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Deleuze and Mereology Multiplicity, Structure and Composition

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Deleuze and Mereology Multiplicity, Structure and Composition Deleuze and mereology Multiplicity, structure and composition IOANNIS CHATZANTONIS Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy. JULY 2010 Στους γονείς μου, Νικήτα και Μαρίνα Contents ACKNOWLEDGEMENTS ............................................................................................................. V DECLARATION ......................................................................................................................... VI ABSTRACT .............................................................................................................................. VII LIST OF ABBREVIATIONS ...................................................................................................... VIII ΙNTRODUCTION ....................................................................................................................... 1 Aim and structure of investigation ............................................................................. 1 Prima facie objections ..................................................................................................... 2 1 ONE AND MANY IN PARMENIDES ................................................................................. 9 1.1 The poem ............................................................................................................... 9 The two ways of inquiry ............................................................................................... 9 The descriptive way of δόξα (B8.51-61; B9) .............................................................. 13 The diagnostic way of ἀλήθεια (B8.1-49) ................................................................. 23 1.2 Parmenides’ ἔλεγχος ......................................................................................... 28 The Eleatic critique of becoming and multiplicity .................................................. 28 Philosophy after Parmenides ..................................................................................... 32 2 PARADOXES AND DILEMMAS IN PLATO ’S ACCOUNT OF MULTIPLICITY ................. 41 2.1 Plato’s theory of Ideas as a logic of multiplicity .......................................... 41 The Eleatic parameters of Plato’s philosophy .......................................................... 41 Plato’s theory of the multiple in the dialogues of the middle period .................. 44 Deleuze on the grounding operation of Platonic Ideas .......................................... 53 2.2 The criticisms of the Parmenides ..................................................................... 63 The dilemma of the first part of the Parmenides ....................................................... 63 The second part of the Parmenides ............................................................................. 68 3 ONE AND MANY : A CONTEMPORARY DISPUTE .......................................................... 74 3.1 Deleuzian antinomies ....................................................................................... 74 A modern φιλονικία .................................................................................................... 74 The doctrine of univocity ............................................................................................ 76 i Monism and/or pluralism ........................................................................................... 80 3.2 Badiou’s criticisms of Deleuze’s pluralism ................................................... 85 Univocity and the One ................................................................................................ 85 The virtual as ground ( le fond) ................................................................................... 88 Philosophies of death .................................................................................................. 91 Badiou’s ἔλεγχος : questions and problems ............................................................ 94 4 DELEUZE AND MEREOLOGY ....................................................................................... 100 4.1 Complexity and structure ............................................................................... 100 The problem of composition .................................................................................... 100 Mereology and the logic of multiplicity ................................................................. 102 Question and plan...................................................................................................... 106 4.2 The paradox of Deleuze’s logic of parts and wholes ................................. 108 Arborescent structures: κόσμος and ἀρχὴ ............................................................. 108 Unity and structure of the assemblage ................................................................... 112 Principles of heterogeneity, connection and multiplicity .................................... 117 5 HUSSERL ’S LOGIC OF PARTS AND WHOLES .............................................................. 121 5.1 Moments and pieces ........................................................................................ 121 On mereology ............................................................................................................. 121 Moments and pieces .................................................................................................. 124 Foundation, wholeness and unity ........................................................................... 127 5.2 The foundationalist paradigm ....................................................................... 130 Separation, divisibility and parthood ..................................................................... 130 Internality and conjunction in Husserl ................................................................... 132 6 EPICUREAN ACCOUNTS OF PARTIAL DIFFERENTIATION ......................................... 139 6.1 How to escape essentialism ............................................................................ 139 Line-parts and structure ........................................................................................... 139 Beyond pieces ............................................................................................................. 141 6.2 Deleuze and atomism ...................................................................................... 143 Naturalist cosmogony (Logic of Sense ) ..................................................................... 143 ii Atomist conception of relations (Immanence: Essays on A Life ) ............................ 145 Fragments, plinths and shattered bricks ................................................................ 146 The problem of atomic independence ( Difference and Repetition ) ........................ 151 6.3 The critique of atomism: entanglement, disjunction, spatium ............... 153 Atoms, the void and entanglement ......................................................................... 153 The Epicurean account of disjunction ..................................................................... 157 The doctrine of minimae partes .................................................................................. 158 Atomist accounts of partial differentiation ............................................................ 163 Atomist notions of structure and composition ...................................................... 165 Lucretius on parts and wholes ( Lucr. 1.602-12) ..................................................... 167 How to escape atomism ............................................................................................ 169 Conclusion: beyond moments and pieces ............................................................... 171 7 DELEUZE ’S THEORY OF COMPOSITION ..................................................................... 174 7.1 Effondement ....................................................................................................... 174 Requirements for ontology ....................................................................................... 174 The notion of foundation in Deleuze ...................................................................... 175 7.2 Towards a Deleuzian account of building .................................................. 183 Fragmentary parthood .............................................................................................. 183 ‘Underneath matters and forms’.............................................................................. 186 Aristotle and representation ..................................................................................... 190 Architecture as ontology ........................................................................................... 196 The complexity of Deleuze’s edict ........................................................................... 200 7.3 Deleuze’s theory of Ideas as a logic of multiplicity .................................. 203 Multiplicity as a substantive .................................................................................... 203 Ideal continuity and relationality ............................................................................ 208 Partial differen tiation and differen ciation .............................................................. 212 7.4 Inter-being and spatium .................................................................................. 218 The being
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