, that is of ‘impersonal’ processes of individuation. Deleuze argues that there are ‘intensive’ processes that function as movements or conditions of actualisation (cf. Chapter Five of DR). For more on ‘dramatisation’ or ‘intensive individuation’, including a comprehensive account of Gilbert Simondon’s theory of individuation, see Bowden, The Priority of Events, in particular sections 3.3 and 3.4. 72. Salanskis, ‘Mathematics, Metaphysics, Philosophy’, p. 52. 73. In The Logic of Sense, Deleuze introduces the notion of a ‘dynamic genesis’ (LS 186/217) in order to account for the counter-process of a static genesis, namely the movement which goes from the actual world of physical mixtures and sensations to the virtuality of Ideas. Joe Hughes argues that the dynamic genesis is already present in Difference and Repetition. It describes the first stage in the process of learning which begins with a material impression encountered by sensibility. This encounter sets our cognitive faculties into motion and the faculty of thought finally extracts the Idea or problem (see Hughes, Deleuze’s ‘Difference and Repetition’, Chapter Three, section 3). Hughes insists on the order of the learning process that, for him, always goes from sensibility, to imagination, to memory and finally to thought. He 207

conditions of thought: deleuze and transcendental ideas allows for no variance in this process. However, it is not clear what he makes of processes which begin with the problem of a philosophical concept or a scientific formula. Moreover, Hughes interprets the faculty of thought as the faculty where Ideas are born (ibid., p. 86). But we learned from Deleuze and Lautman that Ideas subsist in a virtual realm which is not immanent to a faculty or to a thinking subject. Ideas rather constitute a plane of immanence themselves and their actualisation is elicited by internal processes of differentiation. Finally, we very much doubt Hughes’ claim that Difference and Repetition is comparable with the Phenomenology of Spirit or the Critique of Pure Reason; he argues that ‘knowledge, “the supposedly simple result” is the final telos of the entire genesis – of the entire book’ (Hughes, Deleuze’s ‘Difference and Repetition’, p. 86). We would argue that instead of there being a ‘telos’ of the genesis of thought, there is rather a ‘sufficient reason’ of thought which forces us to think (we have no choice). The genesis of thought is a dice-throw and we have no guarantee that the resulting thought is in any way remarkable, notable or interesting. 74. We are indebted to John Protevi for his explanations on this issue, given in a lecture series at the 2nd Deleuze Camp in Cardiff/Wales in August 2008. See Protevi’s series of lecture courses on ‘Deleuze and Biology’, available at (last accessed 22 August 2012). 75. The emergence of the capitalist society, for instance, is conditioned by the contingent conjunction of two flows, as Deleuze and Guattari will later explain in Anti-Oedipus: the flow of labourers from country to town, and the flow of capital which no longer functions only in a local setting as an equivalent for goods, but on a larger scale as a flow of finance and credits (cf. AO 225/266–7). 76. Read, ‘Fetish is Always Actual, Revolution is Always Virtual’, p. 83. 77. Choat, ‘Deleuze, Marx and the Politicisation of Philosophy’, p. 19. 78. Cf. WP 6/11: ‘[Philosophy] is not reflection, because no one needs philosophy to reflect on anything. It is thought that philosophy is being given a great deal by being turned into the art of reflection, but actually it loses everything. Mathematicians, as mathematicians, have never waited for philosophers before reflecting on mathematics, nor artists before reflecting on painting or music. So long as their reflection belongs to their respective creation, it is a bad joke to say that this makes them philosophers.’ 79. See the 1989 interview ‘On A Thousand Plateaus’ with Christian Descamps, Didier Eribon and Robert Maggiori, in N 29/44–5. 80. See also D 3/9: ‘There are no proper words [mots propres], neither are there metaphors (all metaphors are sullied words, or else make them so). There are only inexact words to designate something exactly’ (translation modified, D. V.). 208

Ideas as Problems 81. See Patton’s excellent article ‘Mobile Concepts, Metaphor, and the Problem of Referentiality in Deleuze and Guattari’, pp. 27–46. 82. Plotnitsky also suggests that Jackson Pollock’s paintings can be understood as a realisation of Riemannian space in art. Plotnitsky, ‘Bernhard Riemann’s Conceptual Mathematics’, p. 109. 83. Cf. Salanskis: ‘Mathematics plays the central part in the new [Deleuzian] philosophy of nature, which is at the same time and in the same way philosophy of culture, but it does so in the qualitative, absolute and immediate manner which characterises for Kant dogmatic metaphysics: metaphysics which claims to grasp being and becoming as such with purely conceptual tools. The only difference, but it is an important one, is that the conceptual key is mathematical, and not logical’ (Salanskis, ‘Mathematics, Metaphysics, Philosophy’, p. 54; see also p. 51). 84. Badiou, ‘Mathematics and Philosophy’, pp. 12–30.

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4

Time and the Split Subject

The Kantian Revolution in the Philosophy of Time The concern of this chapter will be to show that the genesis of thought presupposes a fracture or rift in the thinking subject. This fracture, as we will see, is caused by time. Deleuze takes his inspiration from Kant, that is the Kantian notion of time as a pure and empty form, a form of interiority, but he does not follow all the implications that are drawn by Kant. Quite to the contrary, Deleuze criticises Kant for attempting to reconcile the two unequal halves of the split subject, the active faculty of synthesis and the passive faculty of receptivity, and to mediate them in a new form of identity: ‘the fracture is quickly filled by a new form of identity – namely active synthetic identity; whereas the passive self [moi] is defined only by receptivity and, as such, endowed with no power of synthesis’ (DR 87/117).1 Deleuze shifts the attention from the transcendental subject to the transcendental and genetic conditions. He wants to give a genetic account of the act of thinking within thought and of the subject itself. Deleuze assigns to time a very special role with regard to the constitution of the subject of thought and creation. Therefore it will be necessary to examine Deleuze’s three passive syntheses of time. The first synthesis of time is constitutive of the subject, the second synthesis is a constitutive condition for acting and thinking. However, the third synthesis of time is the most important one: Deleuze equates it with the Nietzschean eternal return, which enacts a power of repetition. Through the repetition of the eternal return the identity of the thinking subject is dissolved and turned into a series of little selves or simulacra. Thought occurs only at this extreme point of the fractured I. The transcendental and genetic conditions of thought have thus to be considered in relation to Deleuze’s complex theory of time. As the above outline of the problem of this chapter suggests, the point of departure for Deleuze’s reflections on time and the split subject is Kant’s critical philosophy. The Kantian critique of traditional metaphysics, in particular of the three branches of rational 210

Time and the Split Subject theology, rational cosmology and rational psychology, contested the truth of established speculative Ideas such as the existence of God or the existence of an immortal soul. Hitherto God had played the role of the guarantor God, who constitutes the identity of the subject by creating man in his own image and who judges the subject in accordance with divine laws. With Kant, man has become autonomous, a judge of his own affairs, guided by the rules of reason. But man has also become a finite being, dependent on sensible intuition when he reaches out for truth. The split of the subject into its intelligible and its sensible nature yields a crisis for the unity of the subject. Although Kant was careful to resurrect God and the soul as regulative Ideas and to restore the superiority of the intelligible over the sensible, there nonetheless ensued a significant problem for the subject’s identity. The subject of rationalism – whether Leibniz’s conception of a simple substance or Spinoza’s conception of a particular mode of God’s attribute of thought – was conceived as an analytic identity. With Kant, the conception of the subject undergoes a fundamental change, since the subject is no longer defined as an analytic identity but as a synthetic identity. The Kantian subject is premised on the synthesis of two opposed faculties: the active faculty of thought and the merely passive faculty of receptivity. While the faculty of thought presupposes the transcendental form of the ‘I think’ and the a priori categories of the understanding, the faculty of receptivity provides sensible intuition given in the forms of space and time. In drawing this firm distinction, Kant made the human subject and its claim to knowledge and truth dependent on ‘the touchstone of experience’ (CPR A viii). The human subject has become a finite subject by virtue of its dependence on the receptivity of intuition. This is a point that Heidegger strongly emphasises in his seminal book Kant and the Problem of Metaphysics. Deleuze, however, questions the importance of this change in the philosophical conception of the subject. It is sometimes argued that a considerable philosophical change took place between pre-and post-Kantianism – the former being defined by the negative of limitation, the latter by the negative of opposition; the one by analytic identity, the other by synthetic identity; the one from the point of view of infinite substance, the other from the point of view of the finite Self. [. . .] However, the importance of such changes is open to question. (DR 58/81)

According to Deleuze, no fundamental change has taken place so long as the identity of the subject is still preserved. The issue of 211

conditions of thought: deleuze and transcendental ideas critique is crucial, but Kant’s critique of speculative metaphysics did not go far enough. God is retained inasmuch as the place of God is kept intact. It is true that man has been put in the place of God, but the importance of this change is questionable. The reign of the negative (whether limitation or opposition) and identity (whether analytic or synthetic) continues. ‘That is why the Man–God permutations are so disappointing, and do not advance matters one step’ (DR 58/81). The Kantian subject has conserved its identity, which grounds the harmonious accord of the faculties. What Deleuze finds revolutionary in Kant is not the new synthetic conception of the subject which was adopted by post-Kantian philosophy, but a radical moment in his thought that was all but lost to the philosophy that followed. Rather than being concerned with what happens before and after Kant (which amounts to the same thing), we should be concerned with a precise moment within Kantianism, a furtive and explosive moment which is not even continued by Kant, much less by post-Kantianism – except, perhaps, by Hölderlin. (DR 58/81–2)

Deleuze identifies this great revolutionary moment with Kant’s new conception of time. Time is no longer defined as a cosmological or psychological time, but as a ‘form of interiority’, a pure and empty form of time. There ensue two important consequences which Deleuze summarises by means of the somewhat cryptic formulas ‘time is out of joint’ and ‘I is an Other’.2 In the following, we will first look at Deleuze’s reading of the Kantian philosophy of time and then reconstruct his own theory which is laid out in the three syntheses of time in Chapter Two of Difference and Repetition. In particular, we will focus on the third synthesis of time, the static synthesis or synthesis of the future, and examine its heterogeneous literary, mathematical and philosophical sources. It will be seen that the third synthesis of time which organises time in a series by means of a constitutive caesura or cut is necessarily linked with a split subject which, for Deleuze, is the subject of thought and creation. ‘The Time Is Out of Joint’ Deleuze begins his 1978 lecture course on Kant by declaring that ‘all of the creations and novelties that Kantianism will bring to philosophy turn on a certain problem of time’. Kant introduces ‘an entirely new conception of time, a conception of which we can say that its elaboration by Kant will be decisive for all that happened 212

Time and the Split Subject afterwards’ (LK I, p. 1). Deleuze chooses the formula ‘The time is out of joint’ uttered by Hamlet in Shakespeare’s tragedy Hamlet, Prince of Denmark to summarise what for Deleuze amounts to Kant’s first great reversal in the theory of time (LK I, p. 14).3 In antiquity, the theory of time was bound up with the concept of an enclosed geocentric cosmos, and time was thought of as the measure of the movement of celestial bodies in their orbits.4 The ancient model of the cosmos, the armillary sphere, which was the predominant model until Copernicus, represented a spherical cosmos with eight moving circles and the Earth at the centre. The outermost sphere was conceived as a moving shell of fixed stars, and it carried round with it all the contents of the sphere including the Moon, the lunar planets (Mercury and Venus), the sun and the three outer planets (Mars, Jupiter and Saturn), though the planets had movements of their own in counter-rotation to the outermost sphere. The Earth was at rest in the centre, like a hinge around which the celestial bodies pivot. However, it should be noted that not all theories held the Earth to be stationary – Plato, for example, claimed that the earth revolved on its axis. Both Plato and Aristotle associated time with number, defining it as ‘the number of movement’. In recounting the myth of creation, Plato’s Timaeus imagines a demiurge who creates the universe as an image of the ideal world and its eternal forms: So he bethought him to make a moving image of eternity (aion), and while he was ordering the universe he made of eternity (aion) that abides in unity, an eternal (aionios) image moving according to number, even that which we have named Time (chronos). (Tim. 37d)

Although Aristotle argued against Plato that a temporal beginning of time is impossible (De Caelo I, 279b), he also defined time as ‘a number of change in respect of the before and after’ (Physics IV, 219b1), or simply ‘a number of movement’ (De Caelo I, 279a15).5 Thus time was conceived as the number of movement of the planets, which passed time and again through ‘cardinal points’, that is certain privileged and fixed points. By means of their celestial revolution the planets marked off regular periods of time, the shortest unit of which was the period of day-and-night. Plato said in the Timaeus: ‘But now day and night, being seen of us, and months and the revolution of the years have created number, and they gave us the notion of time’ (Tim. 47a). And Aristotle noted that the uniform circular motion of the planets was most apt to provide a number of measurement, 213

conditions of thought: deleuze and transcendental ideas i.e. time, since ‘there is no uniform qualitative change or uniform increase in size or uniform coming-to-be, but there is uniform locomotion’ (Physics IV, 223b12). Since time in ancient cosmology was the measurement of the circular movements of the planets, it followed that time was naturally thought of as a cycle (cf. Physics IV, 223b12). Furthermore, the definition of time could not be separated from the movement of physical bodies. As Aristotle put it: ‘Time is a number of movement – but there is no movement without physical body’ (De Caelo I, 279a15). This is why Deleuze attributes to the ancient Greeks a concept of time which ‘is a mode and not a being. No more than number is a being, it’s a mode in relation to what it quantifies, in the same way time is a mode in relation to what it measures’ (LK II, p. 2). According to Deleuze, time loses its modal character and ceases to be circular only subsequent to the establishment of modern science in the sixteenth and seventeenth centuries (in particular, in the scientific cosmology of Newton). With Kant finally, time becomes purely formal; it is a pure form, it has unrolled into a ‘straight line’. In Deleuze’s words: ‘The time is out of joint’, time is no longer coiled up in such a way that it is subordinated to the measure of something other than itself, such as, for example, astronomical movement. Time has ceased to be the number of nature, time has ceased to be the number of periodical movement. Everything happens as if, having been coiled up so as to measure the passage of celestial bodies, time unrolls itself like a sort of serpent, it shakes off all subordination to a movement or a nature, it becomes time in itself for itself, it becomes pure and empty time. It measures nothing anymore. Time has taken on its own excessiveness. It is out of its joints, which is to say its subordination to nature; it’s now nature which will be subordinated to it. (LK I, p. 14)

Deleuze invokes the images of a serpent which unrolls itself, or of a circle that snaps, a spring that uncoils itself to become a pure straight line (cf. LK II, p. 2). He further adduces Borges’ idea of a ‘labyrinth composed of a single straight line’ that is all the more tortuous since it is ‘indivisible, incessant’ (KCP vii; DR 111/147).6 These images already suggest that with the modern conception of time something fundamental has changed: the cosmological harmony between the world and the heavens, man and the heavenly gods, has somehow broken down. It is as though Timaeus’ prediction has become true: ‘Be that as it may, Time came into being together with the Heaven, in order that, as they were brought into being together, so they may 214

Time and the Split Subject be dissolved together, if ever their dissolution should come to pass’ (Tim. 38b). The time of antiquity has perished together with the gods and the heavens, and a new time is born. Pure and empty time is now the true subjectivity. It has become an infinite, straight line, which will cut right through the consciousness of the subject. Its effect is tortuous and inhuman in the sense that it carries the subject to the border of the liveable and destroys the well-constituted identity of the subject. ‘I Is an Other’ Deleuze borrows from the French poet Arthur Rimbaud (1854–91) the formula by which he characterises the second novelty of the Kantian theory of time: ‘I is an Other’ (Je est un autre).7 By defining time as a form of interiority, Kant introduced a fundamental split in the subject. The Kantian subject is torn between the form of spontaneity, that is the ‘I think’ which accompanies all concept production and guarantees the unity of synthesis, and the empirical self which experiences the effects of thought rather than initiating the act of thought itself. According to Deleuze, Rimbaud’s formula ‘I is an Other’ is apt to express the alienation to which the Kantian subject succumbs, notwithstanding that Rimbaud’s phrase occurs in a rather different context. Rimbaud puts the formula ‘I is an Other’ in an Aristotelian context, referring to Aristotle’s distinction between determining form and indeterminate matter. Suffice here the following quotation in which Rimbaud distinguishes between matter and form: ‘Too bad for the wood which finds itself a violin! If the copper wakes up a bugle, that is not its fault.’8 By means of the formula ‘I is an Other’, Rimbaud expresses the experience of being formed by thought rather than being the originator. Thought forms me – I am not the master of thought at all. With Kant, the concern is no longer of a form that informs matter but of ‘an infinite modulation, no longer a mould’ (KCP ix). Thought works within me – I am affected by thought that is both mine and the thought of an Other. The fracture or crack in the ‘I’ is produced by the pure and empty form of time. This means that I experience myself, i.e. my feelings, thoughts, actions and bodily sensations, etc., always under the condition of time, which is the interior form of receptivity. But the synthesis of all these different representations within the unity of consciousness is performed by the transcendental I, or the ‘I think’ as the transcendental form of apperception. 215

conditions of thought: deleuze and transcendental ideas Phrased more precisely, the I affects itself under the form of time. The remarkable outcome of this kind of auto-affection is that the difference between being and thought, or matter and form, is interiorised. Deleuze refers to this establishment of internal difference as the moment of ‘discovery of the transcendental, the element of the Copernican Revolution’ (DR 86/117). A transcendental difference separates the a priori syntheses of the ‘I think’ from the empirical, psychological self. In other words, the ‘I think’ is the transcendental condition of the empirical self. In order to better understand the impact of this event, it is worth going back to the historical context of the Cartesian Cogito and Kant’s criticism of it. Descartes’ method of doubt, by means of which he searched for an absolute certainty that contains its ground within itself, famously led him to the formula ‘I think, therefore I am’ (cogito ergo sum). In his Meditations, Descartes first applies his philosophical doubt to everything concerning his body, bodily sensations (such as pain, pleasure, hunger, etc.) and sense impressions, and then continues to doubt the products of his inner faculties (such as memories, imaginings, etc.). He concludes that he could doubt everything except the fact of his doubting. Since, according to Descartes, doubt is a mode of thought, of intellectio in general, and cannot exist separately from thinking, the act of thought manifest in the ‘I think’ appears to be an absolute certainty. The key idea is that the act of thought cannot be doubted the instant that it is performed, and thus it is impossible for it not to be true. Leaving the question of the kind of impossibility involved aside, Descartes continues that in order to think one must be. The act of thought necessarily implies an indeterminate existence. Descartes’ line of argument thus goes from ‘I doubt’ to ‘I think’ to ‘I am’. Now Descartes immediately applies the determination ‘I think’ to the indeterminate existence ‘I am’, which is to say that the ‘I’ is determined as a thing that thinks. I am a thinking thing (res cogitans). Kant agrees with Descartes that the determination ‘I think’ implies an indeterminate existence. As he puts it, ‘the proposition “I think”, insofar as it says only that I exist thinking, is not a merely logical function, but rather determines the subject (which is then at the same time an object) in regard to existence.’ However, ‘this cannot take place without inner sense, whose intuition always makes available the object not as thing in itself but merely as appearance’ (CPR B 429). The second part of this quotation is decisive. To be sure, the indeterminate existence is to be determined by the determination, 216

