The end of the last chapter introduced Deleuze's concept of vice-diction – a procedure which produces individuals from a pre-individual continuum. It is in order to explain this procedure that Deleuze turns to the four connected themes in Leibniz's philosophy which we outlined at the beginning of the last chapter. Again, these are: an inessential, or pre-individual, continuum (the restless infinitely small); a distribution of singularities which are amenable only to a language of cases, properties or events; a theory of compossibility and incompossibility which determines this distribution; and a divine game which selects the best possible distribution and produces the monads which correspond to it. Taken together, these four ideas constitute the Leibnizian structure Deleuze creates in Difference and Repetition and Logic of Sense, and within which vice-diction operates. As we now look at these in more detail, we’ll start to see how Deleuze pushes disparate Leibnizian themes into the service of a new radicalised or vulgarised Leibnizianism.

The Continuum

The first step in this reconstruction is to discover the ‘language’ of cases, properties or events which is adequate to the domain of the infinitely small, and which Deleuze insists is distinct from the language of essences. We’ll introduce this language through one final opposition between Leibniz and Hegel. When writing of the presence of the infinitely large in Hegel's philosophy, Deleuze claims that ‘there is no reason to expect a mathematical treatment of the theological infinitely large’ (DR 45). However, this is not the case with the infinitely small, which can be approached mathematically. Thus, at the same time as Deleuze claims that vice-diction has its own ‘language of properties or events’ he also claims that it is a ‘mistake to impose upon infinitesimal analysis the alternative of being either a language of essences or a convenient fiction’ (DR 46). The implication, then, is that it is ‘infinitesimal analysis’ which provides the language adequate to infinitely small difference and its movement of vice-diction. The infinitely small thus ‘finds its concept’ (DR 46), Deleuze claims, in the form of the mathematical notation ‘dx’.