We have seen that in the name of the multiple Badiou elides the pluralism of regional ontologies and proposes his absolute thesis « mathematics is ontology ». Being just is multiples of multiples, all the way down. He presents this as the only ontology faithful to the multiple, but this is just dogmatic bluff and bravado. This is a matter of empirical investigation, and Laruelle is right to insist that quantum physics is a better guide to ontology than post-Cantorian mathematics. The ontological elements could at least as plausibly be construed as processes or becomings, i.e. multiplicities containing an intrinsic temporal component. The process-hypothesis is one possible specification of what Feyerabend calls a general methodology (or « general ontology », formulation that he avoids because of its possible fixist connotations), as the set-hypothesis is another possible specification, and as such can claim no privileged status.
Does Badiou discuss the relative merits of set-ontology and process ontology? Not at all, he poses set-theory as ontology, under the condition of the mathematic truth-procedure. The sciences in their empirical dimension are evacuated by a form of mathematical reductionism, that Badiou presents as the « way of the concept » in opposition to the « way of life ». However, Badiou is incapable of understanding Deleuze’s idea of multiplicity, which allies both concept and life. For Deleuze, multiplicities are not sets of spatialised elements, except as the product of a high degree of abstraction and stratification. But even here Deleuze and Guattari emphasize that these « abstract » elements correspond to an insufficient degree of abstraction, because the abstract-machine, which is composed of non-formed elements and non-formal functions, is not yet attained. Badiou’s sets are homogeneous assemblages, and we are back to the Althusserian policing function of philosophy: maintaining the purity of each truth procedure, hunting down illegitimate sutures and mixtures.
Deleuze and Guattari are quite clear that for them « multiplicity » enfolds an intrinsic heterogeneity: « Of multiplicities, there must be at least two, two sorts, from the beginning ». The quantic superposition of extensive and intensive multiplicities is the originary datum. So Badiou’s little fiction of a distinction between philosophies of the concept and philosophies of life collapses. Deleuze (and Deleuze-and-Guattari) is a philosopher of the pulsation between the concept and life. This is also Deleuze’s argument concerning Bergson, whose distinction between duration and space he analyses in terms of the distinction between the two types of multiplicities: extensive and intensive. Thus, even Bergson is not a « philosopher of life » in the dualistic sense that Badiou tries to impose.