Time and the Split Subject but this does not yet give us the form under which this indeterminate existence is determinable. Descartes simply assumes that my indeterminate existence is determinable as a substance or thing (res cogitans), and draws out implications concerning the ‘I’ which now enjoys all the attributes of a substance: subsistence, simplicity and identity. Kant rejects all these claims as instances of paralogism in his criticism of rational psychology. As Kant has famously declared with his notion of the phenomenon, something can only be an object for us if it conforms to our conditions of knowledge. These are first and foremost the a priori forms of intuition and secondly the categories of the understanding. The categories can only apply to something that is determinable in space and time. In fact, time is the most universal form under which anything given to us in perception must be determinable. This implies that whatever appears to us in ‘outer space’ has first to be given in the successive flux of our inner sense, that is under the condition of time. So time is an a priori condition of all appearance in general, and indeed the immediate condition of the inner intuition (of our souls), and thereby also the mediate condition of outer appearances. [. . .] From the principle of inner sense I can say entirely generally: all appearances in general, i.e., all objects of the senses, are in time, and necessarily stand in relations of time. (CPR A 34/B 51)

Time as the condition of all appearances in general is also the form under which I appear to myself. I appear to myself under the form of the determinable as a phenomenon in time. This is what Kant offers in reply to Descartes: the determination ‘I think’ indeed actively determines my indeterminate existence, but it can only do so under the form of the determinable (see also CPR B 157–8, footnote 1). Hence the determined thing is not simply ‘a thinking thing’ but a passive being in time. This means that for a subject to internally intuit itself, in order to seek out (apprehend) that which lies in the mind, it must affect the latter, and it can only produce an intuition of itself in such a way, whose form, however, [. . .] determines the way in which the manifold is together in the mind in the representation of time; there it then intuits itself not as it would immediately self-actively represent itself, but in accordance with the way in which it is affected from within, consequently as it appears to itself, not as it is. (CPR B 68–9)9

Time is therefore the form under which the subject affects itself. According to Deleuze, the idea that time is the form of auto-affection 217

conditions of thought: deleuze and transcendental ideas plays an increasingly important role in Kant’s Opus Postumum (LK I, p. 15). Let us now consider some of the consequences of Kant’s new definition of time. Most importantly, time ceases to be defined in terms of succession. Kant thereby contradicts Leibniz who defined time as the order of succession.10 According to Kant, succession is only a mode of time. Equally, coexistence, which for Leibniz was supposed to define space, is just another mode of time. ‘Time, he [Kant] tells us, has three modes, duration or permanence, coexistence and succession. But time cannot be defined by any of the three because you cannot define a thing through its modes’ (LK I, p. 15).11 Instead, ‘time is the form of interiority. It’s the form under which we affect ourselves, it’s the form of auto-affection. Time is the affection of self by self’ (LK I, p. 15). The transcendental difference that Kant introduces into the subject through the form of time as the form of auto-affection is correlated to a certain distribution of the transcendental and the empirical, and of activity and passivity. Kant resurrects the identity of the subject in the ‘transcendental unity of apperception’, which although it is not a substantial being but a universal form, unites all spontaneity, i.e. synthetic activity of thought, in itself. The empirical self, on the other hand, is defined as entirely passive, as pure receptivity, deprived of the power of synthesis. It is at this point that Deleuze parts company with Kant: It is impossible to maintain the Kantian distribution, which amounts to a supreme effort to save the world of representation: here, synthesis is understood as active and as giving rise to a new form of identity in the I, while passivity is understood as simple receptivity without synthesis. The Kantian initiative can be taken up, and the form of time can support both the death of God and the fractured I, but in the course of a quite different understanding of the passive self. (DR 87/118)

Contrary to Kant, Deleuze argues that the passive self is constituted by  a passive synthesis of time. In fact, he analyses three distinct ­syntheses of time: (1) the passive synthesis of contemplation-­ contraction; (2) the passive synthesis of (transcendental) memory; and (3) the static synthesis of empty time. The first synthesis constitutes time as the moment of the lived present, the second constitutes the condition of the pure past, while the third constitutes the pure order of time and opens up the possibility of a future. It produces a fracture or crack in the I, such that it opens itself up for the ­movement of thought. 218

Time and the Split Subject

Deleuze’s Passive Syntheses of Time: The Lived Present and the Pure Past At first glance, the notion of a ‘passive synthesis’ appears self-­ contradictory. ‘Isn’t synthesis a conscious activity that depends on ­representations? Aren’t the capacity to represent and self-­ consciousness pre-conditions for synthesis?’12 According to Deleuze, a ­synthesis can be carried out completely unnoticed by the conscious mind. It takes place subconsciously, which is to say that it does not require a series of conscious representations but rather ‘presentations’ in the sense of Maimonian differentials. Inasmuch as there is no selfconscious agent involved, Deleuze speaks of a ‘passive synthesis’. It is important to note that, for Deleuze, the passive syntheses of time do not occur within a subject, rather they are constitutive of subjectivity itself. This means that there are segments of subjectivity and agency which are engendered by the passive syntheses of time. In other words, only under the condition of passive syntheses are partial identities (i.e. the formation of local selves or egos) and activities (such as the active syntheses of memory and understanding) possible. However, Deleuze refuses any ground on which to build a secure identity of the subject. ‘Selves are larval subjects; the world of passive syntheses constitutes the system of the self, under conditions yet to be determined, but it is the system of a dissolved self’ (DR 78/107). Let us now look at the first synthesis of time: the passive synthesis of contemplation-contraction, constituting time as a lived, or living, present. The Passive Synthesis of the Lived Present Deleuze bases the first synthesis of time on David Hume and partly on the English novelist Samuel Butler (1835–1902), in particular his book Life and Habit (1878). One of the major concerns that Hume dealt with was the problem of custom or habit and how we acquire it. Our psychic life rests to a great extent on habit. Hume’s investigations into causal sequences, for instance, convinced him that the idea of a necessary connection of events is not drawn from the perception of an objective relation in things themselves but is based on a subjective impression or internal sensation of the mind. As Hume famously stated, the idea of necessity involved in causal relations arises from a feeling of determination, acquired by habit.13 How does a habit then become 219

conditions of thought: deleuze and transcendental ideas manifest? Let us suppose that two events A and B constantly appear in conjunction in our mind. Although each pair of AB is distinct and independent from the other, our imagination tends to assimilate the different cases and regard them as repetitions of the same conjunction. The more we experience the constant conjunction of AB, the more the imagination is inclined to associate to a given event A its usual companion B. As Hume says: ‘After a repetition of similar instances, the mind is carried by habit, upon the appearance of one event, to expect its usual attendant.’14 Naturally, a single case of AB yields no expectancy. But if we experience the repetition of similar pairs of events, something in our mind changes. The repetition of AB produces the propensity to think of B when A appears. According to Deleuze’s interpretation of Hume, this act of association is possible by virtue of a specific ‘contractile power’ (DR 70/96) of imagination.15 This means that the imagination is able to retain a preceding event when another occurs, and, upon the repeated contraction of similar pairs of events, to ground them in an ‘internal qualitative impression endowed with a certain weight’ (DR 70/97). In this way, a habit is acquired. As Hume makes clear, the acquisition of a habit is not a cognitive act, but rather belongs to our sensory nature. The imagination contracts past and present experiences and projects them into the future, producing an expectation. Deleuze understands this as a synthesis of time (DR 70/97). The important fact is that the idea of time is not derived from a succession of instants. On the contrary, it is only by means of the contraction of instants that time is constituted and assembled in the lived, or living, present. To it [the present] belong both the past and the future: the past in so far as the preceding instants are retained in the contraction; the future because its expectation is anticipated in this same contraction. The past and the future do not designate instants distinct from a supposed present instant, but rather the dimensions of the present itself in so far as it is a ­contraction of instants. (DR 70–1/97)

For Deleuze, this fusion or contraction of (past, present and future) instants forms the passive synthesis of the living present. It can be expressed in an asymmetrical arrow of time, which goes from the particularity of the past to the generality of the future. Hume’s example of the constant conjunction of pairs of AB in the series AB AB AB A . . . amounts, however, only to a synthesis for us, that is for a perceptive mind. Deleuze distinguishes yet another 220

Time and the Split Subject level of contraction that constitutes not simply the habits that we have, but the habits that we are. In other words, apart from perceptual passive syntheses there are also organic passive syntheses (DR 73/99). ‘What organism is not made of elements and cases of repetition, of contemplated and contracted water, nitrogen, carbon, chlorides and sulphates, thereby intertwining all the habits of which it is composed?’ (DR 75/102). It might be surprising that Deleuze speaks of ‘habits’ when he seems to refer to mere biological, chemical syntheses of elements, which, to be sure, can be described as contractions. Understood in this way, the quotation is misleading. Deleuze does not regard the organism from an objective, scientific viewpoint of chemical syntheses, but rather as a living thing composed of many contemplating selves or ‘souls’ (cf. DR 75/103). It is at this point that he refers to Samuel Butler. Butler described the corn in the fields as composed of thousands of contemplating souls which contract water and minerals in anticipation of turning it into wheat.16 Every contraction is at the same time contemplation, that is contemplation of past experiences and of future expectations. There is a past inscribed in the organs, muscles and nerve cells of an organism, as well as a future dimension. ‘Need is the manner in which this future appears, as the organic form of expectation. The retained past appears in the form of cellular heredity’ (DR 73/100). Thus Deleuze concludes: A soul must be attributed to the heart, to the muscles, nerves and cells, but a contemplative soul whose entire function is to contract a habit. This is no mystical or barbarous hypothesis. On the contrary, habit here manifests its full generality: it concerns not only the sensory-motor habits that we have (psychologically), but also, before these, the primary habits that we are; the thousands of passive syntheses of which we are organically composed. (DR 74/101)

Deleuze further enriches the concept of contemplation by linking it to the Greek myth of Actaeon who contemplates the goddess Diana while she is taking a bath in the woods, and of Narcissus who contemplates his own image in the water. Actaeon and Narcissus are both taking pleasure in contemplating. Pleasure, according to Deleuze, is not just a defined and isolated case in our psyche, but a principle that rules over our psychic and organic life. ‘There is a beatitude associated with passive synthesis, and we are all Narcissus in virtue of the pleasure (auto-satisfaction) we experience in contemplating, even though we contemplate things quite apart from 221

conditions of thought: deleuze and transcendental ideas ourselves’ (DR 74/102). Deleuze subjoins a sort of Freudian interpretation to the syntheses of time. He associates the first synthesis of time with Eros (the narcissistic libido), the second synthesis of time with Mnemosyne, and the third synthesis of time with Thanatos or the death instinct (DR 108–15/143–52). However, we will pass over this psychoanalytic dimension of the syntheses of time, since it opens up another level of interpretation that can be quite misleading. By interpreting the syntheses of time in Freudian terms, there is the danger that they are thought of as inner-psychic syntheses of an already constituted subject. Yet the Deleuzian syntheses of time surpass the view of a composed and well-constituted subject. They form the transcendental, genetic conditions which first of all constitute the local selves or contemplating souls that are connected within the system of a dissolved self. It is important to keep in mind that Deleuze is not interested in a psychology of the subject but in metapsychological, transcendental syntheses of time. What has been shown is that Deleuze substitutes for the Kantian passive self a multiplicity of little selves or contemplative souls, each endowed with a present of a particular duration. The living present of an organism is thus an assemblage of various presents or rhythms, constituted by the contractions and fatigues of the contemplating souls. Thus the passive self is no longer defined in terms of passivity or the form of receptivity. It is no longer the receptacle of sensations already formed according to space and time and on which the a priori categories are superimposed. On the contrary, experience is a product of thousands of passive syntheses performed by the ­contemplative souls. Deleuze’s notion of passive syntheses of contemplation-­ contraction has an important consequence. The conditions of experience cease to be abstract conditions of possibility in order to become genetic conditions of real experience. By means of the elaboration of genetic conditions of real experience, Deleuze achieves a reunification of the aesthetic that Kant had left divided into the aesthetic of sensibility and the aesthetic of the beautiful. Deleuze criticises Kant for dividing aesthetics into two irreducible domains: that of the theory of the sensible which captures only the real’s conformity with possible experience; and that of the theory of the beautiful, which deals with the reality of the real in so far as it is thought. Everything changes once we determine the conditions of real experience, which are not larger than the conditioned and which differ in kind from the categories. (DR 68/94) 222

Time and the Split Subject The two domains of sensible experience and artistic creation become one, since both involve the real of experience (the rhythms of sensible differentials or intensities, the dynamic forces of contraction and expansion) as their genetic condition.17 Thus Deleuze’s first synthesis of time, the passive synthesis of contemplation-contraction, ‘already constitutes a kind of Transcendental Aesthetic’ (DR 98/130) that goes beyond the Kantian Transcendental Aesthetic. Although this synthesis of time resolves some of the problems bequeathed by Kant, it also raises new questions and problems. We have seen that the passive syntheses of contemplation-contraction constitute time as lived, or living, present. In Deleuze’s words, ‘the first synthesis, that of habit, is truly the foundation (fondation) of time’ (DR 79/108), that is of the living present. However, the living present is not to be understood in terms ‘of a perpetual present, a present which is coextensive with time’ (DR 76/105). Quite to the contrary, the living present passes. The first synthesis of time is necessarily ‘intratemporal’ (DR 76/105). This is why Deleuze sees himself compelled to assume a second synthesis of time, one in which the first synthesis of time operates. This second synthesis of time is not to be understood as the foundation (fondation) of time but rather as its ground (fondement). The ground is that which is presupposed by the passing present; it is that which causes the present to pass. According to Deleuze, it is the (transcendental) memory that grounds time (cf. DR 79/108). The Passive Synthesis of the Pure Past With regard to the second synthesis of time, Deleuze draws on Henri Bergson’s notion of a pure past and mobilises examples from Marcel Proust’s In Search of Lost Time. Both Bergson and Proust, although they have quite different concepts of time, admit the idea of a pure past, or in Proust’s words, ‘a bit of time in the pure state’ (un peu de temps à l’état pur).18 This pure past (souvenir pur) is not to be confused with a recollection-image (image-souvenir), that is the psychological or mental image of a former present. The pure past is time in-itself. What is most difficult to understand about Bergson’s virtual cone of memory or Proust’s essences is that they designate a pure time in-itself that exists outside consciousness.19 However, Deleuze is careful to point to a major difference between Bergson and Proust (B 122/55, footnote 16/1): Proust believes that time in-itself can be lived, that it can traverse us in terms of an 223

conditions of thought: deleuze and transcendental ideas involuntary memory and be expressed in a work of art. Bergson, on the contrary, treats the pure past as something that cannot be lived directly. It can only be experienced if it materialises itself in a recollection-image, that is as a nascent sensation (sensation naissante) in the present. But then it is no longer pure past. The pure past coexists with the present as the hidden ground or the condition of the passage of time. Bergson’s pure past is a transcendental memory, an ‘immemorial or ontological Memory’ (B 57/52). In great admiration for Bergson, Deleuze declares in Difference and Repetition: ‘If Matter and Memory is a great book, it is perhaps because Bergson profoundly explored the domain of this transcendental synthesis of a pure past and discovered all its constitutive paradoxes’ (DR 81/110). Yet, by identifying the second passive synthesis of time with the synthesis of a Bergsonian pure past or of memory, Deleuze risks falling into a speculative philosophy of a Platonic type. He seems to forsake critical philosophy for an analysis of a pure, a priori being of time.20 The problem we will have to cope with is how Deleuze can maintain a ‘transcendental’ philosophy that does not fall back into a ‘transcendent’ or pre-critical metaphysics of things in themselves. This can only be achieved by emphasising the role of Proust and the meaning of a ‘transcendental’ aesthetic of signs or Ideas. Deleuze introduces the passive synthesis of the pure past on account of the ‘paradox of the present: to constitute time while passing in the time constituted. We cannot avoid the necessary conclusion – that there must be another time in which the first synthesis of time can occur. This refers us to the second synthesis’ (DR 79/108). The second synthesis constitutes the pure past, not as a dimension of the present but as a ‘past in general’, ‘of which the present and the future are only dimensions’ (DR 82/111). This reasoning appears very biased by spatial metaphors, for it seems to suggest that the past in general is a kind of container in which the present passes. To be sure, Bergson would have opposed such an impression. He declares that the categories of containing and being contained only apply to bodies, which are momentarily perceived in space.21 We must not conceive of the existence of the pure past in this way. On the other hand, we cannot simply define the past in terms of a modification of the present, as what the present becomes. According to our immediate intuition, we assume that in becoming past the present undergoes a kind of metamorphosis, maybe a decrease in intensity. It seems natural to suppose that the past is constituted after having been present, and 224

Time and the Split Subject that the arrival of a new present, i.e. a new sensation, changes the former present into a (less intensive) past. However, this way of talking about time is no less problematic. At what moment does a present become past? How can we distinguish one from the other? If there is only a difference of degree between both, say, a difference in intensity, a distinction is ultimately not possible. For instance, Bergson asks: how could we possibly have the memory of a strong, intense pain? Under the assumption of a mere difference of degree between perception and memory, the memory can by definition only be actualised in a weak sensation. Consequently, it will be impossible for us to distinguish it from a weak sensation that we experience, or a weak sensation that we imagine. This weak sensation can never give us the memory of a strong pain.22 According to Bergson, there must be a qualitative difference, a difference of kind between present and past, or, as he says, between perception and memory.23 The present is what interests us and which extends itself into sensory-motor action, while the past is essentially impotent (impuissant) and of no interest for our body (unless it becomes actualised in a sensation).24 The difference between present and past is marked by the criterion of usefulness for our actual body. Bergson revolutionises our understanding of time, in particular the passing of time. According to Bergson, present and past are not successive instants. One cannot pass from a present to a past. A present would always be present, and there would be no way for a new present to arrive. Bergson argues that past and present exist simultaneously. This implies that whatever happens, happens at least twice: in the present as the moment that I live, and in the past as the moment that has already been lived. This leads us to Bergson’s first paradox of time: ‘the contemporaneity of the past with the present that it was’ (DR 81/111).25 The past and the present do not denote two successive moments, but two elements which coexist: One is the present, which does not cease to pass, and the other is the past, which does not cease to be but through which all presents pass. It is in this sense that there is a pure past, a kind of ‘past in general’: The past does not follow the present, but on the contrary, is presupposed by it as the pure condition without which it would not pass. (B 59/54)

