The claim that ontology is mathematics, then, generates the followingquandary: If mathematical ontology stands to reality as conceptual scheme to empirical content, then Badiou finds himself resurrecting the empiricist dualism of formal scheme and material content which he himself had already castigated in his first book,

The Concept of Model.



But in order to avoid such scheme–content dualism, Badiou must show that presentation occurs in non-ontological (i.e. non-discursive) contexts.


This remains an insuperable difficulty, not only because the claim that the One is not effectively undermines any attempt to privilege the ontological situation as the transcendental ground of access to all other situations; but also because Badiou’s attempt to distinguish between ontological and non-ontological situations in terms of the primacy of inconsistency over consistency or vice versa renders it very difficult to understand how non-discursive presentation could ever ‘occur’.


Consequently, Badiou finds himself confronted by two equally unappetizing alternatives. On the one hand, he faces a relapse into the empiricist,dualism of formal scheme and material content, which he himself had previously sworn to abjure, and one wherein the only available criteria for legitimating the identification of ontology with set-theory are pragmatic since – as Quine and others have convincingly argued – empirical content underdetermines the choice of conceptual scheme.


Or, on the other hand, there is the prospect of a discursive variety of absolute idealism – or crypto-Hegelianism – in which the difference between the conceptual and the extra-conceptual, or discourse and world, is reduced to the distinction between consistent and inconsistent multiplicity, and for which, ultimately, thinking is all that matters.


At this juncture, Badiou can respond in two ways: he can either choose to correct the anti-phenomenological bias of the concept of presentation by supplementing the subtractive ontology of being qua being with a doctrine of appearance and of the ontical consistency of worlds – albeit at the risk of lapsing back into some variant of the ontologies of presence. Or he can accept the stringency of his concept of presentation and embrace the prohibitive consequences of the logic of subtraction.


The recently published Logiques des mondes19 (Logics of Worlds) suggests that he has – perhaps reasonably, albeit somewhat disappointingly from our, point of view – opted for the former. Yet in our eyes, the veritable worth of Badiou’s work lies not in his theory of the event but rather in the subtractive ontology which was merely intended as its propaedeutic.


Badiou’s inestimable merit is to have disenchanted ontology: ‘being’ is insignificant, it means, quite literally, nothing. The question of the meaning of being must be abandoned as an antiquated superstition.


This is the profound import of Badiou’s anti-phenomenological but post-metaphysical rationalism, and one which, despite Badiou’s own fierce antipathy towards empiricism and naturalism, is perfectly consonant with that variant of naturalized epistemology we considered in Chapter 1 and which proposes that nothing has ever meant anything.


As we saw in Part I, this is one of the principal consequences of the disenchantment of sapience which cognitive science is currently undertaking.


Accordingly, rather than pursuing any sort of qualitative supplement to subtractive ontology, we believe it is necessary to sharpen and deepen the letter’s disqualification of phenomenological donation (and of its dyadic structures such as temporalization/spatialization, continuity/discontinuity, quantity/quality).


This sharpening and deepening entails abandoning the discursive idealism which vitiates Badiou’s conception of subtractive presentation and which betrays itself in the fact that the sole real presupposition for the latter is that of the existence of the name of the void. As we have seen, any attempt to deduce this ultimate presupposition by assuming the consistency of multiplicity involves an illegitimate recourse to phenomenological donation and/or empirical experience.


But as we shall see in our discussion of the work of Laruelle in the following chapter, it is possible to presuppose the existence of the void qua being-nothing independently of the discursive structure of mathematical science, without positing the primacy of the signifier, invoking phenomenological donation, or resorting to empirical experience.



As it stands, however, subtractive ontology is compromised by the idealism of the discursive a priori on one hand, and by the dualism of scheme and content on the other, both of which severely undermine Badiou’s avowed commitment to materialism. The discursive structure of presentation seems to stipulate an isomorphy between nomological and ontological structure which conflicts with the realist postulates of the physical sciences, which assume that objects exhibit causal properties rooted in real physical structures that obtain quite independently of the ideal laws of presentation. At the same time, the dualism of ontological form and ontic content generates a dichotomy which also seems to contradict the requirements of scientific realism: either discursively structured presentation or unstructured chaos. But can one maintain that being is mathematically inscribed without implying that nothing exists independently of mathematical inscription? This wouldbe one of the more nefarious consequences of the Parmenidean thesis, which would seem to stipulate a pre-established harmony between thinking and being.


Accordingly, the question must be whether it is possible to demonstrate thought’s purchase on ‘the real’ without invoking the idealism of a priori intuition or inscription on the one hand, yet without relapsing into a pragmatic naturalism wherein the correspondence between scientific representation and reality is evolutionarily guaranteed (cf. Chapter 1) on the other. The next chapter shall pursue this question via an examination of the work of François Laruelle.



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