"Delueze is...a realist philosoper....[but] not a realist about essences or any other transcendent entity...something else is needed to give objects their identity and what preserves this identity through time. Briefly, this something else is dynamical processes" (2-3).
In the "real and false reason" thread I contended that there was another kind of math at the root of an alternative complexity different from the algebraic sets Commons uses to build his hierarchical complexity. I made reference to Deleuze and his use of differential calculus and indeed DeLanda is going into that in chapter 1. He uses this math to ground Deleuze's notion of multiplicity and the manifold. He says:
"A Deleuzian multiplicity takes as its first defining feature these two traits of a manifold: its variable number of dimensions and, more importantly, the absence of a supplementary (higher) dimension imposing an extrinsic coordinatization, and hence, an extrinsically defined unity. As Deleuze writes: 'Multiplicity must not designate a combination of the many and the one, but rather an organization belonging to the many as such, which has no need whatsoever of unity in order to form a system'" (12-13).
"Unlike essences which are always abstract and general entities, multiplicities are concrete universals....[and] is typically divergent....unlike essences, which as abstract general entities coexist side by side sharply distinguished from one another, concrete universals must be thought as meshed together in a continuum. This further blurs the identities of multiplicities, creating zones of indiscernibility where they blend into each other, forming a continuous immanent space very different from a reservoir of eternal archetypes" (22-3).
"Besides the avoidance of essentialist thinking, Deleuze's speculation about virtuality is guided by the closely related constraint of avoiding typological thinking, that style of thought in which individuation is achieved through the creation of classifications and of formal criteria for membership in those classifications. Although some classifications are essentialist, that is, use transcendent essences as the criterion for membership in a class, this is not always the case. For example, unlike Platonic essences which are transcendent entities, Aristotle's 'natural states,' those states toward which an individual tends, and which would be achieved if there were not interfering forces, are not transcendent but immanent to those individuals. But while Aristotelian philosophy is indeed non-essentialist, it is still completely typological, that is, concerned with defining the criteria which group individuals into species, and species into genera" (41).
"Species are individuals, not kinds...[and] does not represent a higher ontological category than the individual organisms that compose it.... The relations of individual species to individual organisms is one of whole to parts, much as the relation between an organism and the individual cells that compose it. Moreover, the relation of parts to whole is causal; the whole emerges from the causal interactions between the component parts.... While an ontology based on relations between general types and particular instances is hierarchical, each level representing a different ontological category (organism, species, genera), an approach in terms of interacting parts and emerging wholes leads to a flat ontology, one made exclusively of unique, singular individuals, differing in spatio-temporal scale but not in ontological status" (46-7).