For Bergson, the defining characteristic of time is not the succession of instants, but the coexistence of different sheets of time. This means that duration or lived time is indeed a succession but it is 225

conditions of thought: deleuze and transcendental ideas so only because of its ‘virtual coexistence’ with the totality of the past (B 60/56). This implies that each present is not only always contemporaneous with its correlative past, it also coexists with the whole of the past in general. The pure past is like a gigantic cone constituted of distinct levels or circles of memory. The larger these circles are, the lesser is their degree of contraction. This means that the base AB of the cone contains an indefinite number of memories in all their various details, while at the level of A9B9 the memories are comparatively more contracted, that is, differences become assimilated. The level of contraction and assimilation of differences increases until the present S, which we incarnate with our bodies. S is the most contracted degree of the past and the greatest simplification of our mental life, in other words, the prolongation in sensory-motor reactions.26 The present S coexists with the past AB, but also with A9B9, and A0B0 and so on to infinity. Thus, whatever happens at the present S is in effect, repeated at all the levels of the pure past simultaneously, in greater or lesser detail depending on the respective distance to the base or the peak of the gigantic cone of memory. ‘The same psychological life, therefore, must be supposed to be repeated an endless number of times on the different storeys of memory, and the same act of the mind may be performed at varying heights.’27 Bergson’s metaphor of the cone illustrates his second paradox of time: the paradox of coexistence of the entire past with the present (cf. DR 81/111). The third paradox is the pre-existence of the pure past. The pure past has never been present. It never passes or comes ‘after’. It is preserved in itself. The mode of being of the pure past is not one of actual existence, but rather of ‘insistence’: ‘it does not exist, but it insists, it consists, it is’ (DR 82/111). Deleuze opposes the terms ‘present’, ‘actual’ and ‘existence’ to the terms ‘pure past’, ‘virtual’ and ‘insistence’. The question that now arises is: can we somehow penetrate this virtual being of the pure past? Is our active synthesis of memory capable of recovering an instant of the pure past? Deleuze warns us against an interpretation of Bergson that uses a psychological model of recollection. One must avoid an overly psychological interpretation of the text. Bergson does indeed speak of a psychological act; but if this act is ‘sui generis,’ this is because it has made a genuine leap. We place ourselves at once in the past; we leap into the past as into a proper element. (B 56/51)28 226

Time and the Split Subject We have to jump into a particular circle of the pure past. As Deleuze states: ‘Memory is not in us; it is we who move in a Being-memory, a world-memory’ (CIT 95/129–30). At this point, Deleuze brings in Proust and the Proustian examples of involuntary memory in In Search of Lost Time. It is not by means of an active synthesis associated with voluntary memory that the hero of the novel recovers his past childhood, his hometown Combray, his dead grandmother, etc. ‘It is within Forgetting, as though immemorial, that Combray reappears in the form of a past which was never present: the in-itself of Combray’ (DR 85/115). A number of threads come together here. Deleuze paradoxically connects the notion of forgetting with the Platonic term ‘reminiscence’ in order to describe this sudden jump into the pure past, the involuntary memory of Proust. In Proust, it is not the effort of recollection but a sensual trigger (such as the taste of the madeleine, the stumbling over a cobblestone, etc.) that suddenly brings back the memory of Combray. It is thus in a state of forgetfulness, when the cognitive effort of active consciousness ceases, that reminiscence occurs. Reminiscence recovers the pure essence of Combray, ‘not as it was or as it could be, but in a splendour which was never lived’ (DR 85/115). Reminiscence is therefore very different from the active synthesis of memory which is simply a tool of representation and reproduces a former present. According to Deleuze, the fragment of the pure past is irreducible to both the former present that it was and the present present in which it might reappear as a recollection. It telescopes these two presents together and insists only in the ‘qualitative difference’ between the two (DR 122/160). It might be tempting to read Deleuze as if he were here suggesting some sort of Platonic forms or essences, but this interpretation is incompatible with Deleuze’s call for a ‘reversal of Platonism’ (see, for instance, DR 126–8/165–8 and Appendix I in LS 253–66/292–306). Deleuze rejects Plato’s hierarchy of transcendent eternal forms and the multitude of copies and simulacra spreading out on the surface of the earth. There are no originals, eternal forms or essences of which we can become ‘reminiscent’. Instead, Deleuze rather specifies ‘reminiscence’ as being simultaneously an act of creation. In fact, it is art that produces pure essences, reveals the in-itself or re-creates the pure past. Thus Proust’s narrator conserves the Combray of his childhood through his writings. However, the Combray that he composes is not a recollection-image. In the original French text, Deleuze describes the artistic image of Combray as a ‘téléscopage’ (DR 115) between the former present that it was and the present present that it could 227

conditions of thought: deleuze and transcendental ideas be. What is meant is perhaps a kind of contraction or condensation of all possible experiences of Combray in a complex intensive impression. More precisely, the artist does not merely represent his own lived experiences, his own perceptions and affections in the artwork, but he also contracts those of the lives of others. Properly speaking, the matter is no longer of perceptions and affections, but of universal ‘percepts’ and ‘affects’ – terms that Deleuze introduces in his late œuvre. We thus deal with a kind of de-subjectified sensation, in Deleuze’s words, a ‘sensation in itself’ (cf. WP 164/155) or a ‘bloc of sensations’ (WP 164/154). As Deleuze says: We write not with childhood memories but through blocs of childhood that are the becoming-child of the present. [. . .] We attain to the percept and the affect only as to autonomous and sufficient beings that no longer owe anything to those who experience or have experienced them: Combray like it never was, is or will be lived; Combray as cathedral or monument. (WP 168/158)

In his early work of the 1960s, Deleuze has not yet found these concepts. With regard to the example of ‘Combray in itself’, Deleuze rather uses the Proustian expression of a pure essence or a shred of pure past (‘a bit of time in the pure state’).29 It is important to keep in mind that Deleuze does not have recourse to a type of mystic experience, a kind of fusion with the pure past, a reminiscence of pure essences, but that he invokes the necessity of an act of artistic creation. It is true, however, that the artist, for Deleuze, does not act as a God-like creator or originator. On the contrary, the artist creates only under the condition of the pressure of the work of art. He is forced to create; he is not free to choose the conditions of his creation. We may perhaps say that there are intensive forces which surpass the artist but which nonetheless demand to be given expression in the work of art, where they become re-created in a ‘bloc of sensation’. Indeed, we must understand Deleuze’s interpretation of a pure past not as an independent transcendent realm, but rather an immanent field of intensive forces that require a re-creation in the work of the artist. They are the condition of any great work of art (or indeed any excessive act) but at the same time they become re-created in the result which is called a pure essence or the in-itself. Deleuze follows up the idea of artistic creation, or rather creation per se: creation can also mean the performance of a transgressing, excessive act. We will see that this issue becomes of crucial importance in the third synthesis of time. It should be noted that between 228

Time and the Split Subject the second and the third syntheses of time prevails an obvious affinity. The Proustian formula ‘a little time in its pure state’ refers first to the pure past, the in-itself of the past [. . .], but more profoundly to the pure and empty form of time, the ultimate synthesis, that of the death instinct which leads to the eternity of the return in time. (DR 122/160)

We would argue that the passive synthesis of the pure past becomes ultimately absorbed in the third synthesis of pure time. A first indication can be found in The Logic of Sense, where Deleuze abandons the model of three syntheses of time and simplifies his account of time by turning to the dual model of Chronos and Aion. It is obvious that Chronos has to be equated with the first synthesis of time, that of perceptual syntheses and habit. Aion bears a strong resemblance to the third synthesis of time, that of empty time which is constituted by the ‘cut’, that is an excessive act or event, dividing past and future. Since the second synthesis of the pure past or Memory signifies an event – the involuntary memory and the artistic creation of a pure essence (‘a bit of time in the pure state’) – it should be counted on the side of Aion.30 Evidence for this thesis can be found in Deleuze’s treatment of Bergson’s notion of the pure past in Cinema 2: The Time-Image. Here Deleuze suggests a third model of Bergson’s cone of Memory: a line, which at one point splits itself into two distinct arrows.31 As Deleuze explains: Time has to split itself in two at each moment as present and past, which differ from each other in nature, or what amounts to the same thing, it has to split the present in two heterogeneous directions, one of which is launched towards the future while the other falls into the past. (CIT 79/108–9)

We will come across this split into a past and a future, a before and an after, with regard to the third synthesis of time. Moreover, Deleuze explicitly brings together Bergson and Kant (although with some reservation): Time is not the interior in us, but just the opposite, the interiority in which we are, in which we move, live and change. Bergson is much closer to Kant than he himself thinks: Kant defined time as the form of interiority, in the sense that we are internal to time (but Bergson conceives this form quite differently from Kant). (CIT 80/110)

In both Bergson and Kant, Deleuze recognises a de-psychologisation of time: time is no longer defined as the succession of moments, 229

conditions of thought: deleuze and transcendental ideas but as a ‘virtual coexistence’ of sheets of time, or respectively as the form of empty time which conditions the empirical subject as a temporal being. Although in a very different manner, both Bergson and Kant conceive of time as a condition that first of all grounds perceptual syntheses or active syntheses of memory and thus allows for processes of subject formation. Speaking boldly, time can be called the true agent, the true subjectivity on which we rely as the constitutive ground. As Deleuze states with reference to Bergson: ‘the only subjectivity is time, non-chronological time grasped in its foundation, and it is we who are internal to time, not the other way round’ (CIT 80/110). It remains to be seen how Deleuze himself will specify the transcendental aspect of time. The transcendental is surely not to be understood in terms of a ground (fondement). As Anne Sauvagnargues aptly says: In order to express this new relationship between time and subjectivity, Deleuze creates the neologism ‘effondement’ [ungrounding], from ‘effondrement’ [collapse] and ‘absence of fondement’ [ground], in order to define the non-original character of time, and to indicate his polemic hostility with respect to phenomenologies of foundation and origins.32

Deleuze’s Static Synthesis of Time As we have seen, Deleuze credits Kant for revolutionising the concept of time by defining it independently from movement as a pure and empty form, that is the form of interiority or inner sense. He particularly points out the revolutionary moment, when Kant introduced ‘that schizophrenia in principle’ (DR 58/82), that is the fractured I or split subject. However, Deleuze deviates from Kant in an important sense: the dissolved self as Deleuze envisages it is not congruent with the Kantian empirico-transcendental subject. Deleuze defies Kant’s reintroduction of a synthetic identity and the attribution of all power of synthesis to the transcendental I. His model of the three syntheses of time in Difference and Repetition challenges the Kantian account of subjectivity with its strict distribution of the empirical and the transcendental, of passivity and activity. We have seen that Deleuze’s first synthesis of time, that of the living present, constitutes subjects as formations of habit. The second synthesis of time, that of the pure past, establishes the coexistence of several levels of the past. It shows that the individual life in fact presupposes the whole of the past, that is not only its own past experiences and memories, but also those of others. Thus by means of the first two syntheses, 230

Time and the Split Subject Deleuze attempts to account for processes of habituation, subjectification and artistic creation. Now, by means of the third synthesis of time, that is the time of the future, Deleuze envisages a process of dissolution of subjective structures and of becoming. Deleuze’s third synthesis of time is arguably the most obscure part of his tripartite theory, as Deleuze mixes different theoretical concepts drawn from philosophy, Greek drama theory and mathematics. Of central importance is the notion of the caesura or cut, which is constitutive of the third synthesis of time defined as an a priori ordered temporal series separated unequally into a before and an after. This ordinal definition of time, we will argue, is heavily inspired by Kant’s definition of time as pure and empty form, Hölderlin’s notion of ‘caesura’ drawn from his ‘Remarks on Oedipus’ (1803) and Dedekind’s method of cuts as developed in his pioneering essay ‘Continuity and Irrational Numbers’ (1872). In the last section of this chapter, we will then see how Deleuze ties together the conceptions of the Kantian empty form of time and the Nietzschean eternal return, both of which are essentially related to a fractured I or dissolved self. Hölderlin’s Caesura At several places, Deleuze cites Hölderlin as the true descendant of Kant (DR 58/82; DR 87/118). Hölderlin is ‘one of Kant’s best disciples’ (LK I, p. 14), who poses the problem of the Kantian theory of time on the level of Greek tragedy and makes the effect of pure and empty time palpable. Time becomes a desert, the straight line which Oedipus wanders (LK I, p. 14). The two core texts which Deleuze refers to are Hölderlin’s cryptic Remarks on Oedipus (presumably written around September 1803)33 and Jean Beaufret’s small book Hölderlin et Sophocle (1965), which gives a very Kantian inspired interpretation of Hölderlin’s Remarks on Oedipus.34 Hölderlin interprets Sophocles’ Oedipus Rex as the undoing of the coupling between man and god: man and god become ‘an unlimited One’ (das grenzenlose Eineswerden), which, however, can be ‘purified’ only through an ‘unlimited separation’ (grenzenloses Scheiden).35 Deleuze describes this unlimited separation as a double deviation: ‘God turns away from man who turns away from God’ (LK II, p. 4). While in the tragedies of Aeschylus or Euripides the gods still ensured justice, they punished and pardoned according to their judgement, Sophocles’ tragedy marks a significant change. The bond 231

conditions of thought: deleuze and transcendental ideas between man and the gods has broken. The gods turn away from mankind. Sophocles’ tragedy Oedipus Rex shows how Oedipus, raging against the divine betrayal (‘göttliche Untreue’ in Hölderlin’s words), searches desperately for who he is and tries to recover his identity. As Hölderlin says, ‘at such moments man forgets himself and the god and turns around like a traitor.’36 Sophocles designated Oedipus as atheos, which not only means being a non-believer but literally being separated from God.37 Even when Oedipus’ crime is finally discovered, that is when the blind seer Tiresias reveals to Oedipus that he had killed his own father Laius and married his own mother Jocasta of Thebes, the gods do not punish Oedipus through an immediate and brutal death. Instead, Oedipus’ death is his long and lonesome wandering with no aim and no end in sight. According to Beaufret’s interpretation, man has to learn to endure the absence of God and to accept the abandonment.38 This is, in effect, the essence of tragedy (in German Trauer-spiel, a ‘play of mourning’). Heaven has become a transcendent realm (the Kantian ‘starry heavens’ above the head), whence follows the unlimited separation of heaven and earth. As we have already mentioned, Sophocles’ tragedy Oedipus Rex clearly breaks with the form of tragedy in Aeschylus and Euripides, where the unity of the cosmos was still intact, and where the divine law revealed itself in the order of the universe, the course of nature and human fate. This means that in the tragedies prior to Sophocles, the destiny of the characters was settled from the beginning. The gods ensured that justice was done and atonement made for every excessive act that violated the divine law. For instance, in Aeschylus’ Agamemnon, we can distinguish three unequal episodes that together form a ‘cycle of limitation, of transgression and of atonement’ (LK II, p. 3). In the first episode, the great Agamemnon rules over Mycenae, the most powerful kingdom in Greece, a realm of order, law and limits. In the second episode occurs the excessive act, the act of injustice: upon Agamemnon’s return to Greece from the Trojan War, his wife Clytemnestra assassinates him. This is the moment of transgression or violation of the limit. In the third and last episode, Orestes, the son of Agamemnon and Clytemnestra, avenges his father by killing his mother and new husband Aegisthus. Thus the atonement for the injustice ‘will be the re-establishment of the equilibrium of the limit which for a moment was overstepped’ (LK II, p. 3).39 Already from the beginning, that is before the murder of Agamemnon is even committed, it is clear that atonement will follow the excessive act. 232

Time and the Split Subject When Agamemnon enters the palace, Cassandra, princess of Troy and abducted as Agamemnon’s concubine, has a vision of both the crime and also Orestes’ subsequent revenge. But her prophecy has no effect on the course of the events at all. Her vision is nothing but a confirmation of what is set from the beginning. Picking up Hölderlin’s phrasing, both Beaufret and Deleuze say that the beginning and end of the tragedy are bent in such a way that they correspond or ‘rhyme’ with each other. Time is conceived as a curve. Sophocles, on the other hand, suggests a new conception of time. He un-curves (décourber) time, turns it into a straight line, and cuts it by a caesura which will produce a ‘before’ and an ‘after’ which no longer rhyme together.40 Indeed, Tiresias’ revelations – that Oedipus is a child of Thebes, that he is brother and father to his own children, and son and husband to his own mother – form a caesura. Hölderlin describes the moment of the caesura as follows: In the utmost form of suffering [. . .] there exists nothing but the conditions of time and space. Inside it, man forgets himself because he exists entirely for the moment, the god [forgets himself] because he is nothing but time; and either one is unfaithful, time, because it is reversed categorically at such a moment, and beginning and end no longer rhyme [und Anfang und Ende sich in ihr schlechterdings nicht reimen läßt]; man because at this moment of categorical reversal he has to follow and thus can no longer resemble the beginning in what follows.41

At the moment of extreme suffering, Oedipus is left with the pure form of time, which is emptied of all meaningful content and announces neither punishment nor relief from the interminable, incessant suffering. As Hölderlin says in very Kantian terms, ‘there exists nothing but the conditions of time and space’.42 How are we to understand this claim? Beaufret exlains that after the turning-away of God, Oedipus has to face ‘the immensity of an empty heaven without ground. God is from then on no longer a father, a friend, not even an adversary to combat.’43 God is nothing but empty time. This is why man is ultimately thrown back on himself. But for Beaufret this means that he has to find the law in his own nature, to reconstitute himself on the basis of the moral nature of reason, in other words it is in Kant’s moral philosophy (the categorical imperative) that Beaufret finds the solution for man abandoned by God.44 Contrary to Beaufret, Deleuze draws a very different conclusion from the turning away of God. Man cannot be thrown back on himself because that self is shattered. Kant breaks time and therefore 233

conditions of thought: deleuze and transcendental ideas the self, but the Kantian moral philosophy is not the solution to this but its covering over. Hence Deleuze identifies Nietzsche rather than Kant as the philosopher who had the courage to face up to the consequences of the Kantian theory of time. The explosive moment opens the possibility of the dissolution of the self and the liberation from law and judgement imposed by the gods or human reason. The caesura marks this explosive moment, the final break-up, the appearance of the fracture or crack in the I. The story of Oedipus, then, goes as follows: Oedipus is trapped in the pure instant of time, ‘from which a past and a future will be produced on the straight line, which is to say a before and an after which no longer rhyme together’ (LK II, p. 4). Tiresias’ intervention has put before Oedipus the thought that he might not be the son of King Polybus of Corinth and his wife Merope who raised him. This is a thought which is almost impossible to think. All of the personal memories in which Oedipus has believed so far, together with his future expectations are eliminated, destroyed at a single blow. He can no longer be and resemble what he has been before. In fact, the caesura is not only a break in time, but also a split of Oedipus’ self. Oedipus is other to himself. He experiences this internal difference in the pure present, the ‘pureness’ of which signifies that it occurs like a cut. The series of former presents do not converge with this present moment. Deleuze compares Oedipus’ experience of splitting with that of Hamlet who, just like Oedipus, is brought to a state of internal difference with himself. Through the apparition of the ghost of his father, Hamlet learns that his father, King Hamlet, was murdered and he swears to exact revenge on the murderer, his uncle Claudius, who has meanwhile married Hamlet’s mother Queen Gertrude. However, Hamlet hesitates for a long time in his task of avenging the father. Only when he is sent on a sea voyage to England by Claudius, who conspires to have him killed on this journey, does Hamlet finally find himself capable of committing the act of vengeance. In projecting an ideal self, that is the future agent of the excessive act, Hamlet detaches himself from his past. The time at which the imagined act appeared to be ‘too big’ is gone. In both cases Oedipus and Hamlet, Deleuze recognises an a priori order of time, determined by the caesura. The caesura must be understood ‘in the image of a unique and tremendous event, an act which is adequate to time as a whole’ (DR 89/120). This excessive act, which draws together a ‘before the act’ and an ‘after the act’ and thereby the totality of time, can symbolically be expressed in many 234

