Five Figures of Folding: Deleuze on Leibniz's Monadological Metaphysics

Abstract

This article is about Gilles Deleuze's book Le Pli. Leibniz et le Baroque from 1988. It shows how Deleuze's notion of folding captures some basic intuitions in Leibniz and how they relate to each other. To this purpose, I propose five figures, all referring to the same basic fold, all illustrating how the consideration of such figures allows developing central elements of Leibniz's monadology. These figures can help, I hope, alleviate some of the fundamental difficulties in understanding Deleuze's approach to the Monadology from the non-Deleuzian perspective of contemporary Leibniz scholarship and give a sense of the synthetic, explanatory force that Deleuze's notion of folding has in relation to Leibniz's monadological metaphysics.

Keywords:

• Leibniz
• Deleuze
• fold
• monadology
• event

Notes

¹I will use the following abbreviations for Leibniz's work: A = Sämtliche Schriften und Briefe; AG = Philosophical Essays; Arthur = The Labyrinth of the Continuum; GM = Leibnizens mathematische Schriften; GP = Die philosophischen Schriften; L = Philosophical Papers and Letters.

²For example, the translator of Le Pli, Tom Conley, writes in his introduction regarding Leibniz's logic: ‘By means of Leibniz's innovation [ … ] the subject is enveloped in the predicate, just as Proust's intension is folded into its effect' (Conley, ‘Translator's Foreword', xiv). In Leibniz, of course, it is the other way round, i.e. the predicate that is included in the subject, and Deleuze never says otherwise. Comments like this display deep ignorance of basic features of Leibniz's metaphysics, a curious comfortableness with nonsensical statements, and warrant great caution when using the translation. Throughout this article, I refer only to the original text and provide my own translations.

³Among other contributions, many of which are referenced below, see in particular the volume edited by S. Van Tuinen and N. McDonnell: Deleuze and The Fold: A Critical Reader.

⁴I should here make an exception of the splendid article by Bouquiaux, ‘Plis et enveloppements chez Leibniz', 39–56.

⁵See Deleuze, Logique de la sensation; L'Image-mouvement; L'Image-temps. On this point, see also Peden, Spinoza Contra Phenomenology, 305, n. 10.

⁶See Benjamin, The Origin of German Tragic Drama; Knecht, La Logique chez Leibniz; Fenves, ‘Autonomasia', 432–52. On Leibniz and Benjamin in Deleuze, see Lærke, ‘Four Things Deleuze Learned from Leibniz', 25–45.

⁷Deleuze, Le Pli, 173.

⁸For discussion of the development of Deleuze's reading of Leibniz, see Robinson, ‘Events of Difference', 141–64; and Smith, ‘Deleuze on Leibniz', 127–8.

⁹See http://www.webdeleuze.com. The site includes lectures from 15/04/1980, 22/04/1980, 29/04/1980, 06/05/1980, 20/05/1980, 16/12/1986, 201/01/1987, 27/01/1987, 24/02/1987, 10/03/1987, 17/03/1987, 18/03/1987, 07/04/1987, 12/05/1987, 19/05/1987/, 20/05/1987, 25/05/1987, and one undated lecture from early 1987. Deleuze's lectures from 28/10/1986, 4/11/1986, 18/11/1986, 06/01/1987, 13/01/1987, 27/01/1987, 03/03/1987, 17/03/1987, 28/04/1987, 05/05/1987, 19/05/1987, 02/06/1987 are also available as sound-files on Gallica, the digital library of the Bibliothèque Nationale de France (http://gallica.bnf.fr).

¹⁰Deleuze repeatedly endorses Serres's readings (see Le Pli, 12, n. 18; 25, n. 9; 30, n. 16; 40, n. 5; 102, n. 38; 104, n. 2; 120, n. 13; 176, n. 17). He does, however, disagree with Serres on a particular point concerning the position of a mathematical law in relation to the series it grounds: Is the law outside or inside the series? Deleuze, contrary to Serres, argues that it is outside, but stresses that ‘this is one of the only points where I cannot follow Serres' (Le pli, 68, n. 20).

