Yannis Chatzantonis

This investigation constitutes an attempt towards (1) understanding issues and problems relating to the notions of one, many, part and whole in Parmenides and Plato; (2) extracting conditions for a successful account of multiplicity and parthood; (3) surveying Deleuzian conceptions and uses of these notions; (4) appraising the extent to which Deleuze’s metaphysics can answer some of these ancient problems concerning the status of multiplicity and the nature of mereological composition, that is, of the relations that pertain between parts and the wholes that they compose.

The aim of this essay is to consider the nature of the philosophical task and of the conditions of its possibility according to Parmenides and Plato. With these thinkers, the task of the philosopher necessitates a propaedeutic activity that makes the doing of philosophy possible; that is, both Parmenides and Plato identify the need for a philosophical education that would alleviate the obstacles that would make philosophy impossible to practise, ensuring and accounting for the possibility of philosophical practice. The impossibility of philosophical practice concerns the philosopher’s claim and obligation to occupy a place (τόπος) from which to contemplate being. The problem becomes conspicuous, for the first time, in the first lines of the first fragment of the first text of pure ontology: in the proemium of Parmenides’ poem. I will argue that the proemium has a crucial philosophical function that binds it integrally to the argument of the poem. This function consists in the implementation of a philosophical propaedeutic that makes possible the articulation of the goddess’s critique. The need for a propaedeutic stems from the nature of the project that lies ahead, that is, the project of the youth’s education. Such education takes the form of the delimitation of the realm of the beings that νοῦς can concern itself with.

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

There are two links that stand in the foreground of Deleuze’s treatment of Epicurus and Lucretius: the themes of immanent naturalism and of the externality of ontological relations. However, the links are problematised in Difference and Repetition, which presents an important critique of the concept of the atom. I will argue that this critique reveals the limits of the intellectual affinity between ancient atomism and Deleuzian metaphysics; in particular, that Deleuze’s notions of relationality and spatium respond to problems raised by the relations between atoms and by the not-being of the atomists’ vacuum. In this sense, Deleuze’s treatment of atomism is significant because it makes clear Deleuze’s aim in shifting the mereological vocabulary from points to lines; it shows what, in Deleuze’s sense, it means to unfound and sets down the conditions for a successful Deleuzian critique of essentialist varieties of the metaphysics of structure.

The critique of the dominant image of thought bears important consequences for pedagogical theory and practice. I discuss how Deleuze can help us think about the role of the teacher, the teaching of thinking and the relationship between knowledge and learning. Reading Deleuze's Difference and Repetition as a treatise on thinking and its education, I argue that Deleuze's philosophy challenges and deepens our understanding of what teachers do, how pupils learn and how they learn to think. I show that Deleuze's philosophy can contribute towards the articulation of sceptical but also creative pedagogical responses to the question of teaching, learning and thinking.