Time and the Split Subject ways: ‘to throw time out of joint, to make the sun explode, to throw oneself into the volcano, to kill God or the father’ (DR 89/120). The symbolic act of killing God recalls Nietzsche’s famous description in The Gay Science. We have killed him – you and I! We are all his murderers. But how did we do this? How were we able to drink up the sea? Who gave us the sponge to wipe away the entire horizon? What were we doing when we unchained this earth from its sun? Where is it moving to now? Where are we moving to? Away from all suns? Are we not continually falling? And backwards, sidewards, forwards, in all directions? Is there still an up and down? Aren’t we straying as though through an infinite nothing? Isn’t empty space breathing at us? Hasn’t it got colder? Isn’t night and more night coming again and again? Don’t lanterns have to be lit in the morning? Do we still hear nothing of the noise of the gravediggers who are burying God? Do we still smell nothing of the divine ­decomposition?45

Nietzsche’s madman goes on to ask: ‘Is the magnitude of this deed not too great for us?’46 When he only encounters silence and incomprehension from the crowd of atheists in the marketplace, he concludes that, indeed, the excessive act of killing God is too big for us, the ‘tremendous event’ has not yet reached the eyes and ears of men. Speaking philosophically, the event has not yet become effective. The moment the event does become effective, it will destroy the subject. The traditional subject, whose identity is guaranteed by God, will be dissolved. Deleuze equates the excessive act, in whatever image it may be ­symbolised, with the caesura which clearly separates a before and an after. Thus the past is defined a priori as the before, that is the time where one is not yet capable of the act. The pure present, which refers to the caesura itself, is ‘the present of metamorphosis, a becoming-equal to the act and a doubling of the self, and the projection of an ideal self in the image of the act (this is marked by Hamlet’s sea voyage and by the outcome of Oedipus’s enquiry: the hero becomes “capable” of the act)’ (DR 89/121). Deleuze remarks that it matters little whether the act has been actually performed or not – ‘Oedipus has already carried out the act, Hamlet has not yet done so’ (DR 89/121). In the case of Nietzsche’s aphorism §125, the madman accuses mankind of having already murdered God (God ‘has bled to death under our knives: who will wipe this blood from us?’), although the people are not conscious of it (‘This deed is still more remote to them than the remotest stars – and yet they have 235

conditions of thought: deleuze and transcendental ideas done it themselves!’).47 In the end, the empirical incarnation of the symbolic act does not count. It is not the empirical content of time that distributes past, present and future. The order of time is a priori determined: the past is the time before the caesura; the pure present is the becoming equal to the act and the experience of internal difference (between the past self and the ideal self in the image of the act); finally, the future is the time after the caesura. The future marks the time when the excessive act turns back against the subject, destroying its identity and dispersing it in a discrete multiplicity of little selves, of egos with many names or, what amounts to the same thing, a universal ego with no name at all (cf. DR 90/121). The theme of the dissolution of the identity of the self in favour of a system of little selves, of the man with no name and no qualities, the universal people or of diverse ‘becomings’ (becoming-plant, ­becoming-woman, ­becoming-animal, becoming-child, becoming-molecule, becomingother, becoming-imperceptible, etc.) is often repeated in Deleuze’s œuvre.48 We will come back to this point later in relation to Nietzsche and Klossowski. Dedekind’s Cut Deleuze reaches for a new conception of time, an ordeal time ‘which ceases to be cardinal and becomes ordinal, a pure order of time’ (DR 88/120). According to this new conception, time is no longer empirically determined by means of the changes that occur, the events that take place within it or the periodical movements of planets that pass through cardinal points. Instead, time is a priori determined by means of the ‘caesura’ which distributes unequally on both sides the before and the after. The future and the past here are not empirical and dynamic determinations of time: they are formal and fixed characteristics which follow a priori from the order of time, as though they comprised a static synthesis of time. The synthesis is necessarily static, since time is no longer subordinated to movement; time is the most radical form of change, but the form of change does not change. (DR 89/120)

The idea of the form of time, which does not change itself, is clearly a Kantian thought. Repeatedly, Kant says in the Critique of Pure Reason that ‘time itself does not alter, but only something that is within time’ (CPR A 41/B 58).49 But is it true that Deleuze still adheres to the traditional philosophical conception of form?50 236

Time and the Split Subject Deleuze’s remarks on a ‘static synthesis’ should make us suspect that Deleuze is not simply repeating Kant’s theory here. Equally, the idea of a ‘caesura’, which constitutes a serial and linear time by distributing a before and an after, indicates a source other than Kant. For sure, Deleuze deduces the term ‘caesura’ first and foremost from Greek drama theory, but in his lecture course on Kant of 21 March 1978, he does not hesitate to compare it to the mathematical terms ‘limit’ and ‘cut’ (coupure).51 Moreover, the word ‘caesura’ derives from the Latin root ‘caes’ and can thus be rendered as ‘cut’. For these reasons, we suggest that the ‘caesura’ can be understood by means of the concept of ‘cut’ in Dedekind’s theory of real numbers, which Deleuze discusses in Chapter Four of Difference and Repetition in the context of the continuousness of Ideas (DR 172/223). The mathematician Richard Dedekind (1831–1916) is famous for giving a rigorous arithmetical foundation to differential calculus, and thereby expunging from calculus undefined geometric concepts such as ‘infinitesimal’ quantities and the limit concept involving the idea of approaching.52 Deleuze acknowledges his achievements, in particular the renewed conception of limit: ‘The limit no longer presupposes the ideas of a continuous variable and infinite approximation. On the contrary, the notion of limit grounds a new, static and purely ideal definition of continuity’ (DR 172/223).53 Indeed, it can be argued that Dedekind invents this new ‘static and purely ideal’ conception of continuity. His thoughts on continuity were first published in the pioneering essay ‘Stetigkeit und irrationale Zahlen’ (‘Continuity and Irrational Numbers’) in 1872, fourteen years after he developed the basic ideas on which it relies. The main question the essay deals with is: what is the nature of continuity? As Dedekind states: An explanation of this continuity is nowhere given; even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but [. . .] they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never ­established in a purely arithmetic manner.54

That is, the notion of continuity was either geometrically explained as a vague hang-togetherness, an ‘unbroken connection in the smallest parts’,55 or was based on insufficiently founded theorems, such as that every magnitude which grows continually, but not beyond all limits, must certainly approach a limiting value. Dedekind set himself the task of securing a real definition of the essence of continuity. 237

conditions of thought: deleuze and transcendental ideas He first approached the problem by trying to ‘map’ the geometrical continuum (the straight line) onto ordered systems of discrete quantities (numbers). Comparing the system of rational numbers with the points of the straight line, he saw that they cannot be put into a one-to-one-correspondence with each other: Although each rational number can be correlated with a point on the line, not every point of the line can be expressed as a rational number. In fact, in the straight line there are infinitely many points which correspond to no rational number. To identify these points, which are inexpressible as rational numbers, Dedekind used a method of division: the Dedekind ‘cuts’ (Schnitte). Any cut divides the points of the line into two classes, such that all the points of one class are always to the left of all the points of the other. Furthermore, there is precisely one and only one point determined by this cut. The cut can correspond to a rational number or else designate a ‘gap’ between the rational numbers, that is an irrational quantity (such as √2). In the latter case, cuts define a new type of number, i.e. the irrational numbers. Dedekind made use of geometrical considerations in order to introduce the notion of the cut. However, he sought to define cuts directly in terms of the number system, so that any reflections on geometric lines can be put aside. As Robert Bunn says: Geometry was to serve only as the source of the idea for constructing an arithmetical foundation. The continuous system which was to be Dedekind’s foundation would be arithmetical in the sense that its operations would ultimately be defined in terms of operations on natural numbers, and no mention would be made of any geometrical objects.56

Dedekind demanded that the system of rational numbers be improved by ‘the creation of new numbers such that the domain of numbers shall gain the same completeness, or as we may say at once, the same continuity, as the straight line’.57 As it is, the system of rational numbers is marked by a certain incompleteness or discontinuity, due to the existence of gaps. Thus, in order to render the domain of rational numbers into a continuous system, Dedekind defined for each cut that is not produced by a rational number a ‘new object’ which he called an irrational number. Thus √2 can be defined as the cut between two classes A and B, where A contains all those numbers whose squares are less than two and B those whose squares are greater than two.58 It should be noted that Dedekind does not identify irrational numbers with cuts, since every definite cut produces either a definite 238

Time and the Split Subject rational or irrational number. Rather, Dedekind cuts constitute ‘the next genus of numbers’ (DR 172/223), namely ‘real numbers’.59 The new genus of real numbers allows the treatment of both rational and irrational numbers as elements in an encompassing number system, which forms a continuous and ordered system. It has to be emphasised that this continuity of the number system is something quite different from the traditional conception of continuity founded on the intuition of the way in which geometric quantities arise: according to an intuitive conception of continuity, a line is considered continuous insofar as it arises from the continuous movement of a point, and a plane from the movement of a line. By contrast, Dedekind’s new conception of continuity claims not to rely on intuition, or any considerations of smooth movement. It claims to contain nothing empirical, since it can be deduced from number systems only. In a way, Dedekind’s project of arithmetising the conception of continuity is grounded on an Idea of reason: the Idea of an infinite, ordered and dense set of numbers each of which can in principle be identified by a Dedekind cut.60 According to Bunn, Dedekind’s ‘continuity’ can better be described as the property of the ‘completeness’ that characterises certain densely ordered number systems.61 Bunn remarks that ‘the term “continuous” is not an especially apt one for the characteristic involved, but it indicated the correlate in the old system – ­continuous magnitude.’62 Boyer explains that the notion of continuity ‘specifies only an infinite, discrete multiplicity of elements, satisfying certain conditions – that the set be ordered, dense, and perfect’.63 He goes on to argue that that there is ‘nothing dynamic in the idea of continuity’.64 As Deleuze says, we gain ‘a new, static and purely ideal definition of continuity’ (DR 172/223), which is grounded on the Dedekind cut, inasmuch as it constitutes this new continuous and ordered system of real numbers. Deleuze also calls the Dedekind cuts the ‘ideal cause of continuity’ (DR 172/223). Now the question to ask is: in what way does Deleuze benefit from Dedekind’s theory of cuts and the new notion of continuity that designates not a ‘vague hang-togetherness’ but rather an infinite, discrete multiplicity of elements whose order is a priori determined? Deleuze uses Dedekind’s ideas in order to construct a time that is not empirically defined through our intuition of a dynamic flux of events, but one that is determined a priori and designates a static state of affairs. This latter time is a ‘static synthesis’ of divergent series of times (series of the past, the enduring interval of the present and future 239

conditions of thought: deleuze and transcendental ideas becomings) which are distributed by the caesura, i.e. ‘a genuine cut [coupure]’ (DR 172/223), into a before and an after. The caesura or cut is constitutive of this ordered system of time which maps onto the straight line. Thus Deleuze transforms the Kantian definition of a purely formal time by means of mathematical considerations of the notion of ‘cut’ and ‘static synthesis’. For Deleuze, the third synthesis of time is not simply an a priori subjective form, but an a priori and a-subjective static synthesis of a multiplicity of series of times. However, it should be noted that Deleuze’s account of serial time as a straight line is not as straightforward as it appears. Deleuze does indeed make use of the Dedekind cut and the idea that it constitutes a static continuum, yet he takes licence in modifying Dedekind in a way that is not Dedekindian at all. The way that Deleuze conceives the series of time retains the idea of the irrational cut designating a ‘gap’. In Difference and Repetition, Deleuze says that ‘the irrational numbers [. . .] differ in kind from the terms of the series of rational numbers’ (DR 172/224). They are ‘constructed on the basis of an essential inequality’ in relation to the next-lowest type of numbers, i.e. the rational numbers. That is to say, they express the ‘impossibility of determining a common aliquot part for two quantities, and thus the impossibility of reducing their relation to even a fractional number’ (DR 232/299). However, they compensate for their characteristic inequality by their ‘limit-equality indicated by a convergent series of rational numbers’ (DR 232/299). Here, Deleuze seems to borrow again from Dedekind, who considered irrationals as limits of convergent series of rationals. Now the interesting move by Deleuze is to ascribe an original intensive nature to irrationals, an implication of difference or inequality, which is cancelled or covered over as soon as they are constructed as elements of an extensive plane of rational numbers. In fact, Deleuze holds that an intensive nature belongs to every type of number, insofar as they are not explicated, developed and equalised in an extensity. Every number is originally intensive and vectorial in so far as it implies a difference of quantity which cannot properly be cancelled, but extensive and scalar in so far as it cancels this difference on another plane that it creates and on which it is explicated. (DR 232/299–300)

Deleuze’s reflections on the nature of irrationals show that he regards the number line as a fiction, a spatial image which covers over an intensive depth. The straight line of rational points is but ‘a false infinity, a simple undefinite that includes an infinity of lacunae; 240

Time and the Split Subject that is why the continuous is a labyrinth that cannot be represented by a straight line’ (FLB 17). We have already come across Borges’ labyrinth of the straight line. Thus it seems that Deleuze, when he speaks of a line of time, does not mean a simple straight line, but one that is perforated by lacunae.65 These lacunae or gaps are precisely designated by the irrational cut, that is the interstice between series of rational numbers. They symbolise the irruption of the virtual event within the empirical continuum of space and the chronological ­succession of instants. Deleuze is thus not faithful to Dedekind, but he uses Dedekind’s mathematical notion of the cut and the static continuum in order to get rid of empirical representations of time. We believe that Deleuze’s recourse to the Dedekind cut can serve as a response to the question that James Williams has raised in his recently published book on Deleuze’s philosophy of time. Considering Deleuze’s references to examples and vocabulary from drama to introduce and explain the third synthesis of time, Williams wonders how Deleuze can claim ‘that the third synthesis involves a formal cut, when in fact it is deduced from a somewhat narrow dramatic event (the appearance of a ghost to the Prince of Denmark)’.66 Williams states that the dramatic event has to be defined formally as a cut that assembles what comes to either side of it, but he does not make any reference to Dedekind cuts. He also rightly insists that Deleuze’s third synthesis of time is a priori and not dependent on empirical observation. We suggest that Dedekind’s theory of static continuity and his method of cuts helps to explain Deleuze’s a priori and ordinal definition of time, which is a point of intersection of various heterogeneous theories. Deleuze does not shy away from bringing together Kant’s empty form of time with Hölderlin’s caesura and Dedekind’s cuts. It is important to note that Deleuze’s method of mixing theoretical concepts is not to be conceived in terms of assimilating differences and blending one concept into the other. Rather Deleuze maintains their heterogeneity and relates them to one another as differences. It can be regarded as a technique of montage operating by cuts commonly used in cinema.67 In Deleuze’s final co-authored work with Guattari, What Is Philosophy?, this method of montage is called ‘thought as heterogenesis’ (WP 199/188). The authors do not deny that the different disciplines that are brought together are distinct with regard to their objects, methods and ‘modes of enunciation’ (WP 127/121) – thus, philosophy creates concepts, art erects blocs of 241

conditions of thought: deleuze and transcendental ideas sensation, and science constructs functions – and that none of them is superior to the other from the point of view of thought or creation.68 However, the respective fields of creation can intersect and establish a ‘rich tissue of correspondences’ (WP 199/188). Deleuze and Guattari are aware of the dangers threatening this method of ‘thought as heterogenesis’: for example, in doing philosophy one could be mistakenly regarded as trying to do science or art, or to employ scientific concepts as mere examples or metaphors. Nevertheless, speaking from the point of view of philosophy only, the authors claim that philosophy has a fundamental need for these encounters with other disciplines (cf. WP 162/153). Events in science and art can provoke new problems in philosophy. In fact, philosophical concepts frequently involve references to science and to art, which is not to say that philosophy inevitably becomes a positivist theory of science or a kind of poetical thought. According to Deleuze and Guattari, philosophy has its own specific task: it creates concepts and brings forth events. However, the components of concepts can incorporate heterogeneous elements from other fields of creation and thus further and enrich the development of the new. ‘Thought as heterogenesis’ means a becoming-other (hetero) of thought, and it does so as a response and resistance to the repressive function of an academic philosophy that buries its young generation under the volumes of the history of philosophy and excludes any lateral encounters.69 Philosophy is not simply an academic discipline, but a power that challenges us to think differently and to create new problems. Deleuze’s theory of time is a particularly telling example of this method of thought as heterogenesis: it exhibits a great variety and heterogeneity of elements demanding much openness and effort on the part of the reader. However, if one is willing to go on this journey, one is rewarded with stunning new thoughts or at least problems that can incite new investigations.