¹¹See, for example, Leibniz to Des Bosses, 15 February 1712, in The Leibniz-Des Bosses Correspondence, 232–3.

¹²In his defense, it should be mentioned that volume A VI, iv (covering the years 1677–1690) only appeared in 1999. The other three volumes were available to him: A VI, i (1663–1672) appeared in 1930, A VI, ii (1663–1672) in 1966, and A VI, iii (1673–1676) in 1980.

¹³Deleuze cites the text in Le Pli, 9

¹⁴See the exchange on ‘transcreation' in Pacidius philalethi, October 1676, A VI, iii, 567–9, trans. Arthur, 21–7. Leibniz here holds that things do not pass from one state to another in virtue of an inherent power of change, but that change should rather be explained by the fact that ‘a permanent substance [ … ] has both destroyed the first state and produced the new one'. On this text, see also Levey, ‘The Interval of Motion', 371–416.

¹⁵Deleuze, Lecture on Leibniz, 06/05/1980: ‘But you can make this abstraction, you consider the world. How do you consider it? You consider it as a complex curve [ … ]. For Leibniz, that is what the world is'. See also Le Pli, 81; and Pourparlers, 217.

¹⁶On this passage, see also Lærke, ‘Compossibility, Compatibility, Congruity'.

¹⁷Leibniz to Arnauld, 14 July 1686, A II, ii, 73.

¹⁸See Deleuze, Le Pli, 81, 121. Deleuze also distinguishes between the ‘remarkable' and the ‘ordinary' in terms of the ‘regular' and the ‘singular'. Hence, ‘a singularity is surrounded by a cloud of ordinaries or singulars' (Le Pli, 81).

¹⁹See Deleuze, Lecture on Leibniz, 22/04/1980: ‘Why is Adam's sin included in the world that has the maximum of continuity? We have to believe that Adam's sin is a formidable connection, that it is a connection that assures continuities of series. There is a direct connection between Adam's sin and the Incarnation and the Redemption by Christ. There is continuity.'

²⁰For Aristotle, see Metaphysics, II, 2, 994a, in The Complete Works, vol. II, 1570.

²¹See, for example, Leibniz, Nouveaux essais sur l'entendement humain, IV, xvi, § 12, A VI, vi, 473. For a somewhat dated, but very insightful paper on the principle of continuity, see Arthur, ‘Leibniz in Continuity', 107–15.

²²Leibniz to Arnauld, 9 October 1687, A II, ii, 250. See also Leibniz to Arnauld, 16 April 1687, A II, ii, 171.

²³For synthetic introduction to Leibniz's dynamics, see, for example, the Specimen dynamicum, 1695, GM, 234–54, trans. AG, 117–38.

²⁴Deleuze, Lecture on Leibniz, 16/12/1986.

²⁵To be sure, there is an element of anachronism in my explanation to the extent that Leibniz himself did not interpret the derivative dy/dx in terms of a limiting process. It is, however, a graphically clear way of illustrating how Deleuze understood the value dy/dx as a kind of pure relation, a relation with no relata, and how this fits with his conception of the Leibnizian predicate as pure event. It is worth noting that, in his interpretation of the calculus, Deleuze owed a great deal to the structuralist reading proposed by the Nicolas Bourbaki group. On this, see Deleuze, ‘A Quoi reconnaît-on le structuralisme?', 299–335. For the notion of structure according to the Bourbaki mathematicians, see, for example, ‘L'architechture des mathématiques’, 35–47. On Deleuze's interpretation of Leibniz's calculus, see also Duffy, ‘Deleuze, Leibniz and Projective Geometry in The Fold', 129–47.

