Introduction

In the last chapter we developed an account of Deleuze's theory of immanent ideas. There are a number of ways to describe a Deleuzean idea – a differential ontological structure, a productive problem, a continuous multiplicity – but common to them all is the three-part problem- structure. The most explicit articulation of this theory appears in Chapter 4 of Difference and Repetition. Directly after this formal account, Deleuze selects an example of the idea, and the selection is important: the atomic idea. This chapter will expand that first application of the basic problem-structure to Lucretian atomism. By the end, if all goes well, we will have a full articulation of the atomic idea.

As we have seen, there are three parts to the Deleuzean idea – differential elements, differential relations and singularities – and the atomic idea is composed of the same three components, with one variation: while the Deleuzean idea is structured in terms of the concept of the differential (dx, dy), the atomic idea is structured by the concept of the atom. Rather than differential elements, differential relations and singularities, the atomic idea is composed of atomic elements, atomic relations and the clinamen. This chapter begins with a review of the basic principles of Lucretian atomism. We will not support or analyse these basic principles in much detail but simply state them at the onset so that what we mean by ‘atomic’ is as clear as possible. After this quick review, the rest of the chapter is divided into three main sections, each one corresponding to a Lucretian articulation of a component of Deleuze's theory of ideas: the first section covers the atomic elements, the second atomic relations, the third the clinamen.

In order to show how atomic elements function, we tell a short story about the emergence of the very concept of the atom. As we will see, Lucretian atomism responds to the problem of indivisibility through a philosophical employment of the mathematical method of exhaustion.