Nietzsche’s Eternal Return As it has been shown, Deleuze’s third synthesis of time is profoundly linked to the notion of a fractured I, and thus takes as its point of departure Kant’s empirico-transcendental subject, split by the empty form of time. However, the Kantian subject of the first Critique is after all a subject of knowing. It strives for the reproduction of representations that can count as knowledge. It is itself the source of representations: the transcendental I affects the passive empirical 242

Time and the Split Subject self through the interior form of time. The Kantian transcendental conditions are conditions of knowledge qua representation. Deleuze, on the contrary, searches for conditions under which something new is produced: a new thought, a new work, a political act, even a new subject. It is in the direction of Nietzsche that we must look in order to specify the transcendental conditions of creative production. The answer lies in Nietzsche’s thought of the eternal return. It should be noted that Nietzsche never fully laid out his thought of the eternal return in his writings and that the existing interpretations in secondary literature vary to a great extent. What interests us here is solely Deleuze’s reconstruction of the eternal return, which is considerably influenced, as we will see, by Pierre Klossowski’s reading of Nietzsche.70 According to Deleuze, the thought of the eternal return is not to be understood as a return of the Same or the Similar. Rather, what passes the test of the eternal return is that which differs internally, simulacra or the dissolved self. The eternal return has to be seen as a test of selection, which banishes identity, that is the identity of God, the identity of the world or the represented object, and the coherence of the self. However, it is important to note that the eternal return does not only have a destructive or lethal impact, rather it manifests a positive and productive power. Thus the subject, which succumbs to the power of eternal return, is carried to a point of metamorphosis, when all its possibilities of becoming are set free. To illustrate this fact, Deleuze quotes from Henry Miller’s book on Rimbaud: ‘I realised that I was free, that the death I had gone through had liberated me’ (DR 19/30).71 Hence the landscape of the eternal return is that of difference-in-itself, the disparate, the irreducibly unequal, and also that of metamorphosis, chance, multiplicity and becoming. In Deleuze’s words: Essentially, the unequal, the different is the true rationale for the eternal return. It is because nothing is equal, or the same, that ‘it’ comes back. In other words, the eternal return is predicated only of becoming and the multiple. It is the law of a world without being, without unity, without identity.72

Therefore, in a first move, it is important to distinguish Nietzsche’s eternal return from the conception of a ‘return of the Same and the Similar’ which is the essence of a cyclical conception of time. Thus the ancient Greeks presupposed an identity or resemblance in general of all the instances that are supposed to recur. They regarded the 243

conditions of thought: deleuze and transcendental ideas recurrence of planetary motion, the uniform change of seasons and qualitative changes in things as laws of nature. According to Deleuze, Nietzsche’s thought of the eternal return cannot be presented as a natural law and identified with the ancient Greek hypothesis of cyclical time.73 First, he argues that as a connoisseur of the Greeks, Nietzsche could not have been ignorant of the Greek hypothesis of time as a cycle. Thus when Nietzsche insists that his thought of the eternal return is something effectively new, we have to take him seriously. Furthermore, Nietzsche is a thinker who is very much opposed to the notion of law. He would not have submitted to the simple notion of a law of nature. As textual evidence, one can adduce two passages in Zarathustra, where Nietzsche explicitly rejects the interpretation of the eternal return as cyclical time: (1) During the  encounter between Zarathustra and the dwarf, the dwarf says ‘All truth is crooked; time itself is a circle’, whereupon Zarathustra replies ‘Thou spirit of gravity! [. . .] do not take it too lightly’.74 (2) On another occasion, Zarathustra rebukes his animals that they have already made a ‘refrain’ out of his doctrine of the eternal return. In a refrain, the same always returns, but apparently Zarathustra does not want the eternal return be understood as a refrain.75 In what way then is the eternal return different from a natural cycle, a cycle of time? The crucial issue is that the eternal return is selective and creative. It is selective with regard to desires or thought and with regard to being. Let us first consider its mechanism of selection with regard to desires. If the doctrine of the eternal return is stated in terms of an ethical rule, it becomes a sort of Kantian imperative: ‘Whatever you will, you have to will it in such a way that you will its eternal return.’ That which is expelled by the selection test of the eternal return are all instances of willing that want a thing ‘only this one time’. In an unpublished note contemporaneous with The Gay Science, Nietzsche says that it does not matter whether the act I am about to perform is informed by ambition, or laziness, or obedience, if only I re-will my present action again, innumerable times.76 The eternal return excludes any half-hearted willing and affirms the extreme forms. It separates an active, superior will, which wants to enact its force to its highest power, from a reactive, gregarious will. Moreover, the eternal return not only excludes any ‘half-desires’, but also any reactive mode of being (such as the passive small man or last man possessed by a will to revenge). Furthermore, it is necessary to note that the superior forms of willing and being do not simply ­pre-exist the eternal return, but are created by the eternal return. 244

Time and the Split Subject The eternal return creates the superior forms. It is in this sense that the eternal return is the instrument and the expression of the will to power: it raises each thing to its superior form, that is, its nth power.77

The eternal return is thus the accomplice of the will to power. Both the will to power and the eternal return are in effect the transcendental conditions for the creation of something new, that is of superior forms that pass the test of eternal return. These superior forms are what Nietzsche refers to with his concept of ‘overman’: ‘The Overman is defined as the superior form of everything that “is” ’ (DR 41/60). But how can we understand this very vague concept of the overman? As Deleuze explains: The overman very much resembles the poet as Rimbaud defines it: one who is ‘loaded with humanity, even with animals,’ and who in every case has retained only the superior form, and the extreme power.78

Elements of the overman can thus be found in the artist, the poet – or as we might say, someone who is willing to undergo metamorphoses and to become-other in favour of an act or a work yet to come. What role exactly does the eternal return play here? According to Deleuze, the eternal return is a power of repetition, which is a truly genetic, creative force. We produce something new only on condition that we repeat – once in the mode which constitutes the past, and once more in the present of metamorphosis. Moreover, what is produced, the absolutely new itself, is in turn nothing but repetition, the third repetition, this time by excess, the repetition of the future as eternal return. (DR 90/121)

For Deleuze, repetition is a condition of action and of creation. He cites as an example the French revolutionaries who identified themselves with Romans, wearing tunic skirts and venerating Roman values. However, these ‘resuscitated Romans’ were not simply ‘representations’ of the original Romans, but actors themselves that have become capable of the revolutionary act under the condition of repetition. At this point it might be helpful to briefly explain Deleuze’s distinction between a material and bare repetition (répétition materielle et nue) and a spiritual and clothed repetition (­répétition spirituelle et vêtue). Bare repetition is defined as a repetition of the same, that is the recurrence of identical elements. It is based on the model of representation according to which Being is distributed in determinable forms (genera of Being or categories), fixed determinations (specific 245

conditions of thought: deleuze and transcendental ideas or individual differences) and determined objects (individuals). Thus, at the sight of several red objects, we can speak of the recurrence of instances of red and subsume these particular instances under a common genus, the colour red. A material or bare repetition is based on generality or universal concepts that subsume particulars. These particulars are in principle exchangeable: one particular may be substituted for another. Hence the bare repetition may involve many instances, but all of these instances point beyond themselves to a common genus (the One or the Same). Material or bare repetition belongs to the order of laws, as we can see from the important role that bare repetition plays in scientific experiments. There the ­repetition of particulars is explained as instances of a natural law. By contrast, spiritual or clothed repetition ‘is against the law: against the similar form and the equivalent content of law’ (DR 2/9). Repetition in this second sense never has to do with generality. It does not deal with particulars that are equivalent in one way or another, but operates on non-exchangeable and non-substitutable singularities. We have already come across this type of repetition, when we discussed the Platonic world of simulacra, of false pretenders and masks. Deleuze sustains a ‘reversed Platonism’ that overturns the Platonic hierarchy of the original or model followed by the copy followed by the simulacrum (cf. DR 126–8/165–8). There is no original: ‘The masks do not hide anything except other masks. There is no first term which is repeated’ (DR 17/28). The clothed repetition denounces any principle or law, in favour, as Deleuze says, ‘of a more profound and more artistic reality’ (DR 3/9). It is in art, for example in theatre, that the deeper reality comes to the surface. In this sense, Deleuze says, ‘history is theatre’ (DR 91/123) and the French revolutionaries are mimes or actors. This idea of theatre resonates with a similar thought that Nietzsche presents in The Gay Science, when he reflects on the ‘problem of the actor’: Falseness with a good conscience; the delight in pretence erupting as a power that pushes aside, floods, and at times extinguishes one’s co-called ‘character’; the inner longing for a role and mask, for an appearance (Schein); an excess of capacities for all kinds of adaptation that can no longer be satisfied in the service of the nearest, most narrowly construed utility – perhaps all of this is distinctive not only of the actor?79

Nietzsche suggests that the actor manifests a power, the power of the false, which is more fundamental than being simply an expression of his profession. This power carries with it a desire for masks 246

Time and the Split Subject and disguise that can even be found among animals in the disposition of ‘mimicry’. This power is so strong that its eruption threatens and destroys the so-called character of a living being. It challenges all the categories and values which are so dear to our scientific and rational world: the identity of a thing, its determinability, its lawfulness and truth. Instead of a will to truth, this obscure power shows a ‘falseness with a good conscience’, a ‘delight in pretence’, an ‘inner longing for a role and mask, for an appearance [Schein]’. This ‘parodic’ power, which sets free metamorphoses and masks, is what Deleuze identifies with Nietzschean repetition, that is to say the thought of the eternal return. This is why he says that Nietzsche is ‘deeply theatrical’: Nietzsche ‘brought theatre into philosophy itself’.80 The philosophical doctrine of the eternal return (i.e. the return of that which differs, of difference-in-itself) is precisely what undermines the privilege of identity and the model of representation. ‘The eternal return affirms difference, it affirms dissemblance and disparateness, chance, multiplicity and becoming’ (DR 300/383). Repelling any identity, the wheel of the eternal return means the death of the one and only God. And as God is dead, this means that the judge supporting the identity of the subject disappears and so the subject dissolves. As Deleuze says, ‘the eternal return concerns only simulacra, it causes only such phantasms to return’ (DR 126/165). It thus becomes clear that the eternal return is more than a ‘theoretical representation’ (DR 41/60) or ethical rule to be made a self-chosen principle of life. Rather it is a positive principle, ‘the royal repetition’ (DR 94/125), that actively creates the superior forms that pass the test of eternal return. In his book Nietzsche and the Vicious Circle, Pierre Klossowski shows how the thought of the eternal return itself enacts this selective and creative power. According to Klossowski’s analysis, the thought of the eternal return jeopardises the subject’s identity; it is an aggression against the apparently limited and closed whole of the subject. The reason for this is that the thought of the eternal return demands that I re-will myself again innumerable times, but this demand makes me at the same time fall into incoherence. In relation to the codes of everyday society, I am a particular identifiable individual, once and for all determined by laws, contractual relations and institutions. The thought of the eternal return addresses me but at the same time demands my destruction as this particular identifiable individual. This is so because I have to re-will all my prior ­possibilities of being: 247

conditions of thought: deleuze and transcendental ideas All that remains, then, is for me to re-will myself, no longer as the outcome of these prior possibilities, no longer as one realization among thousands, but as a fortuitous moment whose very fortuity implies the necessity of the integral return of the whole series.81 I deactualize my present self in order to will myself in all the other selves whose entire series must be passed through.82

Thus the eternal return does not demand that I return the same as I am, ‘once and for all’ (this would amount to a ‘bare repetition’ in Deleuzian terms), but as a variation, a simulacrum, for an infinite number of times (this would be a repetition ‘by excess, the repetition of the future as eternal return’, DR 90/122). The coherence of the subject is thus jeopardised. Nietzsche himself suffered the consequences of the thought of the eternal return: ‘I am every name in history’,83 ‘Dionysus and the Crucified’.84 In Deleuze’s reading, which coincides with Klossowski’s interpretation in this regard, ‘the thinker, undoubtedly the thinker of the eternal return, is [. . .] the universal individual’ (DR 254/327). For Deleuze, the universal individual or the ‘man without a name’ (DR 91/122) designates someone who has relinquished the well-defined identity of the subject with fixed boundaries, and affirmed the system of a dissolved self with all its processes of becoming. What the self has become equal to is the unequal in itself. In this manner, the I which is fractured according to the order of time and the Self which is divided according to the temporal series correspond and find a common descendant in the man without name, without family, without qualities, without self or I, the ‘plebeian’ guardian of a secret, the already-Overman whose scattered members gravitate around the sublime image. (DR 90/121)

The universal individual or man without name is thus to be understood  as Nietzsche’s overman. The overman is not another higher species of man, but a non-identical, a dissolved self, which is ­liberated from the judgement of God and open to intensive processes of becoming. Interpretations that regard the overman as ‘an evolutionary product, rising higher, as man does relative to the worm, to some indeterminate evolutionary height from which he can look back, amused, at that from which he came’,85 treat the overman as someone beyond man, a higher species that is not yet present, while in our view Deleuze’s reading rather suggests that the overman is someone who is always beyond himself, that is never identical with himself, and who allows for all possibilities of becoming, as Klossowski says, becoming 248

Time and the Split Subject stone, becoming plant, becoming animal, becoming star.86 Deleuze takes up this thought and states that the thinker of the eternal return ‘is laden with stones and diamonds, plants “and even animals” ’ (DR 254/327).87 We have seen that examples of the overman are the poet or the artist – another suitable example might be the political subject, someone who exposes himself to the public and engages in processes that not only demand a becoming-other, that is an annihilation of the past self that he or she was, but that also put the existence of a future self at risk and thus leave the process of becoming open to success or failure. The ancient rhetorical practice of parrhesia can serve as an example here: parrhesia can be translated as ‘the telling of the unvarnished truth’ and specifies a type of discourse in which the speaker commits himself to a free and unbound speech and in doing this puts himself at considerable risk, including the risk of death.88 The parrhesiast or ‘truth-teller’ cannot be defined in terms of a selfauthoring subject, but must be understood as a split subject: through his words he constitutes himself as the one who speaks freely and who is willing to pay for it with his life. He forsakes the identity and securities of his past self, and projects an ideal future self that would find the approval of his listeners, but his project might just as well end in failure. All these examples, the poet or artist and the political subject (e.g. the parrhesiast) can be seen as instantiations of a dissolved self, or the overman in Nietzschean terms. Thus the overman is a real possibility or even a present reality, if one thinks the thought of the eternal return and wills oneself through the entire series of all the other selves, that is affirms all possibilities of becoming. What is expelled by the wheel of eternal return and its centrifugal force is only that which desperately clings to its identity. In his recent book Deleuze’s Philosophy of Time, James Williams expresses ‘worries about the human- and subject-centred properties of Deleuze’s account of the third synthesis of time’, which seem to be present in Deleuze’s formula that the image of the excessive act, i.e. the caesura constituting the third synthesis of time, appears ‘too great for me’. He continues that we can avoid this existentialism ‘once we realise that the image applies to any novel process, for instance, when a virus mutates and achieves something “too great for it”, or when pressures on rocks transform an organic layer caught between them into something new’.89 One reason that he gives for linking the third synthesis of time with any process of creation and not only with 249

conditions of thought: deleuze and transcendental ideas human creativity (of the artist, the thinker or the political subject) is his fear of a psychological explanation of time, according to which time is constituted by human imagination. Thus Williams argues: First, the focus on human imagination and particular instances of drama fits very uneasily with Deleuze’s points about an a priori definition. If the past or before was determined each time in the imagination, then we would be dealing with an empirical psychological test; [. . .] Second, psychological explanation is avoided at every turn in Difference and Repetition because it fails to grasp the importance of habit and extramental processes [. . .] Third, Deleuze uses the term image in a technical manner, partly indebted to Bergson. For Deleuze, the notion of image is not one of a mental image, but rather one of a reductive yet necessary process of assembly.90

We agree that Deleuze abandons psychological explanations on the whole; time, for him, is certainly not a synthetic product of the human faculty of imagination (as Heidegger conceives it in his book Kant and the Problem of Metaphysics). Neither can the third synthesis of time be exclusively derived from elements of Greek myth or drama theory, such as Hölderlin’s notion of the caesura. For this reason we took recourse to a mathematical explanation: time as a static synthesis of discrete elements (past and future moments), distributed by a cut (the pure present, or time of the event) in a before and after. It is difficult to see how Williams’ examples of the mutation of a virus or the transformation of organic layers through the pressure of rocks help to attain an a priori definition of time, since they describe empirical (though extra-mental) processes. Let us consider Williams’ last point of critique, namely that the symbolic image of the excessive act (the murder of God, for example) is not simply a mental image. Certainly, the symbolic falls outside the psychoanalytical, binary model of the real and the imaginary and instead constitutes a new order.91 This new order Deleuze will later call – no longer an order of the symbolic (which is still too much Lacanian) – but the order of the virtual or virtual events. Thus we understand the ‘caesura’ or ‘cut’, constituting the third synthesis of time, as the moment when the virtual event breaks into the chronological and empirical order of time. Nietzsche’s death of God and the dissolution of the self is just one such virtual event that becomes manifest in philosophy, in Nietzsche’s life itself and possibly in the life of any other person capable of becoming equal to the event. We certainly do bestow an existentialist dimension to the third synthesis 250

Time and the Split Subject of time and we see no reason why we should not, since Deleuze insists on its disruptive impact on the identity of the subject and its liberating power with regard to all prior possibilities of life. As we see it, Deleuze’s three syntheses of time offer an explanation of the formation of the subject, that is its various habits, practices, agency, memory and creativity. It is important to emphasise, however, that the subject or rather subjective structures are something that emerge, transform, dissolve and are always renewed through the temporal syntheses. Thus we should not presuppose a prior identity of the subject, which then happens to become destroyed in the third synthesis of time. Rather, the discourse on the identity of the subject is part of the dogmatic Image of thought, a cultural machine that produces the illusion of the identical subject and thereby constrains our thinking, feeling and acting. If we follow Deleuze, we always have to do so with fractured subjects, which more or less cling to the traditional notions of identity, agency, free will and so on. With Nietzsche’s words, we can distinguish between noble and base ways of being, that is modes of being that affirm difference and becoming and those that are negative, reactive and conservative. Williams acknowledges that Deleuze’s third synthesis of time is deeply indebted to Nietzsche’s eternal return and to Klossowski’s reading of it. However, he sees a sharp difference between Deleuze and Klossowski: Klossowski introduces an element much harder to reconcile with Deleuze’s philosophy of time: reversibility (as opposed to Deleuze’s insistence on asymmetry). So for Klossowski it is the creative will itself that frees its acts from the past by willing reversibility – a willing incompatible with Deleuze’s account of time – whereas for Deleuze it is the passing of the same and eternal return of difference that accomplish [sic] this freedom without a necessary appeal to will or to affirmation (perhaps in contrast to Deleuze’s work on Nietzsche in Nietzsche and Philosophy).92

In our explanation of Deleuze’s reading of Nietzsche’s eternal return, the selective and creative power of the eternal return has been partly referred to the will and the power of affirmation. We said that the eternal return excluded any instances of half-hearted willing (willing something only this one time) and allowed only that to return which affirms becoming or becoming-other. It is true that for Klossowski this becoming means becoming all prior possibilities of being, in his words ‘to will myself in all the other selves whose entire series must be passed through’.93 But this ‘return of the whole series’ certainly 251

conditions of thought: deleuze and transcendental ideas does not mean a reversal of the order of time, a going back in time, but time as an eternally decentred circle (a ‘vicious circle’), which as Deleuze has shown is compatible with a purely formal, linear time constituted by a cut. ‘The form of time is there only for the revelation of the formless in the eternal return’ (DR 91/122). For us, the main difference between Klossowski and Deleuze lies not so much in the difference between the principle of reversibility or asymmetry with regard to their conception of time. We rather see one major difference in their respective notion of ‘sign’ and its function as a transcendental condition of thought. Let us begin with Klossowski’s notion of ‘sign’. In his essay, in which Klossowski spells out the import that the thought of the eternal return had for Nietzsche and in fact that it would have for anyone taking this thought seriously, he also reconstructs the mental state in which Nietzsche conceived the thought of the eternal return.94 According to this reconstruction, thought occurs like an event, it bursts into the mind as something from outside, a force or intensity which leaves the thinker no choice. As Nietzsche himself says: ‘Everything is in the highest degree involuntary’, a remark which resonates in many of Deleuze’s texts.95 The thinker is exposed to something that exercises an almost unbearable pressure and tension. According to Nietzsche’s description in Ecce Homo a thought flashes up like lightning, with necessity, unfalteringly formed – I have never had any choice. An ecstasy whose tremendous tension sometimes discharges itself in a flood of tears, while one’s steps now involuntarily rush along, now involuntarily lag; a complete being outside of oneself with the distinct consciousness of a multitude of subtle shudders and trickles down to one’s toes; a depth of happiness in which the most painful and gloomy things appear, not as an antithesis, but as conditioned, demanded, as a necessary colour within such a superfluity of light.96