²⁶Deleuze, Le Pli, 103. By this should not be understood that such organizations are constituted within a given spatiotemporal framework, but rather that they are constitutive of the spatiotemporal framework, to the extent that, for Leibniz, space and time are nothing by orders of simultaneity and succession derived from the relative order among phenomena (or here: events). See, for example, Leibniz, Third paper to Clarke, 25 February 1716, GP VII, 363–4, trans. AG, 325.

²⁷For the notion of real phenomena, see Leibniz, De modo distinguendi phaenomena realia ab imaginariis, approx. 1683–85, in A VI, iv, 1498–504, trans. L, 363–6.

²⁸I here follow Deleuze's (in my own view problematic) reconstruction which describes the ‘existentification' of things as a realization of the possible that is distinct from the actualization of the virtual. Deleuze thus argues that there is ‘actuality that remains possible and which is not necessarily real' (see Le Pli, 140). There is however in Leibniz's own texts some evidence in favour of the contrary notion that, by virtue of being conceived in God's mind, the merely possible rather remains real while not being actual. The problem may simply be one of terminology.

²⁹This is one crucial point where I think Deleuze's reading of Leibniz's modal ontology diverges importantly from current standard readings according to which the complete concepts of possible individuals conceived in God's mind can, in some important sense, also be understood as possible substances. On Deleuze's reading, and rigorously speaking, there is no such thing as a possible substance. Complete concepts of things are, insofar as they are conceived in the divine mind, more like bundles of predicates. It would take us too far afield to assess the merits of either reading here.

³⁰See for exemple Leibniz, Discours de métaphysique, sect. 8, A VI, iv, 1539–40. For a commentary, see Fichant, ‘Actiones sunt suppositorum’, 135–48.

³¹Deleuze implicitly relies on Louis Couturat's classic conception of the monad as ‘nothing but the logical subject elevated to substancehood' (see Couturat, ‘Sur la métaphysique de Leibniz', 9).

³²This implies that all properties expressed by predicates are, when properly analysed, reducible to events or actions. Thus, according to Deleuze, the fundamental propositional form in Leibniz's logic is not the traditional attributive proposition S is P (such as ‘Adam is a sinner’), but rather a verbal proposition of the form subject–verb (‘Adam sins’) (see Le Pli, 69–72; Pourparlers, 218; Logique du sens, 200–1; Lecture on Leibniz, 20/01/1987). Leibniz's favourite examples do indeed suggest something like that: ‘Adam sins', ‘Caesar crosses the Rubicon', ‘Alexander combats Porus and Darius.' The point is that the predicates ascribed to subjects in propositional logic correspond to actions ascribed to subjects or, more precisely, to events enacted by subjects. The reading is far from being unwarranted (for a similar reading of the Leibnizian predicate, see Fichant, ‘L'invention philosophique', 57).

³³Leibniz mainly develops his notion of expression in the Discours de métaphysique and the correspondence with Arnauld. The literature on the topic is extensive. See, for example, Kulstad, ‘Leibniz's Conception of Expression', 56–76; and Swoyer, ‘Leibnizian Expression', 65–99.

³⁴See, for example, Leibniz to Arnauld, 28 November (8 December) 1686, A II, ii, 121.

³⁵A monad is ‘by its very nature representative' (La Monadologie, § 60, GP VI, 617, trans. AG, 220).

³⁶Deleuze, Le Pli, 27.

³⁷Lecture on Leibniz, 16/12/1986.

³⁸Leibniz to Arnauld, 30 April 1687, A II, ii, 167.

³⁹This will prove salutary for Leibniz's philosophy in the context of Deleuze's own Nietzschean position, and explains in some measure why Deleuze occasionally is willing to label himself a ‘Leibnizian': the ‘Dionysian' rumbles in the depths of the differential unconsciousness of minute perceptions. On Deleuze's conception of the differential unconscious, see Le Pli, 114–7, and Différence et répétition, 214, 275–6.

⁴⁰I am grateful to Paul Lodge and to the anonymous reviewers of the BJHP for numerous corrections and suggestions that much helped me improve this paper.