According to Klossowski’s analysis, it seems that Nietzsche himself experienced the thought of the eternal return as such an event. In a letter that Nietzsche sent to Peter Gast from Sils-Maria in August 1881, he gives a brief account of the moment when he conceived this thought, and this account matches exactly the description in Ecce Homo.97 Klossowski takes this letter as a cause to reflect upon the mysterious role of intensity as the material condition of thinking. First of all, Klossowski describes Nietzsche’s experience as a fluctuation of intensity that occurred all of a sudden in the midst of a hohe Stimmung, i.e. an elevated tonality of the soul. In order for it to be 252

Time and the Split Subject communicable and to acquire sense, the flow of intensity must turn back on itself and must take itself as an object. A sort of ‘intentionality’, an aiming of intensity at itself, is needed for the creation of sense: ‘For this, the intensity must divide, separate from itself, and come back together.’98 The flow of intensity, the interruption of flow, and a new afflux of intensity make up what Klossowski calls a ‘sign’. According to Klossowski’s analysis, Nietzsche’s experience when he first conceived the thought of the eternal return is to be characterised as such a rise and fall of intensity, i.e. the encounter with a ‘sign’. Klossowski attaches a great importance to the prior experience of the ‘sign’, treating it as a transcendental but material condition that first and foremost generates and constitutes thought. As Klossowski says: It is thanks to this sign, which nonetheless is nothing but an always-­ variable trace of a fluctuation, that we constitute ourselves as thinking, that a thought as such occurs to us – even though we are never quite sure if it is not others who are thinking and continue to think in us. But what is this other that forms the outside in relation to this inside we believe ourselves to be? Everything is led back to a single discourse, namely, to fluctuations of intensity that correspond to the thought of everyone and no one.99

Klossowski relates the ‘sign’ back to a kind of universal flow of intensity, a universal flow of thought that is prior to any segmentation into particular thinking subjects. Although we do not literally find this idea of a universal flow of intensity or thought in Nietzsche, he does write in one of his notebooks: A thought . . . comes up in me – where from? How? I simply don’t know. It comes, independently of my will, usually surrounded and obscured by a mass of feelings, desires, aversions, and also other thoughts . . . One pulls it [the thought] out of this mass, cleans it off, sets it on its feet, and then sees how it stands and how it walks – all of this in an astonishing presto and yet without any sense of hurry. Just who does all this – I have no idea, and I am surely more a spectator than originator of this process.100

In this quotation Nietzsche confirms that there is no ‘I think’ who is the author of thought, but that thought happens to the thinker independently from his will or wish. This is not to say that a particular thought or concept is given to him ready-made. As Nietzsche is careful to emphasise: one has to extract the concept or thought from a mass of feelings and other thoughts; one has to ‘clean’ it and ensure that it can stand upright. In this sense, thinking is both an ­involuntary and impersonal adventure and an act of creation. 253

conditions of thought: deleuze and transcendental ideas At first glance it seems that Deleuze completely aligns with Klossowski (and Nietzsche). In Difference and Repetition Deleuze describes how the encounter with something violent and formless, something beyond the grasp of common sense, creates an intensive impression which triggers a ‘forced movement’ of thought. This thought is not ‘my thought’ in the sense of a well-determined possession; it is rather a violent and involuntary adventure which challenges the categories of inner and outer, ‘I’ and the Other. He points to the dangers involved in thinking, in particular philosophical thought, and the shattering effect it has on the identity of the subject. He tells us that philosophical thought ought not to be related to a substantial, completed and well-constituted subject, such as the Cartesian Cogito; thought is, rather, one of those terrible movements which can be sustained only under the conditions of a larval subject. These systems admit only such subjects as these, since they alone can undertake the forced movement by becoming the patient of the dynamisms which express it. Even the philosopher is a larval subject of his own system. (DR 118/156)101

Thought is thus a ‘forced movement’ that carries the subject to the borders of the liveable, to the point which only larval subjects can support. The ‘larval’ or ‘embryonic subject’ in Deleuze designates those living beings able to tolerate extreme forces and spatio-­temporal dynamisms under which any skeletal system would break.102 It should be noted, however, that not only philosophical thought involves such ‘terrible movement’. On the contrary, Deleuze makes it clear that this might also be true of science and art.103 To conclude, there are certainly similarities between Klossowski’s and Deleuze’s account of the encounter with a ‘sign’ and the ‘forced movement of thought’, but we believe that Deleuze is much more specific than Klossowski in describing the nature of the ‘sign’. Although he does use ‘sign’ in terms of a sensuous, material impression or complex of intensive forces that sets off the forced movement of thought, he rather prefers the notion of differential Ideas-problems. It is problems or questions that force us to think, to liquefy rigid concepts, fixed representations or opinions and also affect our mode of existence. Thus, while Klossowski does not further examine the ‘sign’ and seems to be satisfied with relating it back to a kind of universal flow of intensity, Deleuze takes greater care to analyse this mysterious ‘sign’. As we have seen in Chapter 3, Deleuze elaborates a whole dialectic of Ideas. He also goes beyond 254

Time and the Split Subject the dimension of conditions of thought and considers extra-mental, differential processes of Ideas. Examples of differential Ideas that we already discussed concerned atomism as a physical Idea, the organism as a biological Idea and the socio-economic Idea (with recourse to Marx). In this sense, James Williams is certainly right if he points out that a kind of existentialist, human- or subject-centred reading of Deleuze’s syntheses of time and processes of differential production is reductive, and we need to keep this in mind when dealing with Deleuze. However, the aim of this book has been to narrow down a Deleuzian notion of transcendental conditions that act as a sufficient reason for the production of the new, that is a new thought, a new work, a new act, even a new subject or universal people yet to come. Nietzsche’s eternal return, at least in Deleuze’s understanding as a positive, selective and creative power of repetition, allows the generation of complete novelties. As we have seen, the eternal return is allied with the will to power understood as a differential structure of forces, or with Deleuze’s words as differential Ideas-problems forcing themselves upon those who are ready to welcome the event of thought. Both the will to power and the eternal return, or again in Deleuze’s words the powers of difference and repetition, signify an absence of ground or a ‘universal ungrounding’ from which emerges a world of simulacra or dissolved selves that make up the Deleuzian ‘subject’ of thought and creation.

Notes 1. The French word moi may be translated into English either as ‘ego’ or as ‘self’. Here, the passive, empirical nature of the Kantian subject (le moi passive) is rendered as ‘the passive self’ in contrast to the subject’s active, transcendental nature, which is referred to as ‘I’ (je). The translator Paul Patton maintains the translation ‘self’ for moi in all contexts except those where it is explicitly a question of psychoanalysis, in which case he has used ‘ego’ (cf. Translator’s Preface to DR, p. xiii). 2. Cf. Deleuze’s Lecture Course on Kant, 14 March 1978. See also Deleuze, ‘On four poetic formulas which might summarize the Kantian philosophy’, KCP vii–xiii. 3. Act I, scene v: ‘The time is out of joint: O cursed spite, / That ever I was born to set it right’ (in Shakespeare, Hamlet, p. 74). It should be noted that Hamlet explicitly says ‘the time is out of joint’ referring to a particular time, i.e. the time through which he is living. The French translation ‘le temps est hors de ses gonds’ [literally: ‘time is off its hinges’] is somewhat ambiguous because of the different way 255

conditions of thought: deleuze and transcendental ideas the definite article is used in French and English. The French phrase could be translated back into English as either ‘time is out of joint’ or ‘the time is out of joint’. The English translation of Difference and Repetition renders the French phrase into ‘time is out of joint’ (DR 88/119), thereby indicating the metaphysical import of time in general that Deleuze reads into this formula. According to Deleuze, time in general has become ‘demented time [temps affolé]’ (DR 88/119). This means that it has lost its balance, its groundedness, its stability: time has gone crazy. This meaning is preserved in the French phrase ‘le temps sort de ses gonds’ that Deleuze uses in the Lecture Course on Kant from 14 March 1978. (We are indebted to Nick Midgley for this clarification.) 4. See Wright, Cosmology in Antiquity, Chapters Three and Eight. 5. Aristotle, Aristotle’s Physics: Books III and IV, and Aristotle, On the heavens I & II; hereinafter the Latin De Caelo will stand for On the heavens. 6. Deleuze refers to Borges’ short story ‘Death and the Compass’ (1942). Having walked into the trap of the murderer Scharlach, detective Lönnrot tells him: ‘ “In your labyrinth there are three lines too many [. . .]. I know of one Greek labyrinth which is a single straight line. Along that line so many philosophers have lost themselves that a mere detective might well do so, too.” [. . .] “The next time I kill you,” replied Scharlach, “I promise you that labyrinth, consisting of a single line which is invisible [sic] and unceasing” ’ (Borges, Labyrinths, pp. 86–7). The English translation wrongly renders the Spanish ‘indivisible’ in the phrase ‘una sola línea recta y que es indivisible, incesante’ into English as ‘invisible’. 7. KCP viii–ix. See Rimbaud, Lettres du Voyant, pp. 113 and 135. 8. Cited in KCP ix. In fact, Deleuze contracts here two quotations by Rimbaud from different letters. See Rimbaud’s letter to Georges Izambard from 13 May 1871, p. 113, and his letter to Paul Demeny from 15 May 1871, p. 135. 9. See also CPR B 156: ‘Through inner sense we intuit ourselves only as we are internally affected by our selves, i.e., as far as inner intuition is concerned we cognize our own subject only as appearance but not in accordance with what it is in itself.’ 10. Leibniz says in his letter to Clarke of 25 February 1716: ‘I hold space to be something merely relative, as time is; [. . .] I hold it to be an order of coexistences, as time is an order of successions. For space denotes, in terms of possibility, an order of things which exist at the same time, considered as existing together; without enquiring into their manner of existing’ (in The Leibniz–Clarke Correspondence, pp. 25–6). 11. Cf. Kant, CPR B 67. 256

Time and the Split Subject 12. Williams, Gilles Deleuze’s Difference and Repetition, p. 15. 13. See, for instance, Hume, Enquiries concerning Human Understanding, p. 75: ‘This connexion, therefore, which we feel in the mind, this customary transition of the imagination from one object to its usual attendant, is the sentiment or impression from which we form the idea of power or necessary connexion.’ 14. Hume, Enquiries concerning Human Understanding, p. 75. Corresponding statements can also be found in Hume, A Treatise of Human Nature, pp. 93 and 156. 15. Hume rather speaks of a kind of affinity (‘some bond of union’, ‘some associating quality’) that prevails among simple ideas in the mind and exercises a ‘gentle force’ on the faculty of imagination; see Hume, A Treatise of Human Nature, p. 10. Deleuze’s interpretation of a ‘contractile power’ of the mind reminds one rather of Bergson, for whom the movements of contraction and expansion constitute different levels of our mental life. Bergson, in fact, criticises the theory of associationism for not being able to explain the mysterious attractions between individual, independent ideas; see Matter and Memory, pp. 212–17. 16. ‘For even the corn in the fields grows upon a superstitious basis as to its own existence, and only turns the earth and moisture into wheat through the conceit of its own ability to do so, without which faith it were powerless’ (in Butler, Life and Habit, p. 82). Cited in DR 75/102. 17. Cf. Bryant: ‘Transcendental empiricism reconciles the two halves of aesthetics (the theory of the sensible and the theory of beauty) insofar as it is able to explain how the being of the sensible allows for a genesis of experience (thus treating experience as an aesthetic production in the sense of artistic production), which in turns creates a domain of experience of the given (the aesthetic in the sense of sensible receptivity).’ See Bryant, Difference and Givenness, p. 64. 18. Proust, A la recherche du temps perdu, vol. III, p. 872. Deleuze takes up this formula of Proust in his second book on cinema – see CIT 79/110. 19. For Bergson’s two schemata of the cone, see Matter and Memory, pp. 127–8 and 211. 20. Bryant tries to steer a course between critical and speculative phil­ osophy, emphasising that ‘Deleuze cannot be easily described as either a speculative or a critical philosopher’ (Bryant, Difference and Givenness, p. 176). Yet, his interpretation of Deleuze (in particular, the Deleuzian notion of the transcendental field) unites so many Bergsonian characteristics that it is difficult to see how he can save Deleuze from the accusation of speculative dogmatism. 21. Bergson, Matter and Memory, p. 193. 257

conditions of thought: deleuze and transcendental ideas 22. Ibid., p. 175. 23. Ibid., pp. 173 and 179. 24. Ibid., p. 180: ‘Sensation is, in its essence, extended and localized; it is a source of movement; – pure memory, being inextensive and powerless, does not in any degree share the nature of sensation.’ See also p. 176. 25. See also B 59/54 and CIT 76–7/105–6. In reconstructing Bergson’s three paradoxes of time, Deleuze refers to Bergson, Matter and Memory, ch. III. 26. Bergson, Matter and Memory, p. 217. 27. Ibid., pp. 128–9. 28. Ibid., p. 171: ‘Whenever we are trying to recover a recollection, to call up some period of our history, we become conscious of an act sui generis by which we detach ourselves from the present in order to replace ourselves, first in the past in general, then in a certain region of the past – a work of adjustment, something like the focussing of a camera.’ 29. It should be noted that Deleuze extends this idea that art is able to create pure intensive impressions (affects and percepts) or blocs of sensation (sensation in itself) to other arts besides literature. As Deleuze makes clear in his book on Francis Bacon and his Cinema books, painting and film can equally capture intensive forces or the pure past in a ‘crystal image [image-cristal]’. See CIT 79/109. 30. In the same way, Sauvagnargues argues in her book Deleuze: L’Empirisme transcendantal, p. 98: ‘Chronos, the present that passes, recaptures the actuality of the first synthesis, while Aion in a disjunctive manner joins together the pure past and the achronological becoming of the second and of the third synthesis. Aion comprises the virtual dimensions of the past and of the future that insist in the present and elude actuality’ (my translation, D. V.). 31. The presentation of the schema can be found in Deleuze, CIT 285/109, note 23/22. 32. Sauvagnargues, Deleuze: L’Empirisme transcendantal, pp. 97–8 (my translation, D. V.). 33. Hölderlin, ‘Anmerkungen zum Oedipus’, pp. 729–36. For an English translation see Pfau (ed.), Friedrich Hölderlin: Essays and Letters on Theory, pp. 101–8. 34. For Deleuze’s reference to Hölderlin and Beaufret, see DR 315/118, footnote 10/1. 35. Hölderlin, ‘Anmerkungen zum Oedipus’, pp. 735–6 (my translation, D. V.). 36. Ibid., p. 736 (my translation, D. V.). 37. Beaufret, Hölderlin et Sophocle, p. 21. 38. Ibid., pp. 19–21. 258

Time and the Split Subject 39. It should be mentioned that the three parts of limitation, transgression and atonement, which Deleuze analyses, match neither with the acts of Aeschylus’ Agamemnon, nor with the surviving triology Oresteia (the parts of which are ‘Agamemnon’, ‘The Libation Bearers’ and ‘The Euminides’). We have to understand Deleuze’s structural analysis as independent of any actual structure of the play. What Deleuze tries to illustrate is a certain conception of tragic time which is cyclical, just like the Greeks’ conception of astronomical time. 40. Beaufret, Hölderlin et Sophocle, p. 32 und Deleuze, LK II, pp. 3–4. 41. Hölderlin, ‘Anmerkungen zum Oedipus’, p. 736 (cf. Pfau, Friedrich Hölderlin, p. 108; translation modified, D. V.). 42. Hölderlin’s Oedipus raises the following problem: if Sophoclean tragedy already involves a thinking of the pure and empty form of time, of a time of abandonment by the gods, then the Kantian revolution, i.e. the breaking with ancient cyclical time and the unrolling of time as a straight line, had arguably already been performed in Greece two thousand years before Kant. This view fits well with Deleuze’s thought that Ideas are virtual and that they become actualised in different places at different times. We should therefore read Deleuze’s claim that Kant revolutionised the ancient cyclical model of time not simply in chronological terms, i.e. in terms of a historical development, but as the actualisation of a virtual Idea, which is to say that the movement is not going from one actual term to another, but from the virtual to the actual. (We owe this suggestion to Nick Midgley.) 43. Beaufret, Hölderlin et Sophocle, p. 28. 44. Ibid., pp. 18–19. 45. Nietzsche, The Gay Science, pp. 119–20. 46. Ibid., p. 120. 47. Ibid. 48. For instance, Deleuze refers to the different possibilities of becoming in ‘Literature and Life’, CC 1–6. See also ATP, ch. 10: ‘1730: Becoming-Intense, Becoming-Animal, Becoming-imperceptible’, and WP 169/161: ‘Everything is vision, becoming. We become universes. Becoming animal, plant, molecular, becoming zero.’ 49. See also CPR A 144/B 183 and A 182/B 224–5. 50. Cf. Schaub: ‘Deleuze therefore sticks to a concept of form that still appears somewhat like a secularised Platonic Idea, thinking of form as a neutral, “vanishing” and timeless mediator that neither adds anything to its content nor takes anything from it’ (Schaub, Gilles Deleuze im Wunderland, p. 226; my translation, D. V.). 51. In this lecture course on Kant, Deleuze uses the term ‘limit’ in two different senses. In a first sense, limit means ‘limitation’ and refers to the ancient cyclical conception of time according to which time limits something, that is measures the movements of celestial bodies. Limit 259

conditions of thought: deleuze and transcendental ideas in a second sense is said to be characteristic for the linear conception of time, time as pure and empty form. According to Deleuze, limit designates an internal limit, which he describes as ‘that towards which something tends’. This definition matches with the mathematical definition of limit during the early geometrical phase of infinitesimal analysis, which depended upon theorems stating the continuous and infinite approximation of magnitudes toward a limiting value (LK II, pp. 8–9). 52. Cf. Bunn, ‘Developments in the Foundations of Mathematics’, pp. 220–6. 53. While in his Lecture Course on Kant from 21 March 1978, Deleuze refers to the mathematical notion of ‘limit’ as ‘that towards which something tends’, in Difference and Repetition Deleuze defines ‘limit’ as a ‘genuine cut [coupure]’ ‘in the sense of Dedekind’ (DR 172/223). 54. Dedekind, ‘Continuity and Irrational Numbers’, p. 2. 55. Ibid., pp. 10–11. 56. Bunn, ‘Developments in the Foundations of Mathematics’, p. 223. 57. Dedekind, ‘Continuity and Irrational Numbers’, p. 9. 58. Boyer, The History of the Calculus, p. 292. 59. Summarising Dedekind’s idea of ‘cuts’, Deleuze claims that ‘the cut designates the irrational numbers which differ in kind from the terms of the series of rational numbers’ (DR 172/224). This is not completely correct as the cut defines a real number that can correspond to either an irrational quantity or a rational number. But the important point is that numbers defined in this way do indeed constitute a new kind of number. 60. It should be noted that both the rational numbers and the real numbers are infinite, ordered and dense number systems. The property of denseness means that between any two numbers there is at least one other number. Denseness is not continuity, as Bolzano mistakenly believed. The property of continuity, which is attributed to the system of real numbers (but not to that of rational numbers), is precisely defined by Dedekind’s method of cuts. Cf. Kline, Mathematical Thought, p. 985. 61. As Bunn puts it, ‘a densely ordered system is complete (continuous) in Dedekind’s sense if every cut in the system is produced by exactly one element of the system, that is, if there is an element of the system which is either the maximum of the lower section or the minimum of the upper section’ (Bunn, ‘Developments in the Foundations of Mathematics’, p. 222). 62. Ibid., p. 222. 63. Boyer, The History of the Calculus, p. 294 (emphasis added, D. V.). The German mathematical term ‘vollkommen’ may be rendered either as ‘perfect’ (as Boyer translates it) or as ‘complete’. 64. Ibid., p. 294. However, it is not altogether clear whether Dedekind 260

Time and the Split Subject really succeeded in giving a purely ideal, arithmetic definition of continuity. In fact, he is criticised by Russell and Wittgenstein for failing to get away from the geometrical image of the number line. For more on Russell’s and Wittgenstein’s criticism, see Widder, Reflections on Time and Politics, ch. 2: ‘Point, Line, Curve’, pp. 22–33. 65. Williams rightly insists that Deleuze’s model for the third synthesis of time cannot be the ordered line of time, and that the division produced by the caesura does not equal a thin logical point. In his own words: ‘The caesura is an event and has a depth to it. It is not instantaneous but rather must be considered with its effect on the points before and after it. This is why the caesura implies a drama: it divides time such that a drama is required to encompass this division. This event-like and dramatic division is in contrast with the thin logical point and set account of the line of time where an arbitrary point is taken on a line and every point before it is defined as before in time and every point after as after in time’ (Williams, Gilles Deleuze’s Philosophy of Time, p. 91). It is true that Deleuze’s third synthesis of time cannot be reduced to the number line and the cut to a thin logical point. But it should come as no surprise that Deleuze makes use of Dedekind’s idea of a ‘cut’ and ‘static synthesis’ without following him in everything that he says. Deleuze certainly over-interprets the notion of cut, insofar as he will equate it with the irruption of the virtual event (the unthought, the inexplicable, the incommensurable) and the fracture in the subject. 66. Williams, Gilles Deleuze’s Philosophy of Time, p. 89. 67. I am indebted to Anne Sauvagnargues for pointing out this specific Deleuzian technique of ‘cutting theories together’. 68. ‘The exclusive right of concept creation secures a function for philosophy, but it does not give it any pre-eminence or privilege since there are other ways of thinking and creating, other modes of ideation that,  like scientific thought, do not have to pass through concepts’ (WP 8/13–14). See also WP 127/121 and 66/64. 69. Cf. Deleuze: ‘I belong to a generation, one of the last generations, that was more or less bludgeoned to death with the history of philosophy. The history of philosophy plays a patently repressive role in phil­ osophy, it’s philosophy’s own version of the Oedipus complex: “You can’t seriously consider saying what you yourself think until you’ve read this and that, and that on this, and this on that.” Many members of my generation never broke free of this; others did, by inventing their  own particular methods and new rules, a new approach’ (N  5–6/14). By his critical stance against the history of philosophy, we take it that Deleuze means to criticise only the exclusive occupation with canonical philosophical texts in the manner of a critique or commentary that is not creative. As is well known, Deleuze himself 261

conditions of thought: deleuze and transcendental ideas wrote a number of books on some canonical philosophical authors, but he always understood this commentary as creative: he brought to light new aspects and extracted new concepts, not least by importing heterogeneous elements or points of views into the original text. 70. Suffice here the following references to Klossowski by Deleuze: DR 66–7/92, 90–1/122, 95/127, 312/81–2 note 19/2, 331/313 note 16/1 and in LS Appendix III 280–301/325–50. 71. Deleuze refers to Henry Miller’s book The Time of the Assassins. 72. Deleuze, ‘Conclusions on the Will to Power and the Eternal Return’, DI 124/173. Deleuze gave this paper at the end of a colloquium on Nietzsche which he organised and which took place in the Royaumont Abbey, 4–8 July 1964. Cf. also DR 126/164–5 and 241/311. 73. See DR 6/14, 241–3/311–13 and 299/382. 74. Nietzsche, Thus spake Zarathustra, p. 167. 75. Ibid., p. 234. 76. Nietzsche: ‘My doctrine teaches: live in such a way that you must desire to live again, this is your duty – you will live again in any case! He for whom striving procures the highest feeling, let him strive; he for whom repose procures the highest feeling, let him rest; he for whom belonging, following, and obeying procures the highest feeling, let him obey. Provided that he becomes aware of what procures the highest feeling, and that he shrinks back from nothing. Eternity depends upon it’ (in KSA, vol. 9, p. 505, 11[163], Spring–Fall 1881). 77. Deleuze, ‘Conclusions on the Will to Power’, DI 125/174. See also DR 41/60. 78. Deleuze, ‘Conclusions on the Will to Power’, DI 125/175 (translation modified, D. V.). In order to avoid the misleading connotations of ‘superman’, we prefer to translate ‘Übermensch’ as ‘overman’. We thus agree with the Nietzsche scholar and translator Walter Kaufmann who justified the use of ‘overman’ both in terms of breaking with the connotations of ‘superman’ and of preserving the etymological connections with other words in Nietzsche that contain the prefix ‘über-’ (such as ‘überwinden’ which translates best as ‘overcoming’). 79. Nietzsche, The Gay Science, pp. 225–6. 80. Deleuze, ‘Conclusions on the Will to Power’, DI 127/177. 81. Klossowski, Nietzsche and the Vicious Circle, p. 58. 82. Ibid., p. 57. 83. See Nietzsche’s letter to Jacob Burckhardt, 6 January 1889, in Schlechta (ed.), Werke, p. 1351. 84. See Nietzsche’s letters to Peter Gast, Georg Brandes and Jacob Burckhardt from Turin, 4 January 1889, in Schlechta (ed.), Werke, p. 1350. 85. Grosz, The Nick of Time, p. 148. 262

Time and the Split Subject 86. Klossowski, ‘Nietzsche, le polythéisme et la parodie’, in Un si funeste désir, p. 223. 87. Deleuze makes this remark in the context of discussing Leibniz and the notion of implication, that is enveloping intensities, fields of individuation and individual differences. However, he links these thoughts explicitly to the concept of eternal return, the universal individual and the system of the dissolved self. 88. Michel Foucault analysed the practice of parrhesia in six lectures given at the University of California at Berkeley in 1983 as part of his seminar entitled ‘Discourse and Truth’. The complete text compiled from tape-recordings is published under the title Fearless Speech (2001). 89. Williams, Deleuze’s Philosophy of Time, p. 92. 90. Ibid., pp. 92–3. 91. Deleuze’s rejection of the binary model of the real and the imaginary is clearly expressed in his early essay ‘How Do We Recognize Structuralism?’ (DI 171/240). 92. Williams, Deleuze’s Philosophy of Time, pp. 184–5. 93. Klossowski, Nietzsche and the Vicious Circle, p. 57. 94. Klossowski, ‘The Experience of the Eternal Return’, in Nietzsche and the Vicious Circle, pp. 55–73. 95. Nietzsche, Ecce Homo, p. 73. In Proust and Signs, Deleuze calls the movement of thought an ‘adventure of the involuntary’ (PS 95/187– 8), and in Difference and Repetition Deleuze states: ‘There is only involuntary thought, aroused but constrained within thought, and all the more absolutely necessary for being born, illegitimately, of fortuitousness in the world’ (DR 139/181). 96. Nietzsche, Ecce Homo, p. 73. 97. Letter to Peter Gast, 14 August 1881, in Schlechta (ed.), Werke, pp. 1172–4. An English translation can be found in Klossowski, Nietzsche and the Vicious Circle, pp. 55–6. 98. Klossowski, Nietzsche and the Vicious Circle, p. 60. 99. Ibid., pp. 62–3. 100. Nietzsche, Writings from the Late Notebooks, p. 34. 101. See DI 98/136: ‘And thought itself, considered as a dynamism proper to the philosophical system, is perhaps in its turn one of these terrifying movements that are irreconcilable with a formed, qualified, and composed subject, such as the subject of the cogito in representation.’ 102. Cf. DR 118/155–6 and 250/322. See also DI 97/136. 103. Cf. WP 8/13–14, 66/64 and 127/121. Although this view that philosophical thought is just one specific mode of thinking which is distinct but not superior to science and art is explicitly stated in Deleuze’s and Guattari’s late œuvre, we believe that it can also be ascribed to the Deleuze of Difference and Repetition. Deleuze himself seems to have 263

conditions of thought: deleuze and transcendental ideas seen no contradiction in extending this view to his early text. In the Preface to the English edition of Difference and Repetition, Deleuze says that ‘philosophy obviously cannot claim the least superiority [to arts and sciences], but also creates and expounds its own concepts only in relation to what it can grasp of scientific functions and artistic constructions’ (DR xvi).

264

Conclusion

In this study we have examined Deleuze’s critique of the implicit and tacit Image of thought that emerged in the history of philosophy and that subjects the act of thinking to the postulates of good sense, common sense and recognition, thereby separating thought from its vital and genetic conditions. Calling this classic Image of thought into question, Deleuze sets out to determine the nature of thought anew and to relate it back to those elements which account for the genesis of the act of thinking in thought. He specifies the relation between thought and its conditions as ‘transcendental’, thereby making use of a concept which enjoys a long established tradition and which was first introduced by Kant to bring philosophy onto ‘the secure course of a science’ (CPR B vii) in search of truth. However the original Kantian concept of the transcendental clearly adheres to the classic Image of thought that takes recognition as its model. Given that Deleuze always maintained that ‘philosophy does not consist in knowing and is not inspired by truth’ (WP 82/80), how can we make sense of Deleuze’s appropriation of the notion of the transcendental? How can we understand his apparently paradoxical relation to Kant, whom he describes both as ‘an enemy’1 and as ‘the analogue of a great explorer’ who discovered ‘the prodigious domain of the transcendental’ (DR 135/176)? Deleuze himself indicates the solution to this paradox in the following description of how he believes the history of philosophy should be approached: Criticism implies new concepts (of the thing criticized) just as much as the most positive creation. [. . .] Nothing positive is done, nothing at all, in the domains of either criticism or history, when we are content to brandish ready-made old concepts like skeletons intended to intimidate any creation, without seeing that the ancient philosophers from whom we borrow them were already doing what we would like to prevent modern philosophers from doing: they were creating their concepts, and they were not happy just to clean and scrape bones like the critic and historian of our time. Even the history of philosophy is completely without interest if it does not undertake to awaken a dormant concept and to play it 265

conditions of thought: deleuze and transcendental ideas again on a new stage, even if this comes at the price of turning it against itself. (WP 83/80–1)

Deleuze’s encounter with Kant must be understood as a resumption of critical philosophy and a radicalisation of critique that bears on the presuppositions of Kant’s original project itself. The aim of Deleuze’s ‘deconstructive technique’ is to construct a concept of the transcendental that paves the way for a new model of thought which in his later œuvre co-authored with Guattari will carry the name of the rhizome. In this book we have analysed the characteristics of the Deleuzian concept of the transcendental, determined its sources of inspiration and brought to light its novelty in comparison to the traditional meaning of the term. We have shown that apart from his retention of certain aspects of the transcendental developed by Kant, Deleuze adds new features which can be traced back to the influence of both post-Kantian philosophers and other major thinkers (Leibniz, Maimon, Nietzsche, Bergson, Proust, Lautman, etc.). We have found that the following general features are distinctive for Deleuze’s notion of the transcendental: 1. The emergence of thought is necessitated through the encounter with something exterior (a transcendental sign or Idea) that exercises a force upon thought in order to constrain it to think. Thought is an involuntary adventure and not a naturally given process furthered by good will and guided through method. 2. The transcendental designates a genetic and differential principle by which thought arises. 3. It is essentially a plastic principle: this means that the transcendental condition is not larger than what it conditions. In other words, it is determined at the same time that it determines the conditioned. 4. The transcendental condition does not resemble what it conditions, which is to say that it is not produced retroactively in the image of the empirical and elevated to a transcendental status. 5. Thought’s encounter with the transcendental happens in the confrontation with genetic and differential Ideas which neither belong to reason (the Kantian faculty of Ideas) nor to the understanding (as Maimon’s differential Ideas of the understanding) but to a virtual intersubjective unconscious.2 6. Ideas are problematic objective structures. That is to say, they do not indicate a temporary subjective lack of knowledge and 266

Conclusion cannot be reduced to simple questions whose answers already pre-exist and which disappear in the solution. 7. The theory of Ideas is correlated with a theory of the faculties. More concretely, the encounter with Ideas-problems forces their corresponding faculties to transgress their limits and to merge into a disharmonious transcendent exercise (freed from the ­constraints of empirical recognition). 8. Ideas-problems partake in a dialectic of Ideas, whence follows their status as simultaneously transcendent (i.e. irreducible to the cases of solution) and immanent (that is Ideas-problems are incarnated in sensible nature, history, social life, arts, sciences, philosophy and so on). 9. Ideas are defined as virtual multiplicities consisting of differential relations shaped by the distribution of singular points. They are governed by processes of different/ciation (that is internal processes of differentiation and processes of actualisation and specification). 10. Differential Ideas-problems relate to a split subject, in Deleuze’s words the ‘system of a dissolved self’ which is constituted by thousands of passive syntheses and fractured by the empty form of time. In order to outline this new Deleuzian conception of transcendental philosophy, we have mainly drawn from Deleuze’s early texts, in particular Difference and Repetition. However, a seminal discussion of the transcendental viewpoint returns in his last published essay ‘Immanence: A Life’ (1995). There Deleuze makes it plain that his transcendental philosophy has to be understood as a philosophy of immanence: the transcendental field which has been defined as a genetic or potential milieu swarming with differential Ideas – or as Deleuze prefers to say in the Logic of Sense: populated with impersonal and pre-individual singularities (cf. LS 103/125) – becomes a ‘plane of immanence’. Deleuze emphasises the modification in the meaning of the term ‘transcendental’ that his philosophy of immanence requires, stating that Kant failed in two ways: ‘The transcendental is entirely denatured, for it [. . .] simply redoubles the empirical [. . .], and immanence is distorted, for it [. . .] finds itself enclosed in the transcendent.’3 In other words, he accuses Kant of tracing the transcendental from the empirical – a criticism that we already know from Difference and Repetition – and of enclosing all possible experience in the confines of a transcendental subject. 267

conditions of thought: deleuze and transcendental ideas Deleuze argues that Kant made the field of possible experience immanent to a transcendental subject, which itself is excluded from the empirical spatio-temporal world and constitutes its transcendent ground. Deleuze’s demand for immanence poses a great challenge to Kant but also to post-Kantianism that builds on the transcendental subject and turns it into the absolute subject of German Idealism. For Deleuze, a philosophy of immanence must not distort immanence by making it immanent to something. ‘Absolute immanence is in itself: it is not in something, to something; it does not depend on an object or belong to a subject.’4 The plane of immanence is all there is and, as Deleuze and Guattari suggest in What Is Philosophy?, we must understand it as containing both being and thought: it ‘presents two sides to us, extension and thought, or rather its two powers, power of being and power of thinking’ (WP 48/50). The individuation of subjects and objects is only a secondary, derived phenomenon, a product of immanence. ‘Consciousness becomes a fact only when a subject is produced at the same time as its object, both being outside the field and appearing as “transcendents”.’5 Deleuze rejects any first term – such as a transcendental consciousness, a universal subject or an object which is able to contain ­immanence – and along with it the idea of foundation. Deleuze’s plane of immanence, although he calls it something Absolute and refers to it as THE plane of immanence (WP 59/59), does not fulfil a grounding function. THE plane of immanence is not a universal or abstract totality, but a multiplicity: it is ‘interleaved’ (WP 50/51), that is it has different layers which are sometimes separated and sometimes joined together. Furthermore, THE plane of immanence is itself virtual, that is ‘pure variation’ (WP 39/41) or ‘pure becoming’. In the essay ‘Immanence: A Life’ he describes it ‘as a movement that neither begins nor ends’,6 as an impersonal, indefinite, and immanent life ‘carrying with it the events or singularities that are merely ­actualized in subjects and objects’.7 Although Deleuze in his late œuvre surely introduces new concepts (such as ‘pure becoming’, ‘event’8 or ‘impersonal life’), we can retrieve some motives that he had already elaborated in Difference and Repetition. We have seen that his transcendental empiricism abandons the ultimate ground of the transcendental subject. The Deleuzian transcendental designates a virtual realm of differential Ideas in the depth of the empirical world that different/ciate 268

Conclusion themselves according to different speeds and rhythms and that force themselves through minds generating the act of thinking in thought. We can see here the overriding importance to Deleuze of the two notions of difference and repetition. They are ‘first principles’ in the sense of providing not an ultimate ground, but rather a ‘groundlessness’ or ‘universal ungrounding’ (DR 91/123). They function as principles of genesis, that is as real conditions of experience, thought, consciousness, subjects and objects alike. Even though the aspect of a philosophy of immanence is relatively unelaborated in Difference and Repetition, we have seen that this early work already harbours the seeds of Deleuze’s future philosophical development. Thus it can be argued that the plane of immanence is a revival of the transcendental field, which is conceived as a sub-representative, unconscious, virtual and immanent depth.9 Therefore a thorough understanding of the meaning and use of the notion of the transcendental is all the more important as the notion underpins his later work, either explicitly or in disguise. This is not to say that there is a strict continuity in Deleuze’s œuvre; rather, it must be understood as a discontinuous and interrupted line of solutions or solution curves that revolve around problems and subsets of problems which share the proper name Deleuze.

Notes 1. Deleuze describes his book on Kant as a ‘book about an enemy that tries to show how his system works, its various cogs – the tribunal of Reason, the legitimate exercise of the faculties (our subjection to these made all the more hypocritical by our being characterized as legislators)’ (N 6/14–15). 2. It should be noted that the term ‘intersubjective’ by no means signifies a collective unconscious common to a number of integral subjects. The point of view of the integral subject must be replaced by the split subject which is dissolved in a series of selves (cf. DR 124/162). 3. Deleuze, ‘Immanence: A Life’, p. 27. 4. Ibid., p. 26. 5. Ibid. 6. Ibid. 7. Ibid., p. 29. 8. It might have been noticed that throughout this book we have not discussed the Deleuzian concept of the event. This is so because it plays a minor role in Difference and Repetition and is fully developed only in The Logic of Sense. Nevertheless already in Difference and Repetition 269

conditions of thought: deleuze and transcendental ideas the concept of events is mentioned and it appears that we have to understand Deleuzian Ideas-problems in terms of events rather than essences (cf. DR 187/242–3). According to Deleuze, ‘problems are of the order of events’ (DR 188/244) and he distinguishes ‘real events on the level of the engendered solutions, and ideal events embedded in the conditions of the problem’ (DR 189/244). 9. ‘The transcendental field is defined by a plane of immanence, and the plane of immanence by a life’ (in Deleuze, ‘Immanence: A Life’, p. 28).

270

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Index

Actualisation, 8, 14, 128, 191, 195, 196, 197, 198, 207n, 208n, 259n, 267; see also Differenciation Allison, Henry, 133n, 148, 202n, 203n Alunni, Charles, 205n Appearance, 1, 2, 3, 17n, 74, 78, 79, 83, 216, 217, 256n Apprenticeship, 27, 28, 61, 63, 64, 65, 149 Aristotle, 36–7, 38–41, 55, 57, 69–70n, 87, 146, 152, 179, 180, 187, 213–14, 215 Atlas, Samuel, 92, 138n Badiou, Alain, 201 Beaufret, Jean, 231, 232, 233 Becoming, 68n, 86–7, 89, 128, 149, 209n, 228, 231, 236, 242, 243, 247, 248–9, 251, 258n, 259n, 268 Bergman, Samuel Hugo, 111, 112, 137n Bergson, Henri, 5, 8, 15n, 57, 70n, 75, 91, 126, 127, 185, 190, 201, 207n, 223–6, 229–30, 250, 257n, 266 Borges, Jorge Luis, 214, 241,  256n Boscovich, Roger Joseph, 82–3 Boyer, Carl, 104, 239 Bryant, Levi, 7–8, 17n, 93,  257n Bunn, Robert, 238, 239, 260n Butler, Samuel, 219, 221, 257n

Caesura, 122, 212, 231, 233–7, 240, 241, 249, 250, 261n; see also Cut Calculus, 57, 60, 84, 85, 90, 93, 102, 103–7, 110–11, 118, 121, 122–5, 135n, 140n, 145, 156, 180, 186, 187, 191, 199–200, 202, 237 Cassirer, Ernst, 139n Common sense, 10, 21, 22, 25, 32–4, 35, 41, 43, 62, 129, 160–1, 164, 169, 178, 180, 198, 254, 265 Aesthetic common sense, 33, 160, 161, 164–5, 174, 178 Conceptual persona(e), 46, 47, 70n, 81, 130n Condition(s) (transcendental), 1–4, 9, 12–14, 15n, 21, 24, 25, 26, 28, 29, 44, 47, 48, 49–54, 56, 57, 59, 60, 61, 64, 65, 67n, 68n, 71, 74–5, 79, 87, 88, 89, 90, 92, 95, 98, 113–14, 116, 117, 147, 149, 150, 152–4, 156, 157, 187, 189, 193, 207n, 210, 216, 217, 222–3, 224, 225, 228, 233, 243, 245, 252–5, 265, 266, 269,  270 Consciousness of representation, 111, 112, 116, 117, 118 Couturat, Louis, 59, 60 Critique, 1–2, 3, 19, 22–3, 36, 47, 50, 53, 66n, 67n, 74–5, 76, 79, 84, 87, 118–19, 129n, 159, 210, 212, 261n, 265,  266

281

conditions of thought: deleuze and transcendental ideas Cut, 121, 212, 229, 231, 234, 237–41, 250, 252, 260n, 261n; see also Caesura Cuvier, George, 196–7 Dedekind, Richard, 231, 237–41, 260n, 261n Deduction, 1, 24, 97, 134n, 148, 150–4, 165, 169, 170, 173, 174, 202n Descartes, René, 3, 31, 33, 36, 45–7, 120, 216–17 Dialectic(s), 14, 57, 76, 81, 142, 145, 179–82, 184, 185, 186, 191, 196, 199–200, 254, 267; see also Ideas: dialectical Ideas Difference, 2, 7, 13, 20–1, 38, 41, 42, 43, 53, 64, 65, 66, 76, 82, 83, 84, 85, 86, 93, 99, 125, 127, 128, 132n, 135n, 179, 181, 182, 191, 193, 240, 243, 247, 251, 255, 269 Concept of difference, 21, 37, 38, 41, 42, 93 Conceptual difference, 21, 37, 94 Difference in degree, 127, 225 Difference in kind, 119, 124, 127, 128, 193, 225 External difference, 3, 4 Generic and specific difference, 21, 36, 39–42, 69n, 245 Individual difference, 39, 42, 246 Infinitely small difference, 105–6 Internal/intrinsic difference, 4, 7, 15–16n, 37, 93, 216, 234, 236 Differenciation, 194–6, 267; see also Actualisation Differential(s), 7, 14, 56, 61, 66, 75, 84–5, 93, 102, 103–12, 113, 114, 115, 116, 117, 118–20, 121, 122, 124, 128, 129, 135–6n, 138n, 139n, 140n, 179, 187, 192, 193, 194, 199, 219, 223; see also Relation: differential relation(s)

Differentiation, 83, 106, 115, 122, 128, 140n, 193, 194, 208n, 267 Discordant accord, 157, 178–9; see also Para-sense Duffy, Simon, 12, 140n, 183, 184, 185, 186, 188, 206n Encounter, 21, 25, 27, 61, 63, 65, 143–4, 178–9, 199, 207n, 242, 254, 266, 267 Ens reale, 108, 115 Eternal return, 4, 12, 14–15, 86–7, 210, 231, 242–5, 247–9, 251–3, 255 Event, 16n, 82, 175, 181, 205n, 229, 234, 235, 241, 242, 250, 252, 261n, 268, 269–70n Formal intuition, 3, 51, 98–101; see also Pure intuition Fractured I see split subject Frege, Gottlob, 48–9, 50 Freud, Sigmund, 120, 172 Freudenthal, Gideon, 92 Genesis, 2, 5, 6, 7, 8, 9, 12, 14, 20, 25, 27, 35, 48, 54, 74–5, 84, 87, 88, 90, 92, 93, 102, 113, 117, 120, 125, 127, 142, 150, 154, 156, 158, 165, 168, 169, 173, 177, 178, 184–5, 192, 194, 195, 207n, 208n, 210, 257n, 265, 269 Genius, 156, 158, 165, 173,  174–8 Good sense, 32, 33–4, 37, 41, 43, 129, 178, 265 Guattari, Félix, 5, 6, 29, 30, 66n, 190, 191, 198, 199, 208n, 241, 242, 266, 268 Guéroult, Martial, 116–17, 135n, 138n, 139n Hegel, G. W. F., 10, 23, 24, 36, 42, 76, 92, 110, 179, 181–2

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Index Heidegger, Martin, 6, 24, 47, 182, 205n, 211, 250 Heterogenesis, 241–2 Hölderlin, Friedrich, 9, 212, 231–3, 241, 250 Hughes, Joe, 207–8n Hume, David, 7, 15n, 44, 76, 96, 97, 219–20, 257n Ideas, 1, 2, 3, 8, 9, 12, 14, 15, 22, 25, 26, 27, 33, 37, 38, 53, 56, 61–3, 64, 65, 91, 93, 107, 108, 113, 114, 117, 118, 125, 126, 128, 129, 137n, 142–57, 159, 161, 164, 165–76, 178–99, 203n, 205n, 207n, 208n, 211, 224, 254–5, 259n, 266–8,  270 Aesthetic Ideas, 156, 173, 175–6 Dialectical Ideas, 65, 182–5, 199 Ideas of (theoretical or practical) reason, 22, 26, 108, 119, 138n, 139n, 145–8, 151–7, 165–74, 175, 176, 178, 179, 202n, 204n, 239 Ideas of the understanding, 93, 108, 111, 114, 118, 119, 139n, 142, 266 Problematic Ideas (or Ideasproblems), 12, 14, 25, 56, 61–3, 64, 65, 125, 143, 145, 150, 185, 186, 187, 191, 192, 194, 195, 196, 197, 199, 202, 206n, 254, 255, 266, 267, 270n see also Problems Identity, 4, 13, 20–1, 24, 33, 34, 37, 38, 39, 40, 41, 42, 43, 50, 86, 125, 128, 137n, 192, 210, 211, 212, 215, 217, 218, 219, 230, 235, 236, 243, 247, 248, 249, 251, 254 Illusion, 2, 43, 55, 57, 146, 157, 180, 187 Illusions of reason, 1, 22, 155 Illusions of representation, 1, 20

Image of thought, 1, 11, 13, 18–23, 26–30, 34, 35, 37, 43, 45, 47, 55, 61, 64, 65, 68n, 148, 187, 251, 265 Immanence, 8, 10, 116, 117, 122, 181, 184, 185, 208n, 267–9, 270n Infinite understanding, 111, 112–13, 115–17, 125, 128, 137n, 138n, 203n Intensive magnitude, 102, 109–10; see also Quality Intuitive intellect, 94, 132n Judgement Aesthetic judgement of taste, 157–8, 159, 161–3, 165, 169–71, 173–4, 177, 178,  204n Reflecting judgement, 156, 157, 158, 159, 170 Kant, Immanuel, 1–3, 4, 5, 7, 10, 14, 16n, 21–4, 33, 34, 36, 43–4, 46, 48, 51–3, 56, 66n, 67n, 72n, 74, 75, 76, 87, 88, 90, 92, 93–102, 107–8, 111, 112, 113, 114, 116, 129n, 130n, 131n, 132n, 133n, 137n, 145–8, 149, 150–76, 179, 180, 181, 187, 201, 202n, 203n, 204n, 210, 211, 212, 213, 214, 215–18, 222, 223, 229, 230, 231, 233, 234, 236, 237, 241, 242, 259n, 265, 266, 267, 268 Kerslake, Christian, 9–11, 93, 148, 153, 202n Klossowski, Pierre, 236, 243, 247–8, 251–4 Lautman, Albert, 12, 65, 145, 182–6, 188, 190, 199, 205n, 206n, 208n, 266

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conditions of thought: deleuze and transcendental ideas Leibniz, G. W., 7, 36, 42, 57–61, 62, 72n, 93–4, 100, 102, 103–7, 109, 112, 114, 117–21, 123, 124, 125, 128, 132n, 139n, 140n, 211, 218, 256n, 266 Life, 10–11, 16n, 28, 63, 77–8, 83, 86, 127, 219, 221, 226, 230, 268 Limit, 63, 65, 90, 104, 105, 111, 112, 136n, 143, 146, 167, 237, 240, 259–60n Lord, Beth, 93, 133n, 137–8n Maimon, Salomon, 5, 7, 14, 67n, 75, 92–102, 107–19, 121, 125, 128, 131n, 132n, 133n, 134n, 135n, 137n, 138n, 139n, 142, 185, 203n, 266 Marx, Karl, 198, 255 Metaphor, 173, 192, 200, 208n,  242 Method of Dramatisation, 13, 79, 84 Method of Exhaustion, 105, 196 Midgley, Nick, 93, 97–8, 132n, 256n, 259n Minute perceptions, 62, 114, 118, 119–21, 124, 125, 128, 143 Multiplicity, 12, 13, 15n, 68n, 127, 145, 156, 181, 185, 186, 187, 189–91, 192, 195, 196, 197, 198, 201, 202, 206n, 207n, 239, 243, 247, 267, 268 Necessity, 2–3, 23–5, 46, 52, 53, 58, 59, 60, 67n, 74, 101, 140n, 152, 162, 170, 219, 228, 248, 252 Newton, Isaac, 103–4, 106, 107, 109, 136n, 214 Nietzsche, Friedrich, 4, 5, 12, 13, 14, 35, 46, 67n, 68n, 75–91, 129n, 131n, 234, 235, 236, 243–8, 250, 251–3, 254, 255, 262n, 266 Noumenon, 107–8

Objective Reality, 52, 95, 96–8, 113, 133n, 150, 152, 153, 174 Objective Validity, 52, 94, 95–7, 133n, 152, 153, 154 Overman, 245, 248–9, 262n Para-sense, 129, 157, 178; see also Discordant accord Parrhesia, 249, 263n Passive Synthesis, 6, 195, 210, 218, 219–24, 229, 267 Patton, Paul, 5, 130n, 255n Plasticity/plastic principle, 12, 28, 29, 67, 68n, 76, 88, 90, 91, 149, 266 Plato, 1–2, 5, 23, 26, 35, 36–8, 43, 53, 64, 69n, 74, 78, 146–8, 179, 180–1, 182, 202n, 213, 227 Plotnitsky, Arkady, 201, 207n,  209n Poincaré, Henri, 184, 188–9 Present (living or lived), 218, 219, 220, 222, 223, 230; see also Time Presentations, 112, 116, 117, 119, 121, 219 Problem(s), 9, 12, 14, 15n, 25, 27, 28, 29, 44, 45, 48, 54, 55–61, 63, 65, 70n, 71n, 128, 142, 143, 145, 146, 148–50, 165, 180, 181, 182, 183, 184, 185, 186, 187, 189, 193, 194, 197, 199, 202, 207–8n, 242, 254, 269, 270n; see also Ideas: problematic Ideas Proust, Marcel, 16n, 27, 63, 64, 126, 141n, 144, 223, 224, 227, 266 Pure intuition, 88, 95, 97–8, 100; see also Formal intuition Pure past, 8, 144, 218, 223–30, 258n; see also Time Purposiveness/purposive relationship, 154, 163, 167, 170, 171, 177, 202n, 204n

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Index Quality, 82, 84, 85, 86, 88, 89, 102, 109–10, 119, 124, 127, 128, 193; see also Intensive magnitude Quid juris?, 95, 101, 102, 111, 113, 114, 165 Real thought, 101, 111, 133n Recognition, 14, 22, 24, 32, 33, 34–5, 43, 44, 47, 62, 64, 65, 87, 143, 265, 267 Relation Differential relation(s), 7, 8, 12, 56, 62, 65, 86, 93, 102, 106, 110, 111, 118, 121, 122, 123, 124, 186, 187, 189, 191, 193, 194, 196, 267; see also Differential(s) Pure relations, 109, 110 Reciprocal (or reciprocally determined) relations, 85, 108, 110, 124, 193, 198 Repetition, 9, 13, 64, 131n, 144, 210, 220, 221, 245–8, 255,  269 Representation (order/logic/model of), 1, 2, 13, 19, 20, 23, 26, 28, 31–2, 35, 36–9, 41–3, 46, 65, 69n, 80, 111–12, 115, 117, 124, 125, 143, 218, 242–3, 245,  247 Riemann, Bernhard, 190–1, 207n Rimbaud, Arthur, 63, 72n, 215, 245 Rölli, Marc, 6–7 Saint-Hilaire, Étienne Geoffroy, 196–7 Salanskis, Jean-Michel, 194, 201, 209n Sauvagnargues, Anne, 11, 93, 230, 258n Schaub, Mirjam, 204–5n, 259n Schema, 94, 95, 113, 134n, 152, 153–4, 155, 162, 168, 172, 173, 183, 184, 185

Sense, 3, 12, 13, 14, 44, 47–55, 56, 57, 58, 67n, 70n, 71n, 74, 87, 89–90, 91, 92, 153, 155, 201, 253 Sign, 12, 13, 17, 25, 27, 63–5, 89, 143–5, 179, 224, 252–4, 266 Simulacra, 37–8, 46, 74, 210, 227, 243, 246, 247, 248, 255 Singularity, 62, 65, 121, 122, 124, 128, 139n, 140n, 149, 186, 187, 188–9, 191, 192, 193, 194, 195, 199, 206n, 246, 267, 268 Smith, Daniel, 7, 11, 93, 156, 178, 179, 189 Sophocles, 231–3 Spinoza, Benedictus de, 43, 112–13, 137n, 211 Spinozism, 112–13, 133n, 137n Split subject, 4, 14, 142, 210, 212, 230, 249, 267, 269n Static synthesis (of time), 212, 218, 236–7, 239, 240, 250, 261n; see also Time Sublime, 14, 156, 158, 165–9, 170, 178, 204n Symbolisation, 169, 172–3, 205n Time, 3–4, 8, 12, 14, 26, 28, 51, 64, 66n, 68n, 86, 87, 94, 95, 96, 98, 99, 100, 101, 134n, 195–6, 210, 212–19, 220, 222, 223–5, 226, 228, 229–30, 231, 233–4, 236, 237, 239–42, 243–4, 248, 255–6n, 259n; see also Present (living or lived); Pure Past; Static Synthesis (of time) Third synthesis/empty form of time, 3–4, 12, 14, 210, 212, 214, 215, 216, 218, 222, 228, 229, 230, 231, 233, 236, 240–2, 243, 249–51, 252, 259n, 260n, 261n, 267 Transcendental empiricism, 1, 6–7, 9, 11, 23, 25, 85, 91, 93, 257n, 268

285

conditions of thought: deleuze and transcendental ideas Virtuality/the virtual, 8, 12, 13, 56, 91, 126–8, 184, 185, 189, 195–6, 197–8, 205n, 207–8n, 223, 226, 230, 241, 250, 258n, 259n, 261n, 267, 268, 269 Vuillemin, Jules, 116

Transcendental subject, 1, 2, 52, 181, 210, 230, 242, 267,  268 Truth, 2, 3, 21, 22, 23, 24, 26, 27, 31, 32, 35, 43, 44–54, 57, 59–61, 63–4, 66n, 71n, 74, 76, 77–9, 89–90, 97, 116, 129n, 140n, 144, 154, 180, 187, 202, 203n, 211, 247, 249, 265 Unconditioned, 10, 54, 77, 147, 152, 156 Unconscious (differential), 114, 117, 119–21, 125, 128, 142 Unthought in thought, 114, 116, 117, 169, 261n Untimely, 28, 68n

Weierstrass, Karl, 107, 122–3, 124, 136n, 140n, 187–8, 206n Will to power, 75, 76, 77, 79, 80, 83–7, 88–91, 131n, 245, 255 Williams, James, 241, 249–51, 255, 261n Zammito, John, 159–60, 204n Zourabichvili, François, 5, 67n, 68n, 70n, 71n

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